Abstract
We examine SL(2, ℤ) anomalies in ten and eight-dimensional supergravities, the induced local counterterms and their realization in string theory. Composite connections play an important rôle in the cancellation mechanism. At the same time their global properties lead to novel non-trivial consistency constraints on compactifications.
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References
N. Marcus, Composite Anomalies in Supergravity, Phys. Lett. B 157 (1985) 383 [INSPIRE].
M.R. Gaberdiel and M.B. Green, An SL(2, Z) anomaly in IIB supergravity and its F-theory interpretation, JHEP 11 (1998) 026 [hep-th/9810153] [INSPIRE].
S. Sasmal, One loop amplitude for Heterotic string on T 2, arXiv:1611.09808 [INSPIRE].
T. Pantev and E. Sharpe, Duality group actions on fermions, JHEP 11 (2016) 171 [arXiv:1609.00011] [INSPIRE].
R. Minasian, T.G. Pugh and R. Savelli, F-theory at order α ′3, JHEP 10 (2015) 050 [arXiv:1506.06756] [INSPIRE].
A. Salam and E. Sezgin, D = 8 Supergravity, Nucl. Phys. B 258 (1985) 284 [INSPIRE].
B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy Cosmic Strings and Noncompact Calabi-Yau Manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].
T.W. Grimm, R. Savelli and M. Weissenbacher, On α ′ corrections in N = 1 F-theory compactifications, Phys. Lett. B 725 (2013) 431 [arXiv:1303.3317] [INSPIRE].
T.W. Grimm, J. Keitel, R. Savelli and M. Weissenbacher, From M-theory higher curvature terms to α ′ corrections in F-theory, Nucl. Phys. B 903 (2016) 325 [arXiv:1312.1376] [INSPIRE].
C.P. Bachas, P. Bain and M.B. Green, Curvature terms in D-brane actions and their M-theory origin, JHEP 05 (1999) 011 [hep-th/9903210] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
M. Esole and R. Savelli, Tate Form and Weak Coupling Limits in F-theory, JHEP 06 (2013) 027 [arXiv:1209.1633] [INSPIRE].
M.B. Green, J.A. Harvey and G.W. Moore, I-brane inflow and anomalous couplings on D-branes, Class. Quant. Grav. 14 (1997) 47 [hep-th/9605033] [INSPIRE].
Y.-K.E. Cheung and Z. Yin, Anomalies, branes and currents, Nucl. Phys. B 517 (1998) 69 [hep-th/9710206] [INSPIRE].
R. Minasian and G.W. Moore, K theory and Ramond-Ramond charge, JHEP 11 (1997) 002 [hep-th/9710230] [INSPIRE].
J.F. Morales, C.A. Scrucca and M. Serone, Anomalous couplings for D-branes and O-planes, Nucl. Phys. B 552 (1999) 291 [hep-th/9812071] [INSPIRE].
B. Stefanski Jr., Gravitational couplings of D-branes and O-planes, Nucl. Phys. B 548 (1999) 275 [hep-th/9812088] [INSPIRE].
A. Basu, Supersymmetry constraints on the R 4 multiplet in type IIB on T 2, Class. Quant. Grav. 28 (2011) 225018 [arXiv:1107.3353] [INSPIRE].
G. Bossard and V. Verschinin, Minimal unitary representations from supersymmetry, JHEP 10 (2014) 008 [arXiv:1406.5527] [INSPIRE].
E. Kiritsis and B. Pioline, On R 4 threshold corrections in IIB string theory and (p, q) string instantons, Nucl. Phys. B 508 (1997) 509 [hep-th/9707018] [INSPIRE].
C. Vafa and E. Witten, A One loop test of string duality, Nucl. Phys. B 447 (1995) 261 [hep-th/9505053] [INSPIRE].
M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: A One loop test, Nucl. Phys. B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
A. Salam and E. Sezgin, d = 8 Supergravity: Matter Couplings, Gauging and Minkowski Compactification, Phys. Lett. B 154 (1985) 37 [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].
I. Garcia-Etxebarria, H. Hayashi, R. Savelli and G. Shiu, On quantum corrected Kähler potentials in F-theory, JHEP 03 (2013) 005 [arXiv:1212.4831] [INSPIRE].
M.B. Green and J.H. Schwarz, Anomaly Cancellation in Supersymmetric D = 10 Gauge Theory and Superstring Theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
E. Kiritsis and N.A. Obers, Heterotic type-I duality in D < 10-dimensions, threshold corrections and D instantons, JHEP 10 (1997) 004 [hep-th/9709058] [INSPIRE].
J.A. Harvey and G.W. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182] [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].
M. Gutperle, A Note on heterotic/type-I-prime duality and D0-brane quantum mechanics, JHEP 05 (1999) 007 [hep-th/9903010] [INSPIRE].
M. Gutperle, Heterotic/type-I duality, D instantons and a N = 2 AdS/CFT correspondence, Phys. Rev. D 60 (1999) 126001 [hep-th/9905173] [INSPIRE].
E. Kiritsis, N.A. Obers and B. Pioline, Heterotic/type-II triality and instantons on K(3), JHEP 01 (2000) 029 [hep-th/0001083] [INSPIRE].
W. Lerche and S. Stieberger, Prepotential, mirror map and F-theory on K3, Adv. Theor. Math. Phys. 2 (1998) 1105 [Erratum ibid. 3 (1999) 1199] [hep-th/9804176] [INSPIRE].
W. Lerche, On the heterotic/F theory duality in eight-dimensions, hep-th/9910207 [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
J.T. Liu and R. Minasian, U-branes and T 3 fibrations, Nucl. Phys. B 510 (1998) 538 [hep-th/9707125] [INSPIRE].
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
M.R. Douglas, D.S. Park and C. Schnell, The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds, JHEP 05 (2014) 135 [arXiv:1403.1595] [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].
A. Malmendier and D.R. Morrison, K3 surfaces, modular forms and non-geometric heterotic compactifications, Lett. Math. Phys. 105 (2015) 1085 [arXiv:1406.4873] [INSPIRE].
J. Gu and H. Jockers, Nongeometric F-theory-heterotic duality, Phys. Rev. D 91 (2015) 086007 [arXiv:1412.5739] [INSPIRE].
D. Lüst, S. Massai and V. Vall Camell, The monodromy of T-folds and T-fects, JHEP 09 (2016) 127 [arXiv:1508.01193] [INSPIRE].
M.J. Duff, R. Minasian and E. Witten, Evidence for heterotic/heterotic duality, Nucl. Phys. B 465 (1996) 413 [hep-th/9601036] [INSPIRE].
A. Sagnotti, A Note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
P.S. Aspinwall and M. Gross, The SO(32) heterotic string on a K3 surface, Phys. Lett. B 387 (1996) 735 [hep-th/9605131] [INSPIRE].
M.J. Duff and R. Minasian, Putting string/string duality to the test, Nucl. Phys. B 436 (1995) 507 [hep-th/9406198] [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
L. Álvarez-Gaumé and P.H. Ginsparg, The Structure of Gauge and Gravitational Anomalies, Annals Phys. 161 (1985) 423 [Erratum ibid. 171 (1986) 233] [INSPIRE].
P. van Nieuwenhuizen, Leuven notes in mathematical and theoretical physics. Vol. B 3: Anomalies in quantum field theory: Cancellation of anomalies in d = 10 supergravity, Leuven University Press, Leuven Belgium (1989).
J. Erler, Anomaly cancellation in six-dimensions, J. Math. Phys. 35 (1994) 1819 [hep-th/9304104] [INSPIRE].
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Minasian, R., Sasmal, S. & Savelli, R. Discrete anomalies in supergravity and consistency of string backgrounds. J. High Energ. Phys. 2017, 25 (2017). https://doi.org/10.1007/JHEP02(2017)025
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DOI: https://doi.org/10.1007/JHEP02(2017)025