The decoupling of [formula omitted] in string theory

K.S Narain,A Zein Assi

doi:10.1016/j.nuclphysb.2018.12.013

Abstract

In this note, we study the deformation of the topological string by Ω¯. Namely, adopting the perturbative string amplitudes approach, we identify the Ω¯-deformation in terms of a physical state in the sting spectrum. We calculate the topological amplitudes Fg 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 Ω¯ to decouple. It turns out that this decoupling happens at the full string level, suggesting that this holds non-perturbatively.

Highlights

The interplay between string theory and supersymmetric gauge theories has been very fruitful in the past decades in unravelling new connections and structures both in string theory and gauge theory
The partition function of the -deformed gauge theory [1,2,3] corresponds, in the topological limit, to the topological string theory partition function which calculates a class of gravitational couplings Fg in the string effective action [4]
We provide further support by showing that the decoupling happens in string theory and that it is exact

Summary

Introduction

The interplay between string theory and supersymmetric gauge theories has been very fruitful in the past decades in unravelling new connections and structures both in string theory and gauge theory. The topological nature of Fg implies that this coupling depends holomorphically on some of the moduli of the Calabi–Yau compactifications, modulo anomalous, boundary terms [5] that are absent in the low energy gauge theory.. The topological nature of Fg implies that this coupling depends holomorphically on some of the moduli of the Calabi–Yau compactifications, modulo anomalous, boundary terms [5] that are absent in the low energy gauge theory.1 In the latter, since the -deformation can be thought of as a geometrical twist of space–time [3], one can promote to a complex parameter and supersymmetry implies that the gauge theory partition function is holomorphic in , i.e. independent of. Useful results and technical details are deferred to two appendices

What is

Effective action

Amplitude calculation

Inclusion of quadratic terms

Conclusions