Abstract
It was recently shown that the \( \mathcal{N} \) = 2 string topological amplitudes in the heterotic weak coupling limit generate a six-dimensional Melvin space, providing a description of the Ω-background in string theory, where string propagation can be exactly studied. In this work, we generalise the analysis to the refined case of the Ω-background with two independent deformation parameters. The Melvin space is now ten-dimensional and is extended by an action on the internal K3 compactification manifold of the heterotic superstring, corresponding to an SU(2)R rotation in the field theory description. We identify the class of heterotic topological amplitudes realising this background as the scattering of two anti-self-dual gravitons and arbitrary numbers of anti-self-dual graviphotons, self-dual vector fields of the dilaton multiplet, together with self-dual magnetic fluxes along the K3. In the field theory limit, our result correctly reproduces the perturbative part of the Nekrasov free energy in the case where both equivariant parameters are turned on.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Angelantonj and I. Antoniadis, The String Geometry Behind Topological Amplitudes, JHEP 01 (2020) 005 [arXiv:1910.03347] [INSPIRE].
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys. 165 (1994) 311 [hep-th/9309140] [INSPIRE].
E. Witten, Topological Sigma Models, Commun. Math. Phys. 118 (1988) 411 [INSPIRE].
E. Witten, On the Structure of the Topological Phase of Two-dimensional Gravity, Nucl. Phys. B 340 (1990) 281 [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Topological amplitudes in string theory, Nucl. Phys. B 413 (1994) 162 [hep-th/9307158] [INSPIRE].
M. de Roo, J.W. van Holten, B. de Wit and A. Van Proeyen, Chiral Superfields in N = 2 Supergravity, Nucl. Phys. B 173 (1980) 175 [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math. 244 (2006) 525 [hep-th/0306238] [INSPIRE].
G.W. Moore, N. Nekrasov and S. Shatashvili, Integrating over Higgs branches, Commun. Math. Phys. 209 (2000) 97 [hep-th/9712241] [INSPIRE].
A. Lossev, N. Nekrasov and S.L. Shatashvili, Testing Seiberg-Witten solution, NATO Sci. Ser. C 520 (1999) 359 [hep-th/9801061] [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].
M.A. Melvin, Pure magnetic and electric geons, Phys. Lett. 8 (1964) 65 [INSPIRE].
J.G. Russo and A.A. Tseytlin, Constant magnetic field in closed string theory: An exactly solvable model, Nucl. Phys. B 448 (1995) 293 [hep-th/9411099] [INSPIRE].
J.G. Russo and A.A. Tseytlin, Exactly solvable string models of curved space-time backgrounds, Nucl. Phys. B 449 (1995) 91 [hep-th/9502038] [INSPIRE].
J.G. Russo and A.A. Tseytlin, Heterotic strings in uniform magnetic field, Nucl. Phys. B 454 (1995) 164 [hep-th/9506071] [INSPIRE].
S. Hellerman, D. Orlando and S. Reffert, String theory of the Omega deformation, JHEP 01 (2012) 148 [arXiv:1106.0279] [INSPIRE].
S. Hellerman, D. Orlando and S. Reffert, The Omega Deformation From String and M-theory, JHEP 07 (2012) 061 [arXiv:1204.4192] [INSPIRE].
D. Orlando and S. Reffert, Deformed supersymmetric gauge theories from the fluxtrap background, Int. J. Mod. Phys. A 28 (2013) 1330044 [arXiv:1309.7350] [INSPIRE].
N. Lambert, D. Orlando and S. Reffert, Alpha- and Omega-Deformations from fluxes in M-theory, JHEP 11 (2014) 162 [arXiv:1409.1219] [INSPIRE].
I. Antoniadis, S. Hohenegger, K.S. Narain and T.R. Taylor, Deformed Topological Partition Function and Nekrasov Backgrounds, Nucl. Phys. B 838 (2010) 253 [arXiv:1003.2832] [INSPIRE].
Y. Nakayama and H. Ooguri, Comments on Worldsheet Description of the Omega Background, Nucl. Phys. B 856 (2012) 342 [arXiv:1106.5503] [INSPIRE].
I. Antoniadis, I. Florakis, S. Hohenegger, K.S. Narain and A. Zein Assi, Worldsheet Realization of the Refined Topological String, Nucl. Phys. B 875 (2013) 101 [arXiv:1302.6993] [INSPIRE].
I. Antoniadis, I. Florakis, S. Hohenegger, K.S. Narain and A. Zein Assi, Non-Perturbative Nekrasov Partition Function from String Theory, Nucl. Phys. B 880 (2014) 87 [arXiv:1309.6688] [INSPIRE].
E. Kiritsis, String theory in a nutshell, Princeton University Press, Princeton, U.S.A. (2019).
I. Florakis and A. Zein Assi, \( \mathcal{N} \) = 2* from Topological Amplitudes in String Theory, Nucl. Phys. B 909 (2016) 480 [arXiv:1511.02887] [INSPIRE].
C. Angelantonj, I. Antoniadis and M. Samsonyan, A string realisation of Ω-deformed Abelian \( \mathcal{N} \) = 2* theory, Nucl. Phys. B 923 (2017) 32 [arXiv:1702.04998] [INSPIRE].
M. Samsonyan, C. Angelantonj and I. Antoniadis, \( \mathcal{N} \) = 2* (non-)Abelian theory in the Ω background from string theory, PoS EPS-HEP2017 (2017) 546 [INSPIRE].
J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. B 82 (1979) 60 [INSPIRE].
C. Kounnas and B. Rostand, Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys. B 341 (1990) 641 [INSPIRE].
C. Kounnas and M. Porrati, Spontaneous Supersymmetry Breaking in String Theory, Nucl. Phys. B 310 (1988) 355 [INSPIRE].
E. Kiritsis and C. Kounnas, Perturbative and nonperturbative partial supersymmetry breaking: \( \mathcal{N} \) = 4 → \( \mathcal{N} \) = 2 → \( \mathcal{N} \) = 1, Nucl. Phys. B 503 (1997) 117 [hep-th/9703059] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to the memory of Costas Kounnas and Theodore Tomaras.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2202.13205
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Angelantonj, C., Antoniadis, I., Florakis, I. et al. Refined topological amplitudes from the Ω-background in string theory. J. High Energ. Phys. 2022, 143 (2022). https://doi.org/10.1007/JHEP05(2022)143
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2022)143