Geometry and supersymmetry
What changes on a curved space?
Construct the Killing spinors and free chiral action on a round three-sphere.
Start with the twenty-lesson sphere route.
Supersymmetric Field Theory
Build the theories. Understand the geometry. Calculate exact results.
For readers with basic quantum field theory, gauge theory, and general relativity. No supersymmetry background is assumed. Superspace, complex curves, localization, and large-N methods are taught when you need them.
Choose a physical question
Section titled “Choose a physical question”Each destination has a guided route with its own preparation and calculation checkpoints. The four-dimensional routes share a short beginning; they do not require the curved-space course first.
Four-dimensional N=1
What survives strong coupling?
Use holomorphy, anomalies, and quantum constraints to test a Seiberg-duality pair.
Quantum dynamics and supersymmetric vacua.
Four-dimensional N=2
How does a curve encode a gauge theory?
Calculate periods, the effective coupling, and BPS central charges in Seiberg–Witten theory.
Complex geometry with a physical interpretation.
Four-dimensional N=4
Which observables can we calculate exactly?
Build super Yang–Mills theory and derive its finite-rank circular Wilson loop.
From fields and operators to a matrix integral.
Three-dimensional ABJM
What can a sphere partition function reveal?
Construct a Chern–Simons matter theory and evaluate its rank-one sphere integral.
Quivers, interactions, and protected observables.
Explore all learning paths, including supersymmetric quantum mechanics, SQED–XYZ duality, and a first supersymmetric index. Use the learning guide to browse the full curriculum by subject.
Your first calculation
Section titled “Your first calculation”In What a supercharge does, act on a pair of states and check the anticommutator. Then differentiate and integrate Grassmann variables, keeping track of every sign. These two lessons open both the three- and four-dimensional routes.
Need a refresher? Try the four starting-knowledge questions. Each includes a complete answer and a focused explanation.
Work through the physics
Section titled “Work through the physics”Follow visible derivations, try an exercise, and use its hints and complete solution to find the first step where your reasoning differs. Paper companions connect those calculations to the primary literature. Laboratories let you reproduce results and change their inputs. Once you can explain a capstone, the research entrances help you formulate a bounded next question.
Read About this course for its scope and authorship, and editorial standards for source checks and corrections.