One-dimensional structures behind twisted and untwisted superYang-Mills theory

TL;DR

This paper provides a one-dimensional perspective on 4D twisted and untwisted superYang-Mills theory through dimensional reduction, revealing a superalgebra structure that encompasses both formulations.

Contribution

It introduces a novel one-dimensional interpretation and identifies a superalgebra linking twisted and untwisted superYang-Mills theories.

Findings

Existence of a 6-generator superalgebra without an invariant Lagrangian.

Superalgebra contains subalgebras corresponding to twisted and untwisted theories.

Dimensional reduction connects 4D superYang-Mills to a 1D algebraic structure.

Abstract

We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.