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SIGMA, 2012, Volume 8, 068, 28 pages (Mi sigma745)  

This article is cited in 29 scientific papers (total in 29 papers)

Recent developments in (0,2) mirror symmetry

Ilarion Melnikova, Savdeep Sethib, Eric Sharpec

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

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.


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ArXiv: 1209.1134
MSC: 32L10; 81T20; 14N35
Received: June 4, 2012; in final form October 2, 2012; Published online October 7, 2012

Citation: Ilarion Melnikov, Savdeep Sethi, Eric Sharpe, “Recent developments in (0,2) mirror symmetry”, SIGMA, 8 (2012), 068, 28 pp.

Citation in format AMSBIB
\by Ilarion Melnikov, Savdeep Sethi, Eric Sharpe
\paper Recent developments in (0,2) mirror symmetry
\jour SIGMA
\yr 2012
\vol 8
\papernumber 068
\totalpages 28

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    This publication is cited in the following articles:
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    4. de la Ossa X., Svanes E.E., “Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications”, J. High Energy Phys., 2014, no. 10, 123  crossref  mathscinet  zmath  isi  scopus
    5. Chen J., Cui X., Shifman M., Vainshtein A., “N = (0,2) Deformation of (2,2) SIGMA Models: Geometric Structure, Holomorphic Anomaly, and Exact Beta Functions”, Phys. Rev. D, 90:4 (2014), 045014  crossref  mathscinet  adsnasa  isi  elib  scopus
    6. Garavuso R.S., Sharpe E., “Analogues of Mathai-Quillen Forms in Sheaf Cohomology and Applications To Topological Field Theory”, J. Geom. Phys., 92 (2015), 1–29  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    15. Sharpe E., “A Few Recent Developments in 2D (2,2) and (0,2) Theories”, String-Math 2014, Proceedings of Symposia in Pure Mathematics, 93, eds. Bouchard V., Doran C., MendezDiez S., Quigley C., Amer Mathematical Soc, 2016, 67+  crossref  zmath  isi
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    17. J. Chen, X. Cui, M. Shifman, A. Vainshtein, “Anomalies of minimal ${ \mathcal N }=(0,1)$ and ${ \mathcal N }=(0,2)$ sigma models on homogeneous spaces”, J. Phys. A-Math. Theor., 50:2 (2017), 025401  crossref  mathscinet  zmath  isi  scopus
    18. Ph. Candelas, X. Ossa, J. McOrist, “A metric for heterotic moduli”, Commun. Math. Phys., 356:2 (2017), 567–612  crossref  mathscinet  zmath  isi  scopus
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    22. M.-A. Fiset, C. Quigley, E. E. Svanes, “Marginal deformations of heterotic G(2) SIGMA models”, J. High Energy Phys., 2018, no. 2, 052  crossref  mathscinet  isi
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    24. Bertolini M., Plesser M.R., “(0,2) Hybrid Models”, J. High Energy Phys., 2018, no. 9, 067  crossref  isi  scopus
    25. Caldeira J., Maxfield T., Sethi S., “(2,2) Geometry From Gauge Theory”, J. High Energy Phys., 2018, no. 11, 201  crossref  mathscinet  zmath  isi  scopus
    26. de la Ossa X., Fiset M.-A., “G-Structure Symmetries and Anomalies in (1,0) Non-Linear SIGMA-Models”, J. High Energy Phys., 2019, no. 1, 062  crossref  mathscinet  isi  scopus
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    28. Gu W., Zou H., “Supersymmetric Localization in Glsms For Supermanifolds”, J. High Energy Phys., 2019, no. 5, 019  crossref  isi  scopus
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  • Symmetry, Integrability and Geometry: Methods and Applications
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