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

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.

27 pages

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Cited by in corpus (10)

• A slow review of the AGT correspondence
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Instanton Corrections for m and Omega
• Refined Topological Amplitudes from the $\Omega$-Background in String Theory
• The String Geometry Behind Topological Amplitudes