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arXiv · 1311.0918

A holomorphic anomaly in the elliptic genus

Sameer Murthy
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Abstract

We consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2,2) superconformal field theories in the infra-red, a prototype of which is the SL(2,\IR)/U(1) (cigar) coset. We compute the elliptic genus of the GLSMs as a path-integral on the torus using supersymmetric localization. We find that the result is a Jacobi-like form that is non-holomorphic in the modular parameter $τ$ of the torus, with mock modular behavior. This agrees with a previously-computed expression in the cigar coset. We show that the lack of holomorphicity of the elliptic genus arises from the contributions of a compact boson with momentum and winding around the torus. This boson has an axionic shift symmetry and plays the role of a compensator field that is needed to cancel the chiral anomaly in the rest of the theory.

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Sameer Murthy. 2014-07-24. A holomorphic anomaly in the elliptic genus. https://doi.org/10.1007/jhep06(2014)165

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