## Abstract

We study a class of two-dimensional (Formula presented.) sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global (Formula presented.) symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi–Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter (Formula presented.) coming from the continuum produced by the neck. In the simplest case corresponding to squashed (Formula presented.) the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the (Formula presented.)(Formula presented.) cigar coset.

Original language | English |
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Pages (from-to) | 1-33 |

Number of pages | 33 |

Journal | Communications in Mathematical Physics |

Early online date | 18 Jan 2018 |

DOIs | |

Publication status | E-pub ahead of print - 18 Jan 2018 |