D=10 supersymmetric chern-simons gauge theory

TL;DR

This paper formulates a ten-dimensional supersymmetric Chern-Simons gauge theory using second quantization of superparticle theory, deriving equations of motion and connecting to super Yang-Mills theory.

Contribution

It introduces a novel supersymmetric Chern-Simons gauge theory in ten dimensions via second quantization, linking it to super Yang-Mills and string field theory.

Findings

Derived the equation of motion as a gauge independence condition

Connected the theory to super Yang-Mills on shell

Presented a supersymmetric gauge theory framework in 10D

Abstract

The Chern-Simons ten-dimensional manifestly supersymmetric non-Abelian gauge theory is presented by performing the second quantization of the superparticle theory. The equation of motion is $F = (d+A)^2 = 0$, where $d$ is the nilpotent fermionic BRST operator of the first quantized theory and $A$ is the anti- commuting connection for the gauge group. This equation can be derived as a condition of the gauge independence of the first quantized theory in a background field $A$, or from the string field theory Lagrangian of the Chern- Simons type. The trivial solutions of the cohomology are the gauge symmetries, the non-trivial solution is given by the D=10 superspace, describing the super Yang-Mills theory on shell