Flat equivariant gerbes: holonomies and dualities. (English) Zbl 07693962
Summary: We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise.
MSC:
| 81T45 | Topological field theories in quantum mechanics |
| 81T33 | Dimensional compactification in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
References:
| [1] | P. Deligne et al., Quantum fields and strings: A course for mathematicians. Vol. 1, 2, American Mathematical Society (1999) [ISBN: 9780821820124] [INSPIRE]. |
| [2] | L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B261 (1985) 678 [INSPIRE]. |
| [3] | L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds. II, Nucl. Phys. B274 (1986) 285 [INSPIRE]. |
| [4] | A. Adem, J. Leida and Y. Ruan, Orbifolds and Stringy Topology, Cambridge University Press (2007) [doi:10.1017/CBO9780511543081]. · Zbl 1157.57001 |
| [5] | Fischer, M.; Ratz, M.; Torrado, J.; Vaudrevange, PKS, Classification of symmetric toroidal orbifolds, JHEP, 01, 084 (2013) · Zbl 1342.81360 · doi:10.1007/JHEP01(2013)084 |
| [6] | Fraiman, B.; Graña, M.; Núñez, CA, A new twist on heterotic string compactifications, JHEP, 09, 078 (2018) · Zbl 1398.83105 · doi:10.1007/JHEP09(2018)078 |
| [7] | Font, A., Exploring the landscape of heterotic strings on T^d, JHEP, 10, 194 (2020) · doi:10.1007/JHEP10(2020)194 |
| [8] | Font, A., Exploring the landscape of CHL strings on T^d, JHEP, 08, 095 (2021) · Zbl 1469.83039 · doi:10.1007/JHEP08(2021)095 |
| [9] | M. Cvetic, M. Dierigl, L. Lin and H.Y. Zhang, Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua, Phys. Rev. D104 (2021) 086018 [arXiv:2107.04031] [INSPIRE]. |
| [10] | Fraiman, B.; De Freitas, HP, Symmetry enhancements in 7d heterotic strings, JHEP, 10, 002 (2021) · Zbl 1476.83156 · doi:10.1007/JHEP10(2021)002 |
| [11] | Fraiman, B.; de Freitas, HP, Freezing of gauge symmetries in the heterotic string on T^4, JHEP, 04, 007 (2022) · Zbl 1522.81353 · doi:10.1007/JHEP04(2022)007 |
| [12] | Chaudhuri, S.; Hockney, G.; Lykken, JD, Maximally supersymmetric string theories in D < 10, Phys. Rev. Lett., 75, 2264 (1995) · Zbl 1020.81763 · doi:10.1103/PhysRevLett.75.2264 |
| [13] | Chaudhuri, S.; Polchinski, J., Moduli space of CHL strings, Phys. Rev. D, 52, 7168 (1995) · doi:10.1103/PhysRevD.52.7168 |
| [14] | Lerche, W.; Schweigert, C.; Minasian, R.; Theisen, S., A Note on the geometry of CHL heterotic strings, Phys. Lett. B, 424, 53 (1998) · doi:10.1016/S0370-2693(98)00156-7 |
| [15] | de Boer, J., Triples, fluxes, and strings, Adv. Theor. Math. Phys., 4, 995 (2002) · Zbl 1011.81065 · doi:10.4310/ATMP.2000.v4.n5.a1 |
| [16] | Kachru, S.; Klemm, A.; Oz, Y., Calabi-Yau duals for CHL strings, Nucl. Phys. B, 521, 58 (1998) · Zbl 1047.81548 · doi:10.1016/S0550-3213(98)00228-4 |
| [17] | Tachikawa, Y., Frozen singularities in M and F theory, JHEP, 06, 128 (2016) · Zbl 1388.81608 · doi:10.1007/JHEP06(2016)128 |
| [18] | B.S. Acharya et al., Heterotic strings on 𝕋^3/ℤ_2, Nikulin involutions and M-theory, JHEP09 (2022) 209 [arXiv:2205.09764] [INSPIRE]. · Zbl 1531.81169 |
| [19] | Hull, C.; Israël, D.; Sarti, A., Non-geometric Calabi-Yau Backgrounds and K3 automorphisms, JHEP, 11, 084 (2017) · Zbl 1383.83213 · doi:10.1007/JHEP11(2017)084 |
| [20] | Gautier, Y.; Hull, CM; Israël, D., Heterotic/type II Duality and Non-Geometric Compactifications, JHEP, 10, 214 (2019) · Zbl 1427.83101 · doi:10.1007/JHEP10(2019)214 |
| [21] | Kachru, S.; Vafa, C., Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B, 450, 69 (1995) · Zbl 0957.14509 · doi:10.1016/0550-3213(95)00307-E |
| [22] | Bouwknegt, P.; Evslin, J.; Mathai, V., T duality: Topology change from H flux, Commun. Math. Phys., 249, 383 (2004) · Zbl 1062.81119 · doi:10.1007/s00220-004-1115-6 |
| [23] | Evslin, J.; Minasian, R., Topology Change from (Heterotic) Narain T-Duality, Nucl. Phys. B, 820, 213 (2009) · Zbl 1194.81196 · doi:10.1016/j.nuclphysb.2009.05.021 |
| [24] | Sharpe, E., Discrete torsion and shift orbifolds, Nucl. Phys. B, 664, 21 (2003) · Zbl 1028.83521 · doi:10.1016/S0550-3213(03)00412-7 |
| [25] | Vafa, C., Modular Invariance and Discrete Torsion on Orbifolds, Nucl. Phys. B, 273, 592 (1986) · Zbl 0992.81515 · doi:10.1016/0550-3213(86)90379-2 |
| [26] | E.R. Sharpe, Discrete torsion, Phys. Rev. D68 (2003) 126003 [hep-th/0008154] [INSPIRE]. · Zbl 1028.83521 |
| [27] | Fischer, M.; Ramos-Sanchez, S.; Vaudrevange, PKS, Heterotic non-Abelian orbifolds, JHEP, 07, 080 (2013) · Zbl 1342.81423 · doi:10.1007/JHEP07(2013)080 |
| [28] | L. Charlap, Bieberbach groups and flat manifolds, first edition, Springer-Verlag, New York (1986) [doi:10.1007/978-1-4613-8687-2]. · Zbl 0608.53001 |
| [29] | Auslander, L.; Kuranishi, M., On the holonomy group of locally euclidean spaces, Annals Math., 65, 411 (1957) · Zbl 0079.38304 · doi:10.2307/1970053 |
| [30] | Opgenorth, J.; Plesken, W.; Schulz, T., Crystallographic Algorithms and Tables, Acta Cryst., 54, 517 (1998) · Zbl 1176.20051 · doi:10.1107/S010876739701547X |
| [31] | Lutowski, R.; Putrycz, B., Spin structures on flat manifolds, J. Algebra, 436, 277 (2015) · Zbl 1336.57035 · doi:10.1016/j.jalgebra.2015.03.037 |
| [32] | Dekimpe, K.; Hałenda, M.; Szczepański, A., Kähler flat manifolds, J. Math. Soc. Jap., 61, 363 (2009) · Zbl 1187.53051 · doi:10.2969/jmsj/06120363 |
| [33] | Aldazabal, G., Nonperturbative heterotic D = 6, D = 4, N = 1 orbifold vacua, Nucl. Phys. B, 519, 239 (1998) · Zbl 0945.81050 · doi:10.1016/S0550-3213(98)00007-8 |
| [34] | Stieberger, S., (0, 2) heterotic gauge couplings and their M theory origin, Nucl. Phys. B, 541, 109 (1999) · Zbl 0947.81072 · doi:10.1016/S0550-3213(98)00770-6 |
| [35] | Honecker, G.; Trapletti, M., Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles, JHEP, 01, 051 (2007) · doi:10.1088/1126-6708/2007/01/051 |
| [36] | Aspinwall, PS, Enhanced gauge symmetries and K3 surfaces, Phys. Lett. B, 357, 329 (1995) · doi:10.1016/0370-2693(95)00957-M |
| [37] | P.S. Aspinwall, K3 surfaces and string duality, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, Boulder U.S.A., June 2-28 (1996), p. 421-540 [hep-th/9611137] [INSPIRE]. |
| [38] | T. Banks and L.J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry, Nucl. Phys. B307 (1988) 93 [INSPIRE]. |
| [39] | J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press (2007) [doi:10.1017/CBO9780511618123] [INSPIRE]. · Zbl 1246.81199 |
| [40] | I.V. Melnikov, An Introduction to Two-Dimensional Quantum Field Theory with (0, 2) Supersymmetry, Springer (2019) [doi:10.1007/978-3-030-05085-6] [INSPIRE]. · Zbl 1417.81006 |
| [41] | E. Lauria and A. Van Proeyen, \( \mathcal{N} = 2\) Supergravity in D = 4, 5, 6 Dimensions, Springer Cham (2020) [doi:10.1007/978-3-030-33757-5] [INSPIRE]. · Zbl 1432.81003 |
| [42] | M.A. Walton, The Heterotic String on the Simplest Calabi-yau Manifold and Its Orbifold Limits, Phys. Rev. D37 (1988) 377 [INSPIRE]. |
| [43] | Kaplunovsky, V.; Sonnenschein, J.; Theisen, S.; Yankielowicz, S., On the duality between perturbative heterotic orbifolds and M theory on T^4/Z_N, Nucl. Phys. B, 590, 123 (2000) · Zbl 0991.81091 · doi:10.1016/S0550-3213(00)00460-0 |
| [44] | P.H. Ginsparg, Applied conformal field theory, in the proceedings of the Les Houches Summer School in Theoretical Physics: Fields, Strings, Critical Phenomena, Les Houches France, June 28-August 5 (1988) [hep-th/9108028] [INSPIRE]. |
| [45] | D. Robbins and T. Vandermeulen, Orbifolds from Modular Orbits, Phys. Rev. D101 (2020) 106021 [arXiv:1911.05172] [INSPIRE]. |
| [46] | Melnikov, IV; Minasian, R.; Sethi, S., Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications, Fortsch. Phys., 66, 1800027 (2018) · Zbl 1535.83130 · doi:10.1002/prop.201800027 |
| [47] | K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett. B169 (1986) 41 [INSPIRE]. |
| [48] | Narain, KS; Sarmadi, MH; Witten, E., A Note on Toroidal Compactification of Heterotic String Theory, Nucl. Phys. B, 279, 369 (1987) · doi:10.1016/0550-3213(87)90001-0 |
| [49] | P.H. Ginsparg, Comment on Toroidal Compactification of Heterotic Superstrings, Phys. Rev. D35 (1987) 648 [INSPIRE]. |
| [50] | Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Phys. Rept., 244, 77 (1994) · doi:10.1016/0370-1573(94)90070-1 |
| [51] | M. Green, J. Schwarz and E. Witten, Superstring Theory, Volume 1, Cambridge University Press (1987) [ISBN: 9780521357524] [INSPIRE]. · Zbl 0619.53002 |
| [52] | J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge University Press (2007) [INSPIRE]. · Zbl 1246.81199 |
| [53] | Tan, HS, T-duality Twists and Asymmetric Orbifolds, JHEP, 11, 141 (2015) · Zbl 1388.81190 · doi:10.1007/JHEP11(2015)141 |
| [54] | S. Kobayashi, Differential Geometry of Complex Vector Bundles, Princeton University Press, (1987) [doi:10.1515/9781400858682]. · Zbl 0708.53002 |
| [55] | Bunge, M., The inexhaustible electron, Science and Society, 14, 115 (1950) |
| [56] | E. Witten, Some comments on string dynamics, in the proceedings of the STRINGS 95: Future Perspectives in String Theory, Los Angeles U.S.A., March 13-18 (1995), p. 501-523 [hep-th/9507121] [INSPIRE]. |
| [57] | P.S. Aspinwall and D.R. Morrison, String theory on K3 surfaces, in Mirror symmetry II AMS/IP Studies in Advanced Mathematics 1, American Mathematical Society (1996), pp. 703-716 [doi:10.1090/amsip/001/27] [hep-th/9404151] [INSPIRE]. · Zbl 0931.14020 |
| [58] | Fino, A.; Grantcharov, G.; Vezzoni, L., Solutions to the Hull-Strominger System with Torus Symmetry, Commun. Math. Phys., 388, 947 (2021) · Zbl 1485.53042 · doi:10.1007/s00220-021-04223-7 |
| [59] | Dasgupta, K.; Rajesh, G.; Sethi, S., M theory, orientifolds and G-flux, JHEP, 08, 023 (1999) · Zbl 1060.81575 · doi:10.1088/1126-6708/1999/08/023 |
| [60] | Fu, J-X; Yau, S-T, The Theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampere equation, J. Diff. Geom., 78, 369 (2008) · Zbl 1141.53036 |
| [61] | Becker, K., Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys. B, 751, 108 (2006) · Zbl 1192.81312 · doi:10.1016/j.nuclphysb.2006.05.034 |
| [62] | Melnikov, IV; Minasian, R.; Theisen, S., Heterotic flux backgrounds and their IIA duals, JHEP, 07, 023 (2014) · doi:10.1007/JHEP07(2014)023 |
| [63] | Ploger, F.; Ramos-Sanchez, S.; Ratz, M.; Vaudrevange, PKS, Mirage Torsion, JHEP, 04, 063 (2007) · doi:10.1088/1126-6708/2007/04/063 |
| [64] | D. Chatterjee, On gerbs, Ph.D. Thesis, University of Cambridge, U.K. (1998). |
| [65] | Yang, H., Equivariant cohomology and sheaves, J. Algebra, 412, 230 (2014) · Zbl 1298.55004 · doi:10.1016/j.jalgebra.2014.05.009 |
| [66] | C. Voisin, Hodge theory and complex algebraic geometry. I, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, U.K. (2007) [doi:10.1017/cbo9780511615344]. · Zbl 1129.14019 |
| [67] | C. Voisin, Hodge theory and complex algebraic geometry. II, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, U.K. (2007) [doi:10.1017/cbo9780511615177]. · Zbl 1129.14020 |
| [68] | Lectures on special lagrangian submanifolds, in Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds, Cambridge U.S.A., January 4-15 (1999) [American Mathematical Society (2001), pp. 151-182] [doi:10.1090/amsip/023/06] [math/9907034] [INSPIRE]. · Zbl 1079.14522 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
