Abstract
AbstractWe study mass‐deformed N = 2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)‐brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M‐strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of ℂ2 through a (singular) theta‐transform. This form appears naturally as a specific class of one‐loop scattering amplitudes in type II string theory on T2, which we calculate explicitly.
Highlights
The world-volume theory of multiple coincident M5 branes is among the most fascinating objects of current interest in high energy physics
We show that the torus integral mentioned before can be obtained from a very particular series of one-loop amplitudes in type II string theory compactified on T 2 with massive external legs
In the second part of the paper, we have explored a fourth approach, namely linking the gauge theory partition function to the equivariant elliptic genus of C2 through a particular Hecke transformation, as well as through a thetatransform
Summary
The world-volume theory of multiple coincident M5 branes is among the most fascinating objects of current interest in high energy physics It is a conformal field theory in six dimensions with N = (2, 0) supersymmetry and a non-abelian gauge group of ADE type [1]. M-strings: M5/M2 branes in non-trivial geometry equivariant (2,0) elliptic genus instanton calculus partition functions of mass deformed N=2 gauge theories gauge theories from (p,q) branes in type IIB string th. In the case of the CY3fold obtained from the orbifold ZN × ZM we can choose the preferred direction corresponding to the curves coming from the resolution of ZN action or the ZM action leading to two different, yet equal, expressions for the partition functions
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