A holomorphic anomaly in the elliptic genus

Sameer Murthy*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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 languageEnglish
Article number165
Number of pages28
JournalJournal of High Energy Physics
Issue number6
Publication statusPublished - 27 Jun 2014


  • Supersymmetric gauge theory
  • Conformal Field Models in String Theory
  • Anomalies in Field and String Theories


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