$\Omega$ versus Graviphoton

TL;DR

This paper investigates the complex conjugate of the Omega-deformation, called arOmega, in topological string theory, identifying its physical state representation and analyzing its effects on deformed gauge actions and string amplitudes.

Contribution

It explicitly identifies arOmega in the string spectrum and demonstrates its role in reproducing deformed gauge actions, completing the understanding of the full Omega-deformation.

Findings

arOmega decouples from one-loop topological amplitudes in heterotic string theory

Quadratic terms in the effective action are crucial for the full Omega-deformation realization

Differences between graviphoton and Omega-deformation are discussed, with potential arOmega remnants at moduli space boundaries

Abstract

I study the deformation of the topological string by $\bar\Omega$, the complex conjugate of the $\Omega$-deformation. Namely, I identify $\bar\Omega$ in terms of a physical state in the string spectrum and verify that the deformed Yang-Mills and ADHM actions are reproduced. This completes the study initiated recently [1] where we show that $\bar\Omega$ decouples from the one-loop topological amplitudes in heterotic string theory. Similarly to the N=2* deformation, I show that the quadratic terms in the effective action play a crucial role in obtaining the correct realisation of the full $\Omega$-deformation. Finally, I comment on the differences between the graviphoton and the $\Omega$-deformation in general and discuss possible $\bar\Omega$ remnants at the boundary of the string moduli space.