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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.

DOI: https://doi.org/10.3842/SIGMA.2012.068

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Full text: http://emis.mi.ras.ru/.../068
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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
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Citation: Ilarion Melnikov, Savdeep Sethi, Eric Sharpe, “Recent developments in (0,2) mirror symmetry”, SIGMA, 8 (2012), 068, 28 pp.

Citation in format AMSBIB
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\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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Melnikov I., Quigley C., Sethi S., Stern M., “Target Spaces From Chiral Gauge Theories”, J. High Energy Phys., 2013, no. 2, 111  crossref  mathscinet  zmath  isi  scopus
    2. Israel D., “T-Duality in Gauged Linear SIGMA-Models with Torsion”, J. High Energy Phys., 2013, no. 11, 093  crossref  mathscinet  isi  elib  scopus
    3. Jia B., Sharpe E., Wu R., “Notes on Nonabelian (0,2) Theories and Dualities”, J. High Energy Phys., 2014, no. 8, 017  crossref  isi  elib  scopus
    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
    7. Donagi R., Lu Zh., Melnikov I.V., “Global Aspects of (0,2) Moduli Space: Toric Varieties and Tangent Bundles”, Commun. Math. Phys., 338:3 (2015), 1197–1232  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Anderson L.B., Jia B., Manion R., Ovrut B., Sharpe E., “General Aspects of Heterotic String Compactifications on Stacks and Gerbes”, Adv. Theor. Math. Phys., 19:3 (2015), 531–611  crossref  mathscinet  zmath  isi  scopus
    9. Quigley, C., “Mirror symmetry in physics: The basics”, Fields Institute Monographs, 34 (2015), 211-278  crossref  mathscinet  zmath  scopus
    10. Peterson A.J., Kurianovych E., Shifman M., “More on Two-Dimensional O(N) Models With N = (0,1) Supersymmetry”, Phys. Rev. D, 93:6 (2016), 065016  crossref  mathscinet  adsnasa  isi  elib  scopus
    11. Vainshtein A., “Beta functions in Chirally deformed supersymmetric sigma models in two dimensions”, Int. J. Mod. Phys. A, 31:28-29, SI (2016), 1645040  crossref  zmath  isi  elib  scopus
    12. Chen J., Cui X., Shifman M., Vainshtein A., “On isometry anomalies in minimal $\mathcal{N}= (0,1)$ and $\mathcal{N}= (0,2)$ sigma models”, Int. J. Mod. Phys. A, 31:27 (2016), 1650147  crossref  zmath  isi  elib  scopus
    13. Blaszczyk M., Oehlmann P.-K., “Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications”, J. High Energy Phys., 2016, no. 4, 068  crossref  mathscinet  isi  scopus
    14. Closset C., Gu W., Jia B., Sharpe E., “Localization of twisted $ \mathcal{N}=(0,\;2) $ gauged linear sigma models in two dimensions”, J. High Energy Phys., 2016, no. 3, 070  crossref  mathscinet  isi  elib  scopus
    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
    16. J. Guo, Zh. Lu, E. Sharpe, “Quantum sheaf cohomology on Grassmannians”, Commun. Math. Phys., 352:1 (2017), 135–184  crossref  mathscinet  zmath  isi  scopus
    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
    19. W. Gu, E. Sharpe, “A proposal for $(0,2)$ mirrors of toric varieties”, J. High Energy Phys., 2017, no. 11, 112  crossref  zmath  isi  scopus
    20. J. Guo, Zh. Lu, E. Sharpe, “Classical sheaf cohomology rings on Grassmannians”, J. Algebra, 486 (2017), 246–287  crossref  mathscinet  zmath  isi  scopus
    21. Zh. Chen, J. Guo, E. Sharpe, R. Wu, “More Toda-like $(0,2)$ mirrors”, J. High Energy Phys., 2017, no. 8, 079  crossref  mathscinet  isi  scopus
    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
    23. J. McOrist, “On the effective field theory of heterotic vacua”, Lett. Math. Phys., 108:4 (2018), 1031–1081  crossref  mathscinet  zmath  isi  scopus
    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
    27. Bertolini M., “Testing the (0,2) Mirror Map”, J. High Energy Phys., 2019, no. 1, 018  crossref  mathscinet  isi  scopus
    28. Gu W., Zou H., “Supersymmetric Localization in Glsms For Supermanifolds”, J. High Energy Phys., 2019, no. 5, 019  crossref  isi  scopus
    29. Kreshchuk M., Kurianovych E., Shifman M., “Grassmannian Heterotic SIGMA Model”, Phys. Rev. D, 99:12 (2019), 125005  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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