Abstract
We test a proposed mirror map at the level of correlators for linear models describing the (0,2) moduli space of superconformal field theories with a (2,2) locus associated to Calabi-Yau hypersurfaces in toric varieties. We verify in non-trivial examples that the correlators are exchanged by the mirror map and we derive a correspondence between the observables of the A/2- and B/2-twisted theories. We also comment on the global structure of the (0,2) moduli space and present a simple non-renormalization argument for a large class of B/2 model subfamilies.
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I. Melnikov, S. Sethi and E. Sharpe, Recent Developments in (0, 2) Mirror Symmetry, SIGMA 8 (2012) 068 [arXiv:1209.1134] [INSPIRE].
B.R. Greene and M.R. Plesser, Duality in Calabi-Yau Moduli Space, Nucl. Phys. B 338 (1990) 15 [INSPIRE].
P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
P.S. Aspinwall, B.R. Greene and D.R. Morrison, The Monomial divisor mirror map, alg-geom/9309007 [INSPIRE].
J. Distler and S. Kachru, Duality of (0, 2) string vacua, Nucl. Phys. B 442 (1995) 64 [hep-th/9501111] [INSPIRE].
J. Distler, B.R. Greene and D.R. Morrison, Resolving singularities in (0, 2) models, Nucl. Phys. B 481 (1996) 289 [hep-th/9605222] [INSPIRE].
M. Kreuzer, J. McOrist, I.V. Melnikov and M.R. Plesser, (0, 2) Deformations of Linear σ-models, JHEP 07 (2011) 044 [arXiv:1001.2104] [INSPIRE].
I.V. Melnikov and M.R. Plesser, A (0, 2) Mirror Map, JHEP 02 (2011) 001 [arXiv:1003.1303] [INSPIRE].
J. McOrist and I.V. Melnikov, Summing the Instantons in Half-Twisted Linear σ-models, JHEP 02 (2009) 026 [arXiv:0810.0012] [INSPIRE].
C. Closset, W. Gu, B. Jia and E. Sharpe, Localization of twisted \( \mathcal{N}=\left(0,\ 2\right) \) gauged linear σ-models in two dimensions, JHEP 03 (2016) 070 [arXiv:1512.08058] [INSPIRE].
C. Closset, N. Mekareeya and D.S. Park, A-twisted correlators and Hori dualities, JHEP 08 (2017) 101 [arXiv:1705.04137] [INSPIRE].
C. Closset, S. Cremonesi and D.S. Park, The equivariant A-twist and gauged linear σ-models on the two-sphere, JHEP 06 (2015) 076 [arXiv:1504.06308] [INSPIRE].
D.A. Cox and S. Katz, Mirror symmetry and algebraic geometry, AMS, Providence, U.S.A. (2000) [INSPIRE].
V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [INSPIRE].
M. Bertolini and M.R. Plesser, Worldsheet instantons and (0, 2) linear models, JHEP 08 (2015) 081 [arXiv:1410.4541] [INSPIRE].
D.R. Morrison and M.R. Plesser, Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys. B 440 (1995) 279 [hep-th/9412236] [INSPIRE].
D.R. Morrison and M.R. Plesser, Towards mirror symmetry as duality for two-dimensional abelian gauge theories, Nucl. Phys. Proc. Suppl. 46 (1996) 177 [hep-th/9508107] [INSPIRE].
J. McOrist and I.V. Melnikov, Half-Twisted Correlators from the Coulomb Branch, JHEP 04 (2008) 071 [arXiv:0712.3272] [INSPIRE].
C. Vafa, Topological Landau-Ginzburg models, Mod. Phys. Lett. A 6 (1991) 337 [INSPIRE].
I.V. Melnikov and S. Sethi, Half-Twisted (0, 2) Landau-Ginzburg Models, JHEP 03 (2008) 040 [arXiv:0712.1058] [INSPIRE].
I.V. Melnikov, (0, 2) Landau-Ginzburg Models and Residues, JHEP 09 (2009) 118 [arXiv:0902.3908] [INSPIRE].
P. Griffiths and J. Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience, John Wiley & Sons, New York (1978) [DOI:https://doi.org/10.1002/9781118032527].
M. Bertolini and M. Romo, Aspects of (2, 2) and (0, 2) hybrid models, arXiv:1801.04100 [INSPIRE].
M. Bertolini, I.V. Melnikov and M.R. Plesser, Hybrid conformal field theories, JHEP 05 (2014) 043 [arXiv:1307.7063] [INSPIRE].
M. Bertolini and M.R. Plesser, (0, 2) hybrid models, JHEP 09 (2018) 067 [arXiv:1712.04976] [INSPIRE].
R. Donagi, J. Guffin, S. Katz and E. Sharpe, A Mathematical Theory of Quantum Sheaf Cohomology, Asian J. Math. 18 (2014) 387 [arXiv:1110.3751] [INSPIRE].
R. Donagi, J. Guffin, S. Katz and E. Sharpe, Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, Adv. Theor. Math. Phys. 17 (2013) 1255 [arXiv:1110.3752] [INSPIRE].
R. Donagi, Z. Lu and I.V. Melnikov, Global aspects of (0, 2) moduli space: toric varieties and tangent bundles, Commun. Math. Phys. 338 (2015) 1197 [arXiv:1409.4353] [INSPIRE].
V.V. Batyrev and L.A. Borisov, On Calabi-Yau complete intersections in toric varieties, alg-geom/9412017 [INSPIRE].
V. Batyrev and B. Nill, Combinatorial aspects of mirror symmetry, math/0703456.
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Bertolini, M. Testing the (0,2) mirror map. J. High Energ. Phys. 2019, 18 (2019). https://doi.org/10.1007/JHEP01(2019)018
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DOI: https://doi.org/10.1007/JHEP01(2019)018