Equation index

Use a paper number when you are reading a source, and a site label when you are returning to a calculation here. For example, the paper’s (8.11) and the site’s (O09.2) belong to different numbering systems. A map connects their arguments; it does not assert that the formulas are identical in every convention or away from a stated limit.

The tables below are also used in the paper companions. They give selected, checked landmarks and their teaching homes. Open the linked guide for its notation dictionary, omitted steps and exit calculations. The version beside each paper is the version used for its equation numbers; printed page numbers and PDF page numbers may differ by one or more pages.

Follow a source equation to its derivation and back

Suppose you need the curved D-term prescription in P, equation (6.13).

Open the Section 6 map under Supersymmetric Field Theories on Three-Manifolds. Its (6.13)–(6.14) row sends you to the D-term prescription.
Read the calculation immediately above that anchor. The general multiplet must be neutral, and the background terms complete its highest component:
$\mathcal L_D=-\frac12\left(D_{\mathcal S}-a_{\mathcal S\mu}V^\mu-\sigma_{\mathcal S}H\right).$
The lesson exhibits its variation as a divergence, using $\nabla_\mu V^\mu=0$ . A globally defined integrand and vanishing integrated boundary flux are still required for an invariant action.
Follow the lesson’s source link back to P v3, printed page 24/PDF page 25. Check the neutral charges and the coefficient $-1/2$ in (6.13). You have recovered both the formula and the conditions behind it.

This is a lookup exercise, not a second derivation of the prescription. Its full proof belongs to the linked lesson.

Keep the qualification attached to the formula

An equation label cannot replace a convention check. The Section 8 map distinguishes the printed fixed-shift free-chiral expression from a fixed-R-charge family. The Seiberg–Witten map keeps the electric-charge and period units together. The four-sphere guide explains the physical versus equivariant mass. The ABJM and Fermi-gas guides retain the contour, phase, approximation and source-correction qualifications.

For an exact site equation already in your notes, follow its linked label in a map or use the site’s search with that label. The tables concentrate on useful paper-to-lesson connections rather than repeating every displayed formula. Unnumbered derivations remain available through their section links.

Paper equations and teaching calculations

Open a paper to see its checked passages. A paper number and a site number identify different equations; the reading question explains their connection. Directions such as “below” refer to the linked guide.

Supersymmetric Field Theories on Three-Manifolds (P, v3)

Open the pinned paper, v3. Read the associated guide for its conventions and the limits of the comparison.

Reading Supersymmetric Field Theories on Three-Manifolds

Introduction: identify every term

Read in v3	What to identify	Detailed teaching calculation
(1.1), printed 3/PDF 4	Which quantities are potentials and which are dual field strengths?	The dual background fields
(1.2), printed 3/PDF 4	Why is the central charge different from an R charge?	Fields and their units
(1.3), printed 3/PDF 4	Why must a zero gravitino also have zero variation?	Preserving the frozen background
(1.4)–(1.5), printed 4/PDF 5	Which signs change between the two charge sectors?	Both Killing spinor equations

Reading Supersymmetric Field Theories on Three-Manifolds

A map through the rest of the paper

Paper passage and checked landmark	Reading goal	Teaching route
Section 2: (2.15), printed 10/PDF 11	Recover the rigid gravitino variation from current/source couplings.	The R-multiplet and the supplied variation
Section 3: (3.1)–(3.8), printed 10–12/PDF 11–13	Separate differential uniqueness, pointwise bilinears and global spin/R lifts.	The Section 3 guide maps the full argument and reconstructs a spinor from its charged bilinear.
Section 4: (4.1)–(4.21), printed 12–16/PDF 13–17	Follow transverse integrability into a local spinor and then global patching.	The Section 4 guide maps the construction and checks a cylinder-to-annulus overlap with its spin and R seams.
Section 5: (5.1)–(5.14), printed 17–20/PDF 18–21	Distinguish opposite-charge pairs, maximal local enhancement and global transport.	The Section 5 guide
Section 6: (6.1), printed 21/PDF 22; (6.32), printed 29/PDF 30	Read the source-dependent algebra and then check an action.	Section 6 guide, with the full component/action map and a compensated R/flavor-source calculation
Section 7: (7.1), printed 30/PDF 31	Compare the first-order curved coupling with flat current operators.	Section 7 guide reconstructs a current preimage and tests its first-order scope, building on the canonical flat-space check.
Section 8: (8.2)–(8.3), printed 34/PDF 35	Relate the real sphere response to a separated-point correlator, retaining the source and contact prescription.	The Section 8 guide connects squashing response with the free-chiral check.
Appendices A and B	Look up conventions, then the definitions used by the transverse geometry.	The Appendices A/B guide maps the conventions and reconstructs the spin-curvature identity; its separate geometry entrance introduces the compatible connection.
Appendices C and D: (C.1), printed 43/PDF 44; (D.1)–(D.19), printed 45–48/PDF 46–49	Compare the four-dimensional construction with its twisted reduction.	The Appendices C/D guide maps the complete reduction. The four-dimensional rigid background derives (C.1); twisted reduction derives the 3d source and multiplet dictionary. Neither branch is a prerequisite for the introduction.

Paper guide: Section 2, currents and rigid backgrounds

Read from operators to sources

Read in v3	Question to resolve	Canonical calculation
(2.1)–(2.2), printed 6/PDF 7	How do a linear-multiplet constraint and a conserved vector fit together?	R-multiplet constraints and components; the simpler linear package
(2.3), printed 6/PDF 7	Which operators change when the R-current is improved?	Flavor improvement of the components and the associated curvature coupling
(2.4)–(2.7), printed 7/PDF 8	What does the full superspace integral pair, and what has Wess–Zumino gauge removed?	The two superfield expansions
(2.8)–(2.9), printed 7/PDF 8	Which source transformations are gauge redundancies, and which fields are dual field strengths?	The dual background fields
(2.10), printed 8/PDF 9	Which combination actually sources the R-current?	The linear component coupling

Paper guide: Section 2, currents and rigid backgrounds

From source transformations to a rigid symmetry

Read in v3	Question to resolve	Canonical calculation
(2.11), printed 8/PDF 9	Why must a supersymmetry transformation be accompanied by a transformation restoring Wess–Zumino gauge?	The linearized reconstruction
(2.12)–(2.13), printed 9/PDF 10	Why does making the spinor parameter local produce a derivative in the gravitino variation?	Local parameters and the gravitino source
(2.14)–(2.15), printed 9–10/PDF 10–11	Which covariant terms can survive when the gravitini are zero?	The supplied transformation
(2.15), then (1.4)–(1.5)	Why must a zero source also have zero variation?	Preserving the frozen background and both spinor equations

Paper guide: Section 3, geometry from one spinor

Read the whole section in three stages

P v3 passage	What to establish	Canonical calculation and equation
(3.1), printed 10/PDF 11	The two charge equations use the same specified background	The Killing-spinor equations
(3.2), printed 10/PDF 11	Reversing $A,V$ exchanges the equations; $H$ stays fixed	The opposite-charge substitution
Bundle paragraphs, printed 10–11/PDF 11–12	Which transition functions multiply the spin lift?	Charged spinor sections
Footnote 5, printed 11/PDF 12	Why one zero forces a global solution to vanish	Local uniqueness and global existence
(3.3)–(3.4), printed 11/PDF 12	Normalize the Hermitian direction and check its unit length	M01.3–M01.4: normalized direction
(3.5)–(3.6), printed 11/PDF 12	Fix the sign of $\Phi$ and its transverse square	M01.6–M01.8: transverse tensor; M02.1–M02.2: metric compatibility
Text after (3.6) and footnote 6, printed 12/PDF 13	Compare the $+i$ vector eigenspace with Clifford annihilation	M01.10–M01.11: annihilator and index lowering
(3.7)–(3.8), printed 12/PDF 13	Track R-charge two and the antiholomorphic one-form	M01.12–M01.15: charged bilinear
Closing paragraph, printed 12/PDF 13	Repeat the algebra for the independent negative-charge label	The norm and bundle assumptions, with $L$ replaced by $L^{-1}$

Paper guide: Section 4, transverse holomorphic geometry

Read the necessity argument first

P v3 landmark	Reading question	Canonical calculation
(4.1), printed 12/PDF 13	Which sources are fixed in the differential equation?	The Killing-spinor equations
(4.2)–(4.3), printed 13/PDF 14	Which shifts preserve this spinor, and which constraint remains?	Source freedom and its divergence, M05.14–M05.16
(4.4)–(4.7), printed 13/PDF 14	Why is there no transverse shear?	The bilinear derivative and projector, M03.3–M03.9
(4.8)–(4.12), printed 14/PDF 15	What does an adapted overlap preserve?	Coordinate transitions, M04.6–M04.7
(4.13), printed 14/PDF 15, footnote 7	Why use a metric connection with torsion?	Compare its preservation of $\eta$ with the Levi-Civita connection, M05.6; they are different connections.
(4.14), printed 15/PDF 16	Which combination becomes the reduced R connection?	Component reconstruction, M05.7–M05.9; keep the source's $\widehat A$ distinct from $A$ .
Bundle paragraph and (4.15)–(4.16), printed 15/PDF 16	What cancels the adapted frame phase?	The bilinear bundle constraint, M06.8–M06.9
(4.17)–(4.19), printed 15–16/PDF 16–17	How does the charge-two equation determine a connection locally?	The reconstruction below, followed by the full overlap equation, M06.6–M06.7
(4.20)–(4.21), printed 16/PDF 17, footnotes 8–9	In which frame is the solution a simple column, and what flat data remain?	The explicit adapted spinor and global transport

Paper guide: Section 5, additional supercharges

Read in two passes

Read in P v3	Question for your notes	Canonical calculation
(5.1)–(5.2), printed 17/PDF 18	Which terms cancel in the derivative?	M07.2–M07.4: mixed vector
(5.3)–(5.5), printed 17/PDF 18	Where is reality imposed? Which vector is normalized?	M07.7–M07.9: real direction
(5.6)–(5.7), printed 17–18/PDF 18–19	Do both labels use the same sources?	M07.11–M07.12: a complete pair
After (5.7), printed 18/PDF 19	Does the chosen flow close?	M08.1: exceptional-fiber model
(5.8), printed 18/PDF 19	Is curvature annihilating a line or a basis?	R09.4: full obstruction
(5.9)–(5.10), printed 19/PDF 20	What is local, and what remains global?	M09.3: enhancement conditions
(5.11)–(5.12), printed 20/PDF 21	Are radius and squashing conventions matched?	M10.2: homogeneous family
(5.13)–(5.14), printed 20/PDF 21	Which base curvature does each case require?	M09.3 and its local cases

Paper guide: Section 6, curved multiplets and actions

Systematic actions

P v3 landmark	What to establish	Canonical teaching target
(6.1)–(6.2), printed 21/PDF 22	Isometry plus R and central transformations	The algebra and its scope, R07.5–R07.9
(6.3)–(6.6), printed 22/PDF 23	The general package and its charge-dependent rules	The component package; the following scalar calculation checks the needed part of (6.5)
(6.7)–(6.10), printed 23/PDF 24	Constrain the general package to a chiral or antichiral multiplet	The chiral rules and their subsequent closure calculation
(6.11)–(6.12), printed 23–24/PDF 24–25	A neutral linear multiplet has a conserved vector component	Its embedded components, then the field-strength example below
(6.13)–(6.14), printed 24/PDF 25	Neutrality and the background completion make an invariant integral	D-term prescription and F-term charge conditions
(6.15), printed 24/PDF 25	Complete an R-current improvement nonlinearly	Mixed coupling to the R source
(6.16), printed 25/PDF 26	Multiply components with graded signs and summed charges	Chiral product and charged product expansion
(6.17)–(6.22), printed 25–26/PDF 26–27	Gauge freedom, its compensation and the field-strength multiplet	Vector rules, gauge closure, and the linear field strength
(6.23)–(6.25), footnote 10, printed 27/PDF 28	Charged matter requires the gauge completion	Expand the gauge-invariant product, including $\widetilde\Phi e^{-2q\mathcal V}\Phi$
(6.26), printed 28/PDF 29	A frozen source must itself preserve the retained labels	Freeze the whole flavor multiplet, A05.1
(6.27)–(6.29), printed 28/PDF 29	FI, gauge CS and gauge–R CS have different completions	Curved CS/FI construction, A06.6–A06.7
(6.30), printed 29/PDF 30	The field-strength square supplies Yang–Mills terms	Complete gauge action
(6.31)–(6.32), printed 29/PDF 30	Assemble the matter action and check its limits	Complete matter action and the direct sphere variation

Paper guide: Section 7, the linearized check

Read the comparison in two stages

P v3 passage	What to establish	Canonical calculation
(7.1)–(7.2), printed 30/PDF 31	Fix the metric variation, the three source couplings and the selected spinor.	Expansion and supercharge, R08.1
(7.3)–(7.5), printed 30–31/PDF 31–32	Distinguish closed operators from explicit supersymmetry variations.	A fermionic preimage, R08.2–R08.5; the additional preimage below
(7.4), footnote 11	Translate complex components without losing factors of two.	Adapted coordinates and the explicit dictionary below
(7.6)–(7.7), printed 31/PDF 32	Integrate derivatives onto the sources and check the field-strength constraint.	The small metric background, R08.6–R08.7; the flat-metric source direction below
Paragraph after (7.7), printed 32/PDF 33	Identify the unproved nonlinear step.	The limits of first-order exactness, R08.9
(7.8)–(7.10), printed 32/PDF 33	Compare the vector currents with the YM and FI actions; understand the absence of an explicit CS contribution to this multiplet.	Gauge kinetic terms and curved CS/FI terms
(7.11)–(7.13), printed 33/PDF 34	Keep $z=-m$ , the chosen R improvement and the nonminimal stress tensor together.	The chiral curvature check, R08.8, and stress-tensor improvements

Paper guide: Section 8, physical observables

Response capstone: follow the equation map

Paper equations	Role in the argument	Where to reconstruct the step
(8.1)	Define the complex free energy.	Source derivatives, (O06.1), fixes the response sign for $-\log Z$ .
(8.2)	Relate its real round-point Hessian to $\tau_{RR}$ .	Squashing response, (O08.9).
(8.3)	Define the R-current coefficient and its stress-tensor partner.	Current correlators, (O07.2), (O07.7)–(O07.9); the last equations define any conversion to $C_T$ .
(8.4)–(8.5)	Specify the metric and auxiliary sources, in a positive- $H$ branch.	Squashing response, (O08.2), (O08.6).
(8.6)	Identify the first-order current insertion.	Squashing response, (O08.3); use $A-3V/2$ , not the matter derivative's $A-V/2$ .
(8.7)–(8.8)	Convert the Hessian into an integrated correlation with local terms.	Source derivatives, (O06.1), and squashing response, (O08.4)–(O08.5).
(8.9)–(8.10)	Weyl-map the correlator and introduce chordal distance.	Squashing response, (O08.7)–(O08.9), includes the regulated integral omitted in the paper.
(8.11)	Give the printed free-chiral integral.	Free-chiral response, (O09.2)–(O09.5), distinguishes its fixed shift from fixed R-charge.
(8.12)	Evaluate the free round Hessian.	Free-chiral response, (O09.6)–(O09.11), gives the integral, spectral subtraction and $\tau_{RR}=1/4$ .
(8.13)–(8.14)	Check a separate leading large- $N$ supergravity regime.	Exit calculation 2 below checks the implication and its limits; these are not general free-field formulas.

Paper guide: Appendices A and B, conventions and geometry

Read the conventions by operation

Source passage	Operation to check	Canonical explanation
(A.1)–(A.2), printed 38/PDF 39	Raise an index without conjugating; reverse odd products under adjunction.	Index contraction and independent Euclidean variables
(A.3)–(A.4), printed 38/PDF 39	Keep the oriented Clifford product and the lowered gamma indices distinct.	Gamma multiplication and ordered Fierz identity
(A.5)–(A.6), printed 38/PDF 39	Identify which Grassmann coordinates are differentiated and which top coefficient is integrated.	The superspace expansion; this is a later application, not extra preparation for the curvature calculation
(A.7)–(A.9), printed 38–39/PDF 39–40	Translate the input-first connection and the Ricci contraction.	Frame covariance and the explicit curvature trace
(A.10)–(A.12), printed 39/PDF 40	Reduce spin curvature to the Ricci tensor in three dimensions.	Sphere spin connection, followed by the reconstruction below
(A.13)–(A.14), printed 39/PDF 40	Distinguish transport of a spinor from transport of a mixed tensor.	The spin rotation in the curved algebra and the tensor Lie derivative

Paper guide: Appendices A and B, conventions and geometry

Read the geometric definitions with their hypotheses

Source passage	What is, and is not, asserted	Canonical calculation
(B.1)–(B.2), printed 40/PDF 41	A one-form $\eta$ , vector $\xi$ and endomorphism $\Phi$ obey pointwise almost contact identities; compatibility adds a metric.	The algebraic definitions, M02.1–M02.3
(B.3)–(B.6), printed 40–41/PDF 41–42	A metric-compatible connection preserving $\eta$ generally has torsion and a free one-form $W$ .	The connection dictionary immediately below; spinor connection construction
(B.7), printed 41/PDF 42	The paper selects one representative of that freedom for its later background construction.	Adapted-frame derivatives, M05.4–M05.6, and the subsequent source solution
(B.8)–(B.11), printed 41–42/PDF 42–43	A projector condition preserves the transverse complex line and supplies local holomorphic coordinates.	The projector and the local coordinate argument, M03.9 and M03.12–M03.13
(B.12)–(B.14), printed 42–43/PDF 43–44, footnote 14	Compatible adapted metrics have a conformal transverse plane, with a fixed symmetric-product and volume convention.	The metric components, M04.2–M04.5, and overlaps, M04.6–M04.7
(B.15) and the three closing comments, printed 43/PDF 44	A local choice of a new distinguished direction is different from preserving a given direction; global extension is additional. Normality is stronger than the projected condition.	Scope of integrability and exit 3 below

Paper guide: Appendices C and D, four-dimensional origin

Read the background before the component table

Paper landmark	Question it answers	Canonical calculation
(C.1)	Which fixed sources preserve a spinor?	New minimal equations, (B02.4)–(B02.5).
(C.2)–(C.3)	What transforms, and which algebra closes?	Twisted reduction, (B03.12)–(B03.15); read the component dictionary before applying the table.
(D.1)–(D.2)	Which direction is removed, and how are dotted indices identified?	Twisted reduction, (B03.4) and its frame discussion.
(D.3)–(D.7)	How do the metric, frame and horizontal components reduce?	Twisted reduction, (B03.1)–(B03.2), (B03.5).
(D.8)–(D.11)	Where do central charge, spin rotations and curvature terms come from?	Twisted reduction, (B03.3), (B03.6), and the curvature check following (B03.14).
(D.12)–(D.16)	Which source identification avoids an extra spinor projection?	Reduction source dictionary, (B03.7)–(B03.9).
(D.17)–(D.18)	Which three-dimensional fields and derivatives enter the transformations?	Twisted reduction, (B03.12)–(B03.14).
(D.19)	How does translation along the fiber become a central transformation?	Twisted reduction, (B03.15).

Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory (SW1, v1)

Open the pinned paper, v1. Read the associated guide for its conventions and the limits of the comparison.

Reading the first Seiberg–Witten paper

Read the low-energy argument

Passage in v1	Question to answer while reading	Canonical preparation
Section 2.2, (2.6), p.6/PDF 7	Why are inequivalent vacua labeled by one complex invariant?	Solve the vacuum equation.
Section 2.3, (2.7)–(2.16), pp.6–9/PDF 7–10	Which couplings belong to the same prepotential, and where does the scale enter?	The local prepotential action and the running scale.
Section 3.2, (3.18)–(3.21), p.14/PDF 15	Why does the dual photon use $a_D$ and $\tau_D=-1/\tau$ ?	Dualize the whole multiplet. Section 3.3's gravity extension can wait.
Section 4, (4.3)–(4.5), p.17/PDF 18; decay discussion, pp.19–20/PDF 20–21	What is the exact central charge, and what additional question determines stability?	The physical BPS bound and the marginal threshold.
Section 5.1, (5.1)–(5.4), pp.21–22/PDF 22–23; sections 5.4–5.5, (5.7)–(5.15), pp.26–27/PDF 27–28	How do a weak-coupling logarithm and a light monopole constrain continuation around punctures?	The light-field threshold and based monodromy paths.

Reading the first Seiberg–Witten paper

Read the curve and the periods as one specification

Landmark in v1	Object to identify	Teaching home
(6.6), p.35/PDF 36	The cubic family and its degenerations	Reconstruction inputs.
(6.7), (6.14), pp.35–36/PDF 36–37	Cycle ordering and period ordering	The sheet and oriented periods.
(6.15)–(6.20), pp.37–38/PDF 38–39	A meromorphic differential whose vacuum derivative is holomorphic	Find and normalize the differential.
(6.22)–(6.23), p.39/PDF 40	The two complete-cycle integrals	Evaluate the oriented periods.
(6.24)–(6.30), pp.39–40/PDF 40–41	Weak coupling and the monopole limit	The local period expansion.
“The Spectrum,” pp.40–41/PDF 41–42	Why monodromy is not a proof of an unchanged stable spectrum	Supply the spectral information.

Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD (SW2, v1)

Open the pinned paper, v1. Read the associated guide for its conventions and the limits of the comparison.

Reading the second Seiberg–Witten paper

A selected reading order

Paper passage	Question to answer	Canonical calculation
Convention note, (1.6), pp. 5–6	Which period changes when the elementary electric label becomes an integer?	Charge dictionary
(3.1), p. 10; (5.3), p. 19	Does the central charge reproduce the actual fundamental mass?	Matter mass
(6.1)–(6.4), p. 20; (15.1)–(15.4), pp. 51–52	Why can massive periods acquire additive flavor shifts?	Differential and residues
(11.1)–(11.7), pp. 37–38; (12.5)–(12.8), p. 45	Why does removing a fundamental produce a different pure curve?	Heavy-flavor limit and the reconstruction below
(16.1)–(16.3), p. 56; (16.10), p. 58	Which normalization is used for the adjoint theory?	Adjoint periods and coupling
(16.17)–(16.25), pp. 61–63	Which modulus and scale stay fixed in the adjoint decoupling limit?	Two different limits

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops (PES, v3)

Open the pinned paper, v3. Read the associated guide for its conventions and the limits of the comparison.

Reading Pestun's four-sphere localization paper

Read the argument in this order

Source passage	Question to answer	Canonical calculation
(1.1), p. 2; (2.18)–(2.19), p. 13	Which scalar accompanies the connection, and which spinor preserves the equatorial loop?	The circle's supersymmetry condition
(2.2)–(2.6), p. 9; (2.12)–(2.14), pp. 11–12; Appendix B, pp. 44–45	How do the conformal spinor and curvature term enter?	Solve the sphere spinor equations
(2.26)–(2.33), pp. 15–16; Appendix C, pp. 45–50	What closes off shell for the selected charge, and what does its square do?	Identify the selected square and auxiliaries
(3.16)–(3.18), pp. 19–20	Why is a tempting extra smooth scalar branch excluded? Which auxiliary survives?	The Bianchi-identity test
(3.19), p. 21	Why is the classical coefficient proportional to three, rather than two?	Evaluate the physical auxiliary action
(4.20)–(4.22), p. 27; (4.39)–(4.46), pp. 30–32	Which unpaired modes determine the ratio, and why are the two pole expansions different?	Normal fluctuations and their signed index
(4.47)–(4.50), p. 33; (4.58)–(4.59), pp. 34–35	When do vector and hypermultiplet weights actually cancel?	The determinant product
Section 5, pp. 36–39; especially (5.11) and footnote 9	Which mass vanishes in N=4, and what happens to the polar sectors?	The shifted mass and the nonempty sectors
Return to (1.2)–(1.4), p. 3	How are the trace and the finite-dimensional integral normalized?	Finite-color evaluation and central-mode removal

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (AB, v4)

Open the pinned paper, v4. Read the associated guide for its conventions and the limits of the comparison.

Reading the original ABJM paper

Read the action and its symmetry argument

Verified passage	Question to answer	Canonical calculation
(2.1)–(2.2), printed pp. 3–4/PDF pp. 4–5	Which vector fields have algebraic equations rather than Yang–Mills kinetic terms?	Opposite levels and complete multiplets
(2.4)–(2.6), printed pp. 5–6/PDF pp. 6–7	How does eliminating the two adjoint chirals fix the relative sign and coefficient?	Recover the coefficient
(A.1)–(A.4), printed p. 30/PDF p. 31	Why is the F-term potential only part of the answer?	Eliminate the vector auxiliaries
(A.5)–(A.7), printed p. 31/PDF p. 32	Which ordered sextic invariants combine into an $SU(4)$ expression?	A finite R-symmetry rotation
Section 2.2 after (2.6), printed p. 6/PDF p. 7	What acts on the supercharges, rather than only on scalar polynomials?	Full-action enhancement

Reading the original ABJM paper

Read the vacuum and operator arguments

Verified passage	Question to answer	Canonical calculation
Section 2.3, (2.7)–(2.9), printed pp. 7–8/PDF pp. 8–9	Why does the phase quotient remain finite?	Compact dualization
Paragraph after (2.9), printed p. 8/PDF p. 9	What is permuted on the diagonal branch?	Permute whole tuples
Section 2.4, (2.10) and footnote 6, printed pp. 10–11/PDF pp. 11–12	Which flux cancels which matter charge?	Derive the CS gauge weight
Section 2.4, printed pp. 11–12/PDF pp. 12–13	Which further input makes the special operators into symmetry currents?	Protection and nonzero descendants
Sections 2.5–2.6, printed pp. 13–15/PDF pp. 14–16	Why are the $SU(N)$ variants separate global theories?	The global group matters

Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter (KWY, v4)

Open the pinned paper, v4. Read the associated guide for its conventions and the limits of the comparison.

Reading three-dimensional localization with matter

Read the reduction in this order

Checked source landmark	Reading question	Canonical explanation
(3.1)–(3.5), pp. 7–9	Which positive deformation and contour select the locus?	Deformation identity
(3.10)–(3.20), pp. 10–11	Which zero modes and gauge volumes remain?	The remaining scalar
(3.21)–(3.30), pp. 12–13	Why does an extra Vandermonde double count?	Completed gauge measure
(3.39)–(3.58), pp. 15–18	Which multiplicities survive cancellation?	Paired factors
(3.60)–(3.67), pp. 18–19	What fixes the constant and phase?	Finite determinant prescription
(3.68)–(3.69), p. 20	How do the measure and insertion combine?	Normalized integral

Reading three-dimensional localization with matter

The ABJM application

Source landmark	What to reconstruct	Canonical location
(2.13) and section 2.2, pp. 6–7	Curved matter and the superconformal input	Curvature completion
(3.5), (3.37), pp. 9, 15	Vector zero modes and vanishing matter	The locus
(4.2)–(4.4), pp. 20–21	Two conjugate pairs per color pair	Bifundamental weights
(3.69), (4.1), pp. 20–21	Node and normalized representation	Loop insertion
(4.5)–(4.9), pp. 21–22	A perturbative expansion with its phase	Finite-rank contour check

ABJM theory as a Fermi gas (FG, v3)

Open the pinned paper, v3. Read the associated guide for its conventions and the limits of the comparison.

Reading ABJM as a Fermi gas

A reading order with questions to answer

Passage	Reading question	Canonical calculation
Introduction (1.3)–(1.4), p. 3; Section 2, especially (2.1), p. 5	Which parameter is fixed, and which normalized integral is being transformed?	Specify the limit
Section 3.1, (3.1)–(3.5), pp. 9–10	Where do the exchange sign, the single remaining factorial and the kernel measure come from?	Cauchy identity and Fourier integrations
(3.6)–(3.16), pp. 10–11	Why is a cycle trace different from a fixed-particle partition function?	Occupation statistics
(3.17)–(3.34), pp. 12–13	What operator has the required eigenvalues, and why is its Hamiltonian not exactly a sum of two functions?	The one-particle operator
Sections 4.1–4.2, (4.1)–(4.27), pp. 17–20	How does a spectral count lead to a filled-state free energy?	Count and fill levels
Section 5.2, (5.25)–(5.37), pp. 25–27	Which three coefficients enter the cubic grand potential, and what information is lost on discarding its remainder?	Separate the three inputs and invert the cubic
Section 5.3, (5.38), p. 27, and (5.64)–(5.68), p. 31; footnote 3, p. 32	What is established in the WKB expansion, and which proposal for the constant term is withdrawn?	Quantum counting input and absolute normalization
Section 5.4, especially (5.74)–(5.80), p. 33	What lies beyond a power expansion in the auxiliary Planck constant?	The omitted exponential sectors