N=2 string amplitudes and the Omega background

TL;DR

This paper reviews recent developments in realizing the Omega background within N=2 supergravity, connecting it to the Nekrasov partition function and refined topological string theory, with implications for string amplitudes.

Contribution

It introduces a specific series of higher-derivative F-terms in supergravity that realize the Omega background and links these to worldsheet approaches and refined topological strings.

Findings

Established a connection between Omega background and supergravity F-terms

Linked supergravity couplings to Nekrasov partition function

Connected the framework to refined topological string theory

Abstract

We review recent work [1, 2] on obtaining a realisation of the $\Omega$-background in terms of a special series of higher-derivative generalised F-terms in the effective $\mathcal{N}=2$ supergravity action. We discuss the motivation behind the identification of these couplings, their relation to the Nekrasov partition function and connect them to a worldsheet approach towards the refined topological string. Presented by the authors at the Corfu Summer Institute 2013 "Workshop on Noncommutative Field Theory and Gravity", September 8-15, 2013 Corfu, Greece