Abstract
The metric on the hypermultiplet moduli space of Calabi-Yau compactifications of type II string theory is known to receive D-brane and NS5-brane instanton corrections. We compute explicit expressions for these corrections in the one-instanton approximation, but to all orders in the string coupling expansion around the instantons. As a consistency check, we prove that in the case of one (universal) hypermultiplet, the resulting metric fits the Przanowski description of self-dual Einstein spaces. We also show that in the small string coupling limit the metric acquires a certain square structure, consistently with expectations from the string amplitudes analysis. This result provides explicit predictions for yet mysterious string amplitudes in the presence of NS5-branes.
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References
A. Sen, D-instanton Perturbation Theory, JHEP 08 (2020) 075 [arXiv:2002.04043] [INSPIRE].
A. Sen, D-instantons, string field theory and two dimensional string theory, JHEP 11 (2021) 061 [arXiv:2012.11624] [INSPIRE].
A. Sen, Normalization of D-instanton amplitudes, JHEP 11 (2021) 077 [arXiv:2101.08566] [INSPIRE].
A. Sen, Normalization of type IIB D-instanton amplitudes, JHEP 12 (2021) 146 [arXiv:2104.11109] [INSPIRE].
A. Sen, Muti-instanton amplitudes in type IIB string theory, JHEP 12 (2021) 065 [arXiv:2104.15110] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, D-instantons in Type IIA string theory on Calabi-Yau threefolds, JHEP 11 (2021) 018 [arXiv:2108.04265] [INSPIRE].
S. Alexandrov, A. Sen and B. Stefański, Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds, JHEP 12 (2021) 044 [arXiv:2110.06949] [INSPIRE].
D.S. Eniceicu, R. Mahajan, C. Murdia and A. Sen, Normalization of ZZ instanton amplitudes in minimal string theory, JHEP 07 (2022) 139 [arXiv:2202.03448] [INSPIRE].
D.S. Eniceicu, R. Mahajan, C. Murdia and A. Sen, Multi-instantons in minimal string theory and in matrix integrals, JHEP 10 (2022) 065 [arXiv:2206.13531] [INSPIRE].
D.S. Eniceicu et al., The ZZ annulus one-point function in non-critical string theory: A string field theory analysis, JHEP 12 (2022) 151 [arXiv:2210.11473] [INSPIRE].
S. Alexandrov et al., D-instanton induced superpotential, JHEP 07 (2022) 090 [arXiv:2204.02981] [INSPIRE].
K. Becker, M. Becker and A. Strominger, Five-branes, membranes and nonperturbative string theory, Nucl. Phys. B 456 (1995) 130 [hep-th/9507158] [INSPIRE].
D. Robles-Llana et al., 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].
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].
R. Bohm, H. Gunther, C. Herrmann and J. Louis, Compactification of type IIB string theory on Calabi-Yau threefolds, Nucl. Phys. B 569 (2000) 229 [hep-th/9908007] [INSPIRE].
S. Alexandrov and F. Saueressig, Quantum mirror symmetry and twistors, JHEP 09 (2009) 108 [arXiv:0906.3743] [INSPIRE].
S. Alexandrov and B. Pioline, S-duality in Twistor Space, JHEP 08 (2012) 112 [arXiv:1206.1341] [INSPIRE].
S. Alexandrov, J. Manschot and B. Pioline, D3-instantons, Mock Theta Series and Twistors, JHEP 04 (2013) 002 [arXiv:1207.1109] [INSPIRE].
S. Alexandrov, S. Banerjee, J. Manschot and B. Pioline, Multiple D3-instantons and mock modular forms II, Commun. Math. Phys. 359 (2018) 297 [arXiv:1702.05497] [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].
V. Cortés and I. Tulli, Quaternionic Kähler Metrics Associated to Special Kähler Manifolds with Mutually Local Variations of BPS Structures, Annales Henri Poincare 23 (2022) 2025 [arXiv:2105.09011] [INSPIRE].
V. Cortés and I. Tulli, S-duality and the universal isometries of instanton corrected q-map spaces, arXiv:2306.01463 [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, 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].
J. Bagger and E. Witten, Matter Couplings in N = 2 Supergravity, Nucl. Phys. B 222 (1983) 1 [INSPIRE].
S. Alexandrov, Twistor Approach to String Compactifications: a Review, Phys. Rept. 522 (2013) 1 [arXiv:1111.2892] [INSPIRE].
C. LeBrun, Fano Manifolds, Contact Structures, and Quaternionic Geometry, 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].
M. Przanowski, Locally Hermite Einstein, selfdual gravitational instantons, Acta Phys. Polon. B 14 (1983) 625 [INSPIRE].
S. Alexandrov, Quantum covariant c-map, JHEP 05 (2007) 094 [hep-th/0702203] [INSPIRE].
I. Antoniadis, S. Ferrara, R. Minasian and K.S. Narain, R**4 couplings in M and type II theories on Calabi-Yau spaces, Nucl. Phys. B 507 (1997) 571 [hep-th/9707013] [INSPIRE].
H. Gunther, C. Herrmann and J. Louis, Quantum corrections in the hypermultiplet moduli space, Fortsch. Phys. 48 (2000) 119 [hep-th/9901137] [INSPIRE].
I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003) 5079 [hep-th/0307268] [INSPIRE].
D. Robles-Llana, F. Saueressig and S. Vandoren, String loop corrected hypermultiplet moduli spaces, JHEP 03 (2006) 081 [hep-th/0602164] [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].
E. Witten, Five-brane effective action in M theory, J. Geom. Phys. 22 (1997) 103 [hep-th/9610234] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and M. Vonk, On the partition sum of the NS five-brane, hep-th/0205281 [INSPIRE].
B. Pioline and D. Persson, The Automorphic NS5-brane, Commun. Num. Theor. Phys. 3 (2009) 697 [arXiv:0902.3274] [INSPIRE].
L. Bao et al., Instanton Corrections to the Universal Hypermultiplet and Automorphic Forms on SU(2, 1), Commun. Num. Theor. Phys. 4 (2010) 187 [arXiv:0909.4299] [INSPIRE].
A. Neitzke, B. Pioline and S. Vandoren, Twistors and black holes, JHEP 04 (2007) 038 [hep-th/0701214] [INSPIRE].
D. Joyce and Y. Song, A theory of generalized Donaldson-Thomas invariants, arXiv:0810.5645 [INSPIRE].
J. Manschot, Wall-crossing of D4-branes using flow trees, Adv. Theor. Math. Phys. 15 (2011) 1 [arXiv:1003.1570] [INSPIRE].
S. Alexandrov and B. Pioline, Theta series, wall-crossing and quantum dilogarithm identities, Lett. Math. Phys. 106 (2016) 1037 [arXiv:1511.02892] [INSPIRE].
S. Alexandrov and S. Banerjee, Modularity, quaternion-Kähler spaces, and mirror symmetry, J. Math. Phys. 54 (2013) 102301 [arXiv:1306.1837] [INSPIRE].
A. Strominger, Loop corrections to the universal hypermultiplet, Phys. Lett. B 421 (1998) 139 [hep-th/9706195] [INSPIRE].
S. Alexandrov, F. Saueressig and S. Vandoren, Membrane and fivebrane instantons from quaternionic geometry, JHEP 09 (2006) 040 [hep-th/0606259] [INSPIRE].
S. Alexandrov, B. Pioline and S. Vandoren, Self-dual Einstein Spaces, Heavenly Metrics and Twistors, J. Math. Phys. 51 (2010) 073510 [arXiv:0912.3406] [INSPIRE].
M. de Vroome and S. Vandoren, Supergravity description of spacetime instantons, Class. Quant. Grav. 24 (2007) 509 [hep-th/0607055] [INSPIRE].
D. Belov and G.W. Moore, Holographic Action for the Self-Dual Field, hep-th/0605038 [INSPIRE].
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge University Press (2007) [https://doi.org/10.1017/CBO9780511618123] [INSPIRE].
S. Hosono, A. Klemm, S. Theisen and S.-T. Yau, Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Commun. Math. Phys. 167 (1995) 301 [hep-th/9308122] [INSPIRE].
I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press (1943) [https://doi.org/10.1016/B978-0-12-294757-5.X5000-4] [INSPIRE].
Acknowledgments
We are grateful to Ashoke Sen for valuable correspondence. SA is grateful to the organizers of the program “Black holes: bridges between number theory and holographic quantum information” and to the Isaac Newton Institute for Mathematical Sciences where this work was finished for the kind hospitality.
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Alexandrov, S., Bendriss, K. Hypermultiplet metric and NS5-instantons. J. High Energ. Phys. 2024, 140 (2024). https://doi.org/10.1007/JHEP01(2024)140
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DOI: https://doi.org/10.1007/JHEP01(2024)140