# nLab N=4 D=3 super Yang-Mills theory

supersymmetry

## Applications

### Ingredients

• quantum field theory

• effective background QFT

• ### Critical string models

• heterotic string theory

• type II string theory

• string field theory

• duality in string theory

• brane

• D-brane

• NS-brane

• M-brane

• ### Topological strings

• topological M-theory

• ## Backgrounds

• twisted smooth cohomology in string theory

• landscape of string theory vacua

• ## Phenomenology

• string phenomenology

• # Contents

## Idea

The special case of super Yang-Mills theory over a spacetime of dimension 3 and with $N = 4$ supersymmetry.

## Properties

### Reduction from $N = 2$, $D = 4$

The $N = 4$, $D = 3$ SYM theory can be obtained by dimensional reduction from N=2 D=4 super Yang-Mills theory (Seiberg-Witten 96)

### Mirror symmetry

A version of mirror symmetry acts on the $N = 4$, $D = 3$ SYM moduli space of vacua and exchanges the Coulomb branch with the Higgs branch. (Intriligator-Seiberg 96)