SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry

TL;DR

This paper constructs a twisted form of ten-dimensional super Yang-Mills theory using SU(5) invariance, revealing a new decomposition related to topological and supersymmetric structures with fewer generators.

Contribution

It introduces a novel SU(5)-invariant decomposition of 10D super Yang-Mills, deriving a twisted action with a scalar supersymmetry operator and analyzing its cohomological properties.

Findings

Decomposition involves a fermionic Chern-Simons term.

Action is expressed as a sum of Q-closed and Q-exact parts.

The theory is characterized by 6 supersymmetry generators.

Abstract

The N=1,d=10 superYang-Mills action is constructed in a twisted form, using SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q derive from a Chern-Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)<SO(10)$ invariant decomposition, the N=1, d=10 theory is determined by only 6 supersymmetry generators, as in the twisted N=4, d=4 theory. There is a superspace with 6 twisted fermionic directions, with solvable constraints.