A holomorphic anomaly in the elliptic genus

Sameer Murthy

doi:10.1007/JHEP06(2014)165

A holomorphic anomaly in the elliptic genus

Sameer Murthy^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

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, R)/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 tau 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 carrying momentum and winding excitations. 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.

Original language	English
Article number	165
Number of pages	28
Journal	Journal of High Energy Physics
Issue number	6
DOIs	https://doi.org/10.1007/JHEP06(2014)165
Publication status	Published - 27 Jun 2014

Keywords

Supersymmetric gauge theory
Conformal Field Models in String Theory
Anomalies in Field and String Theories
STRING THEORY
MODULAR INVARIANCE
FIELD-THEORIES
CONSTRUCTION
GENERA

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10.1007/JHEP06(2014)165

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title = "A holomorphic anomaly in the elliptic genus",

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, R)/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 tau 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 carrying momentum and winding excitations. 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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N2 - 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, R)/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 tau 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 carrying momentum and winding excitations. 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.

AB - 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, R)/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 tau 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 carrying momentum and winding excitations. 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.

KW - Supersymmetric gauge theory

KW - Conformal Field Models in String Theory

KW - Anomalies in Field and String Theories

KW - STRING THEORY

KW - MODULAR INVARIANCE

KW - FIELD-THEORIES

KW - CONSTRUCTION

KW - GENERA

U2 - 10.1007/JHEP06(2014)165

DO - 10.1007/JHEP06(2014)165

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SN - 1029-8479

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 6

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ER -

A holomorphic anomaly in the elliptic genus

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Keywords

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