$\mathcal{N}=2^\star$ from Topological Amplitudes in String Theory

TL;DR

This paper constructs string theory backgrounds that realize the $ =2^ ext{star}$ gauge theory, verifies their consistency through partition functions, and reproduces the Nekrasov partition function via topological amplitudes, unifying different string models.

Contribution

It provides explicit string constructions of $ =2^ ext{star}$ gauge theories and demonstrates their universality and consistency, including the instanton sector uplift.

Findings

Constructed consistent string backgrounds for $ =2^ ext{star}$ gauge theories.

Reproduced Nekrasov partition function from string models.

Unified heterotic, type II, and type I constructions.

Abstract

In this paper, we explicitly construct string theory backgrounds that realise the so-called $\mathcal N=2^\star$ gauge theory. We prove the consistency of our models by calculating their partition function and obtaining the correct gauge theory spectrum. We further provide arguments in favour of the universality of our construction which covers a wide class of models all of which engineer the same gauge theory. We reproduce the corresponding Nekrasov partition function once the $\Omega$-deformation is included and the appropriate field theory limit taken. This is achieved by calculating the topological amplitudes $F_g$ in the string models. In addition to heterotic and type II constructions, we also realise the mass deformation in type I theory, thus leading to a natural way of uplifting the result to the instanton sector.