Abstract
We study the moduli spaces of heterotic/type II dual pairs in four dimensions with \( \mathcal{N} \) = 2 supersymmetry corresponding to non-geometric Calabi-Yau backgrounds on the type II side and to T-fold compactifications on the heterotic side. The vector multiplets moduli space receives perturbative corrections in the heterotic description only, and non- perturbative correction in both descriptions. We derive explicitely the perturbative corrections to the heterotic four-dimensional prepotential, using the knowledge of its singularity structure and of the heterotic perturbative duality group. We also derive the exact hypermultiplets moduli space, that receives corrections neither in the string coupling nor in α′.
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P.S. Aspinwall, Compactification, geometry and duality: N = 2, in Theoretical Advanced Study Institute in elementary particle physics (TASI 99): strings, branes, and gravity, (2000), pg. 723 [hep-th/0001001] [INSPIRE].
S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450 (1995) 69 [hep-th/9505105] [INSPIRE].
S. Ferrara, J.A. Harvey, A. Strominger and C. Vafa, Second quantized mirror symmetry, Phys. Lett. B 361 (1995) 59 [hep-th/9505162] [INSPIRE].
C. Vafa and E. Witten, Dual string pairs with N = 1 and N = 2 supersymmetry in four-dimensions, Nucl. Phys. B Proc. Suppl. 46 (1996) 225 [hep-th/9507050] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
P.S. Aspinwall, Some relationships between dualities in string theory, Nucl. Phys. B Proc. Suppl. 46 (1996) 30 [hep-th/9508154] [INSPIRE].
S. Ferrara and C. Kounnas, Extended supersymmetry in four-dimensional type II strings, Nucl. Phys. B 328 (1989) 406 [INSPIRE].
J.H. Schwarz and A. Sen, Type IIA dual of the six-dimensional CHL compactification, Phys. Lett. B 357 (1995) 323 [hep-th/9507027] [INSPIRE].
S. Chaudhuri, G. Hockney and J.D. Lykken, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett. 75 (1995) 2264 [hep-th/9505054] [INSPIRE].
S. Datta, J.R. David and D. Lüst, Heterotic string on the CHL orbifold of K 3, JHEP 02 (2016) 056 [arXiv:1510.05425] [INSPIRE].
Y. Gautier, C.M. Hull and D. Israël, Heterotic/type-II duality and non-geometric compactifications, JHEP 10 (2019) 214 [arXiv:1906.02165] [INSPIRE].
D. Israël and V. Thiéry, Asymmetric Gepner models in type-II, JHEP 02 (2014) 011 [arXiv:1310.4116] [INSPIRE].
D. Israël, Nongeometric Calabi-Yau compactifications and fractional mirror symmetry, Phys. Rev. D 91 (2015) 066005 [Erratum ibid. 91 (2015) 129902] [arXiv:1503.01552] [INSPIRE].
C. Hull, D. Israel and A. Sarti, Non-geometric Calabi-Yau backgrounds and K 3 automorphisms, JHEP 11 (2017) 084 [arXiv:1710.00853] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
J. McOrist, D.R. Morrison and S. Sethi, Geometries, non-geometries, and fluxes, Adv. Theor. Math. Phys. 14 (2010) 1515 [arXiv:1004.5447] [INSPIRE].
E. Plauschinn, Non-geometric backgrounds in string theory, Phys. Rept. 798 (2019) 1 [arXiv:1811.11203] [INSPIRE].
V. Kaplunovsky, J. Louis and S. Theisen, Aspects of duality in N = 2 string vacua, Phys. Lett. B 357 (1995) 71 [hep-th/9506110] [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, N = 2 type-II heterotic duality and higher derivative F terms, Nucl. Phys. B 455 (1995) 109 [hep-th/9507115] [INSPIRE].
J.A. Harvey and G.W. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182] [INSPIRE].
S. Alexandrov, J. Manschot, D. Persson and B. Pioline, Quantum hypermultiplet moduli spaces in N = 2 string vacua: a review, Proc. Symp. Pure Math. 90 (2015) 181 [arXiv:1304.0766] [INSPIRE].
S. Alexandrov, J. Louis, B. Pioline and R. Valandro, N = 2 heterotic-type II duality and bundle moduli, JHEP 08 (2014) 092 [arXiv:1405.4792] [INSPIRE].
I. Antoniadis, S. Ferrara, E. Gava, K.S. Narain and T.R. Taylor, Perturbative prepotential and monodromies in N = 2 heterotic superstring, Nucl. Phys. B 447 (1995) 35 [hep-th/9504034] [INSPIRE].
B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [INSPIRE].
N. Seiberg, Observations on the moduli space of superconformal field theories, Nucl. Phys. B 303 (1988) 286 [INSPIRE].
P.S. Aspinwall and D.R. Morrison, String theory on K 3 surfaces, in Mirror symmetry II, B. Greene and S.-T. Yau eds., (1996), pg. 703 [hep-th/9404151] [INSPIRE].
M. Artebani, S. Boissière and A. Sarti, The Berglund-Hübsch-Chiodo-Ruan mirror symmetry for K 3 surfaces, J. Math. Pures Appl. 102 (2014) 758.
P. Comparin, C. Lyons, N. Priddis and R. Suggs, The mirror symmetry of K 3 surfaces with non-symplectic automorphisms of prime order, Adv. Theor. Math. Phys. 18 (2014) 1335 [arXiv:1211.2172] [INSPIRE].
P. Comparin and N. Priddis, BHK mirror symmetry for K 3 surfaces with non-symplectic automorphism, arXiv:1704.00354.
C.J. Bott, P. Comparin and N. Priddis, Mirror symmetry for K 3 surfaces, arXiv:1901.09373 [INSPIRE].
B.R. Greene and M.R. Plesser, Duality in Calabi-Yau moduli space, Nucl. Phys. B 338 (1990) 15 [INSPIRE].
P. Berglund and T. Hubsch, A generalized construction of mirror manifolds, Nucl. Phys. B 393 (1993) 377 [hep-th/9201014] [INSPIRE].
A. Dabholkar and C. Hull, Duality twists, orbifolds, and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].
K.S. Narain, M.H. Sarmadi and C. Vafa, Asymmetric orbifolds, Nucl. Phys. B 288 (1987) 551 [INSPIRE].
B. de Wit and A. Van Proeyen, Potentials and symmetries of general gauged N = 2 supergravity: Yang-Mills models, Nucl. Phys. B 245 (1984) 89 [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Superstring threshold corrections to Yukawa couplings, Nucl. Phys. B 407 (1993) 706 [hep-th/9212045] [INSPIRE].
K. Forger and S. Stieberger, String amplitudes and N = 2, d = 4 prepotential in heterotic K 3 × T 2 compactifications, Nucl. Phys. B 514 (1998) 135 [hep-th/9709004] [INSPIRE].
C. Angelantonj, I. Florakis and B. Pioline, A new look at one-loop integrals in string theory, Commun. Num. Theor. Phys. 6 (2012) 159 [arXiv:1110.5318] [INSPIRE].
C. Angelantonj, I. Florakis and B. Pioline, One-loop BPS amplitudes as BPS-state sums, JHEP 06 (2012) 070 [arXiv:1203.0566] [INSPIRE].
C. Angelantonj, I. Florakis and B. Pioline, Rankin-Selberg methods for closed strings on orbifolds, JHEP 07 (2013) 181 [arXiv:1304.4271] [INSPIRE].
C. Angelantonj, I. Florakis and B. Pioline, Threshold corrections, generalised prepotentials and Eichler integrals, Nucl. Phys. B 897 (2015) 781 [arXiv:1502.00007] [INSPIRE].
L.J. Dixon, V. Kaplunovsky and J. Louis, Moduli dependence of string loop corrections to gauge coupling constants, Nucl. Phys. B 355 (1991) 649 [INSPIRE].
S. Cecotti, P. Fendley, K.A. Intriligator and C. Vafa, A new supersymmetric index, Nucl. Phys. B 386 (1992) 405 [hep-th/9204102] [INSPIRE].
E. Kiritsis and C. Kounnas, Infrared regularization of superstring theory and the one loop calculation of coupling constants, Nucl. Phys. B 442 (1995) 472 [hep-th/9501020] [INSPIRE].
V. Kaplunovsky and J. Louis, On gauge couplings in string theory, Nucl. Phys. B 444 (1995) 191 [hep-th/9502077] [INSPIRE].
D. Persson and R. Volpato, Fricke S-duality in CHL models, JHEP 12 (2015) 156 [arXiv:1504.07260] [INSPIRE].
E. Kiritsis, C. Kounnas, P.M. Petropoulos and J. Rizos, Solving the decompactification problem in string theory, Phys. Lett. B 385 (1996) 87 [hep-th/9606087] [INSPIRE].
P.S. Aspinwall and M. Plesser, T duality can fail, JHEP 08 (1999) 001 [hep-th/9905036] [INSPIRE].
F. Diamond and J. Shurman, A first course in modular forms, Springer, New York, NY, U.S.A. (2006).
J. Bagger and E. Witten, Matter couplings in N = 2 supergravity, Nucl. Phys. B 222 (1983) 1 [INSPIRE].
S. Cecotti, S. Ferrara and L. Girardello, Geometry of type II superstrings and the moduli of superconformal field theories, Int. J. Mod. Phys. A 4 (1989) 2475 [INSPIRE].
I.V. Dolgachev and S. Kondō, Moduli of K 3 surfaces and complex ball quotients, in Arithmetic and geometry around hypergeometric functions, Birkh¨auser, Basel, Switzerland (2007), pg. 43.
S. Ferrara and M. Porrati, The manifolds of scalar background fields in Z (N ) orbifolds, Phys. Lett. B 216 (1989) 289 [INSPIRE].
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Gautier, Y., Israël, D. Moduli spaces of non-geometric type II/heterotic dual pairs. J. High Energ. Phys. 2020, 82 (2020). https://doi.org/10.1007/JHEP09(2020)082
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DOI: https://doi.org/10.1007/JHEP09(2020)082