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Three-Dimensional Supersymmetric Gauge Theory and Duality Webs

In three dimensions, supersymmetric gauge dynamics joins local monopole operators to quantized Chern–Simons couplings and parity anomalies. This chapter follows those ingredients into Coulomb branches, mirror symmetry, and duality flows, retaining the background contact terms needed to compare theories.

Enter this chapter

Section titled “Enter this chapter”

Begin with Three-Dimensional Supersymmetry Algebras and Multiplets to identify the real supercharges and scalar content of three-dimensional multiplets.

Helpful background. Chern–Simons Actions and Level Quantization; Disorder Operators and Singular Boundary Conditions; Fixed Points and Linearized RG Flow provide the level quantization, disorder insertions, and RG flow used here.

Topics

Section titled “Topics”
  1. Three-Dimensional Supersymmetry Algebras and Multiplets — Builds the dimension-specific algebra and field multiplets.
  2. Yang–Mills and Chern–Simons–Matter Actions — Fixes gauge and Chern–Simons action data.
  3. Parity Anomalies and Background Contact Terms — Tracks regulator-dependent parity-odd contact terms.
  4. Monopole Operators and Quantum Coulomb Branches — Defines monopole insertions by magnetic flux.
  5. Three-Dimensional N=4 Mirror Symmetry — Exchanges Higgs and Coulomb descriptions in N=4 theories.
  6. Aharony and Giveon–Kutasov-Type Dualities — States monopole and level data in N=2 dual pairs.
  7. Real-Mass, FI, and Compactification Flows — Transports vacua and induced terms across deformations.
  8. Supersymmetric Parents of Mirror, Particle–Vortex, and Bosonization Webs — Separates protected supersymmetric tests from nonsupersymmetric extrapolation.

How the ideas fit together

Section titled “How the ideas fit together”

Integrating out a massive charged fermion shifts parity-odd gauge and background terms according to its mass sign and regulator. A real-mass flow can therefore change the effective Chern–Simons levels as well as the light particle spectrum. Comparing only the massless fields can miss a mismatch in the background generating functional. Monopole operators and their charges must be tracked with the same quantized data, making contact terms a substantive part of a duality test. Closset et al. 2012, §§ 2–3.

Where to go next

Section titled “Where to go next”

Continue to Rigid Backgrounds, Topological Twists, and Localization to check that the theory has a current multiplet compatible with the proposed background.

References

Section titled “References”
  • Closset, C., Dumitrescu, T. T., Festuccia, G., Komargodski, Z., and Seiberg, N. (2012), “Comments on Chern–Simons Contact Terms in Three Dimensions,” Journal of High Energy Physics 2012(09), 091. doi:10.1007/JHEP09(2012)091. Open PDF