This article is cited in 36 papers

Recent developments in (0,2) mirror symmetry

Ilarion Melnikov^a, Savdeep Sethi^b, Eric Sharpe<sup>c

a</sup> 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

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.

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

MSC: 32L10; 81T20; 14N35

Received: June 4, 2012; in final form October 2, 2012; Published online October 7, 2012

Language: English

DOI: 10.3842/SIGMA.2012.068

Bibliographic databases:

• 
• 
• 

ArXiv: 1209.1134