Abstract
Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.
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K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
M.B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061] [INSPIRE].
M.B. Green and P. Vanhove, D instantons, strings and M-theory, Phys. Lett. B 408 (1997) 122 [hep-th/9704145] [INSPIRE].
E. Kiritsis and B. Pioline, On R4 threshold corrections in IIB string theory and (p, q) string instantons, Nucl. Phys. B 508 (1997) 509 [hep-th/9707018] [INSPIRE].
B. Pioline and E. Kiritsis, U duality and D-brane combinatorics, Phys. Lett. B 418 (1998) 61 [hep-th/9710078] [INSPIRE].
M.B. Green, H.-h. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].
A. Basu, The D4 R4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106003 [arXiv:0708.2950] [INSPIRE].
A. Basu, The D6 R4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106004 [arXiv:0712.1252] [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81 (2010) 086008 [arXiv:1001.2535] [INSPIRE].
M.B. Green, S.D. Miller and P. Vanhove, SL(2, ℤ)-invariance and D-instanton contributions to the D6 R4 interaction, Commun. Num. Theor. Phys. 09 (2015) 307 [arXiv:1404.2192] [INSPIRE].
B. Pioline, D6 ℛ4 amplitudes in various dimensions, JHEP 04 (2015) 057 [arXiv:1502.03377] [INSPIRE].
G. Bossard, A. Kleinschmidt and B. Pioline, 1/8-BPS Couplings and Exceptional Automorphic Functions, SciPost Phys. 8 (2020) 054 [arXiv:2001.05562] [INSPIRE].
S. Alexandrov, Twistor Approach to String Compactifications: a Review, Phys. Rept. 522 (2013) 1 [arXiv:1111.2892] [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].
B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 Supergravity-Matter Systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
J. Bagger and E. Witten, Matter Couplings in N = 2 Supergravity, Nucl. Phys. B 222 (1983) 1 [INSPIRE].
D. Robles-Llana, F. Saueressig, U. Theis and S. Vandoren, Membrane instantons from mirror symmetry, Commun. Num. Theor. Phys. 1 (2007) 681 [arXiv:0707.0838] [INSPIRE].
S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, D-instantons and twistors, JHEP 03 (2009) 044 [arXiv:0812.4219] [INSPIRE].
S. Alexandrov, D-instantons and twistors: Some exact results, J. Phys. A 42 (2009) 335402 [arXiv:0902.2761] [INSPIRE].
D. Robles-Llana, M. Roček, F. Saueressig, U. Theis and S. Vandoren, Nonperturbative corrections to 4D string theory effective actions from SL(2, ℤ) duality and supersymmetry, Phys. Rev. Lett. 98 (2007) 211602 [hep-th/0612027] [INSPIRE].
B. Pioline and S. Vandoren, Large D-instanton effects in string theory, JHEP 07 (2009) 008 [arXiv:0904.2303] [INSPIRE].
S. Alexandrov and S. Banerjee, Fivebrane instantons in Calabi-Yau compactifications, Phys. Rev. D 90 (2014) 041902 [arXiv:1403.1265] [INSPIRE].
S. Alexandrov and S. Banerjee, Dualities and fivebrane instantons, JHEP 11 (2014) 040 [arXiv:1405.0291] [INSPIRE].
S. Alexandrov, D. Persson and B. Pioline, Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces, JHEP 03 (2011) 111 [arXiv:1010.5792] [INSPIRE].
S. Alexandrov and S. Banerjee, Hypermultiplet metric and D-instantons, JHEP 02 (2015) 176 [arXiv:1412.8182] [INSPIRE].
S. Alexandrov, S. Banerjee and P. Longhi, Rigid limit for hypermultiplets and five-dimensional gauge theories, JHEP 01 (2018) 156 [arXiv:1710.10665] [INSPIRE].
E. Witten, Nonperturbative superpotentials in string theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
M. Demirtas, M. Kim, L. McAllister, J. Moritz and A. Rios-Tascon, A Cosmological Constant That is Too Small, arXiv:2107.09065 [INSPIRE].
M. Demirtas, M. Kim, L. McAllister, J. Moritz and A. Rios-Tascon, Small Cosmological Constants in String Theory, arXiv:2107.09064 [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, ZZ Instantons and the Non-Perturbative Dual of c = 1 String Theory, arXiv:1907.07688 [INSPIRE].
A. Sen, Fixing an Ambiguity in Two Dimensional String Theory Using String Field Theory, JHEP 03 (2020) 005 [arXiv:1908.02782] [INSPIRE].
B. Balthazar, V.A. Rodriguez and X. Yin, Multi-Instanton Calculus in c = 1 String Theory, arXiv:1912.07170 [INSPIRE].
A. Sen, Normalization of D-instanton Amplitudes, arXiv:2101.08566 [INSPIRE].
A. Sen, Normalization of Type IIB D-instanton Amplitudes, arXiv:2104.11109 [INSPIRE].
A. Sen, Muti-instanton Amplitudes in Type IIB String Theory, arXiv:2104.15110 [INSPIRE].
Y. Wang and X. Yin, Constraining Higher Derivative Supergravity with Scattering Amplitudes, Phys. Rev. D 92 (2015) 041701 [arXiv:1502.03810] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop Calculations in Covariant Superstring Theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [INSPIRE].
H. Suzuki, Calabi-Yau compactification of type IIB string and a mass formula of the extreme black holes, Mod. Phys. Lett. A 11 (1996) 623 [hep-th/9508001] [INSPIRE].
T.W. Grimm and J. Louis, The Effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B 718 (2005) 153 [hep-th/0412277] [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].
S. Ferrara and S. Sabharwal, Quaternionic Manifolds for Type II Superstring Vacua of Calabi-Yau Spaces, Nucl. Phys. B 332 (1990) 317 [INSPIRE].
C. LeBrun, Fano manifolds, contact structures, and quaternionic geometry, Int. J. Math. 6 (1995) 419 [dg-ga/9409001].
S. Alexandrov, B. Pioline, F. Saueressig and S. Vandoren, Linear perturbations of quaternionic metrics, Commun. Math. Phys. 296 (2010) 353 [arXiv:0810.1675] [INSPIRE].
V. Cortés and I. Tulli, Quaternionic Kähler metrics associated to special Kähler manifolds with mutually local variations of BPS structures, arXiv:2105.09011 [INSPIRE].
J. Polchinski, String theory. Vol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007).
J. Polchinski, String theory. Vol. 2: Superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007).
A. Sen, Universality of the tachyon potential, JHEP 12 (1999) 027 [hep-th/9911116] [INSPIRE].
R. Blumenhagen, M. Cvetič, S. Kachru and T. Weigand, D-Brane Instantons in Type II Orientifolds, Ann. Rev. Nucl. Part. Sci. 59 (2009) 269 [arXiv:0902.3251] [INSPIRE].
W. Krauth, H. Nicolai and M. Staudacher, Monte Carlo approach to M-theory, Phys. Lett. B 431 (1998) 31 [hep-th/9803117] [INSPIRE].
G.W. Moore, N. Nekrasov and S. Shatashvili, D particle bound states and generalized instantons, Commun. Math. Phys. 209 (2000) 77 [hep-th/9803265] [INSPIRE].
M.S. Marinov, Invariant volumes of compact groups, J. Phys. A 13 (1980) 3357 [INSPIRE].
M.S. Marinov, Correction to ‘Invariant Volumes of Compact Groups’, J. Phys. A 14 (1981) 543.
R. McLean, Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998) 705.
L. Álvarez-Gaumé, Supersymmetry and the Atiyah-Singer Index Theorem, Commun. Math. Phys. 90 (1983) 161 [INSPIRE].
M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].
S.M. Chester, M.B. Green, S.S. Pufu, Y. Wang and C. Wen, New modular invariants in \( \mathcal{N} \) = 4 Super-Yang-Mills theory, JHEP 04 (2021) 212 [arXiv:2008.02713] [INSPIRE].
C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed Superstring Field Theory and its Applications, Int. J. Mod. Phys. A 32 (2017) 1730021 [arXiv:1703.06410] [INSPIRE].
M. Bodner, A.C. Cadavid and S. Ferrara, (2, 2) vacuum configurations for type IIA superstrings: N = 2 supergravity Lagrangians and algebraic geometry, Class. Quant. Grav. 8 (1991) 789 [INSPIRE].
P.K. Townsend, P-brane democracy, in PASCOS/HOPKINS 1995 (Joint Meeting of the International Symposium on Particles, Strings and Cosmology and the 19th Johns Hopkins Workshop on Current Problems in Particle Theory), pp. 375–389 (1995) [hep-th/9507048] [INSPIRE].
S. Faroogh Moosavian, A. Sen and M. Verma, Superstring Field Theory with Open and Closed Strings, JHEP 01 (2020) 183 [arXiv:1907.10632] [INSPIRE].
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Alexandrov, S., Sen, A. & Stefański, B. D-instantons in Type IIA string theory on Calabi-Yau threefolds. J. High Energ. Phys. 2021, 18 (2021). https://doi.org/10.1007/JHEP11(2021)018
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DOI: https://doi.org/10.1007/JHEP11(2021)018