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# Communications in Number Theory and Physics

## Volume 14 (2020)

### Number 2

### Aspects of $(2,2)$ and $(0,2)$ hybrid models

Pages: 325 – 412

DOI: https://dx.doi.org/10.4310/CNTP.2020.v14.n2.a3

#### Authors

#### Abstract

In this work we study the topological rings of two dimensional $(2,2)$ and $(0,2)$ hybrid models. In particular, we use localization to derive a formula for the correlators in both cases, focusing on the $\mathrm{B}$- and $\frac{\mathrm{B}}{2}$-twists. Although our methods apply to a vast range of hybrid CFTs, we focus on hybrid models suitable for compactifications of the heterotic string. In this case, our formula provides unnormalized Yukawa couplings of the spacetime superpotential. We apply our techniques to hybrid phases of linear models, and we find complete agreement with known results in other phases. We also obtain a prediction for a certain class of correlators involving twisted operators in $(2,2)$ Landau–Ginzburg orbifolds. For $(0,2)$ theories, our argument does not rely on the existence of a $(2,2)$ locus. Finally, we derive vanishing conditions concerning worldsheet instanton corrections in $(0,2)$ $\frac{\mathrm{B}}{2}$-twisted hybrid models.

MB is supported by NSF Grant PHY-1521053. MR gratefully acknowledges the support of the Institute for Advanced Study, DOE grant DE-SC0009988 and the Adler Family Fund. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

Received 27 August 2018

Accepted 11 November 2019

Published 30 March 2020