The Decoupling of $\bar\Omega$ in String Theory

TL;DR

This paper investigates the effects of $ar ext{Omega}$-deformation in topological string theory, demonstrating its decoupling at the full string level through perturbative and non-perturbative analysis.

Contribution

It identifies the $ar ext{Omega}$-deformation as a physical state and shows that including quadratic terms in the effective action is essential for decoupling.

Findings

$ar ext{Omega}$-deformation can be represented by a physical state.

Decoupling of $ar ext{Omega}$ occurs at the full string level.

Quadratic terms are crucial for $ar ext{Omega}$ decoupling.

Abstract

In this note, we study the deformation of the topological string by $\bar\Omega$. Namely, adopting the perturbative string amplitudes approach, we identify the $\bar\Omega$-deformation in terms of a physical state in the sting spectrum. We calculate the topological amplitudes $F_g$ in heterotic string theory in the presence of the latter. In particular, we show that it is crucial to include quadratic terms in the effective action in order for $\bar\Omega$ to decouple. It turns out that this decoupling happens at the full string level, suggesting that this holds non-perturbatively.