Parity Invariance For Strings In Twistor Space

TL;DR

This paper demonstrates that tree and loop diagrams in twistor space topological string theory exhibit parity symmetry, clarifying an aspect of the relationship between twistor string theory and Yang-Mills theory.

Contribution

It proves that tree diagrams from connected D-instanton configurations are parity-symmetric, extending the result to loop diagrams, thus revealing hidden symmetries in twistor string formulations.

Findings

Tree diagrams are parity-symmetric in twistor space.

Loop diagrams also exhibit parity symmetry.

Clarifies the symmetry properties of twistor string theory.

Abstract

Topological string theory with twistor space as the target makes visible some otherwise difficult to see properties of perturbative Yang-Mills theory. But left-right symmetry, which is obvious in the standard formalism, is highly unclear from this point of view. Here we prove that tree diagrams computed from connected $D$-instanton configurations are parity-symmetric. The main point in the proof also works for loop diagrams.