Twisted Superspace

TL;DR

This paper develops a twisted superspace formulation for super-Yang-Mills theories in various dimensions, providing new insights into their constraints, equations of motion, and path-integral structure, including a novel superspace action for N=2, d=4.

Contribution

It introduces a twisted superspace approach for ten-dimensional super-Yang-Mills and formulates a superspace path-integral for N=2, d=4 super-Yang-Mills, advancing the understanding of their geometric and quantum structures.

Findings

Formulated 10D super-Yang-Mills in twisted superspace with 8+1 supercharges.

Solved the superspace constraints that do not imply equations of motion.

Provided a superspace path-integral formulation for N=2, d=4 super-Yang-Mills.

Abstract

We formulate the ten-dimensional super-Yang-Mills theory in a twisted superspace with 8+1 supercharges. Its constraints do not imply the equations of motion and we solve them. As a preliminary step for a complete formulation in a twisted superspace, we give a superspace path-integral formulation of the N=2, d=4 super-Yang-Mills theory without matter. The action is the sum of a Chern--Simons term depending on a super-connection plus a BF-like term. The integration over the superfield B implements the twisted superspace constraints on the super-gauge field, and the Chern-Simons action reduces to the known action in components.