Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 068, 28 pages      arXiv:1209.1134      https://doi.org/10.3842/SIGMA.2012.068
Contribution to the Special Issue “Mirror Symmetry and Related Topics”

Recent Developments in (0,2) Mirror Symmetry

Ilarion Melnikov a, Savdeep Sethi b and Eric Sharpe c
a) Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Golm, Germany
b) Department of Physics, Enrico Fermi Institute, University of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637, USA
c) Department of Physics, MC 0435, 910 Drillfield Dr., Virginia Tech, Blacksburg, VA 24061, USA

Received June 04, 2012, in final form October 02, 2012; Published online October 07, 2012

Abstract
Mirror symmetry of the type II string has a beautiful generalization to the heterotic string. This generalization, known as (0,2) mirror symmetry, is a field still largely in its infancy. We describe recent developments including the ideas behind quantum sheaf cohomology, the mirror map for deformations of (2,2) mirrors, the construction of mirror pairs from worldsheet duality, as well as an overview of some of the many open questions. The (0,2) mirrors of Hirzebruch surfaces are presented as a new example.

Key words: mirror symmetry; (0,2) mirror symmetry; quantum sheaf cohomology.

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