Comments on worldsheet description of the Omega background. (English) Zbl 1246.81288
Summary: Nekrasov’s partition function is defined on a flat bundle of \(R^{4}\) over \(S^{1}\) called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes scattering amplitudes of self-dual gravitons and graviphotons in type II superstring compactified on a Calabi-Yau manifold. We propose a generalization of this correspondence when the fibration is not necessarily self-dual.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 83C45 | Quantization of the gravitational field |
| 83E30 | String and superstring theories in gravitational theory |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
References:
| [1] | Bershadsky, M.; Cecotti, S.; Ooguri, H.; Vafa, C., Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Commun. Math. Phys., 165, 311-428 (1994) · Zbl 0815.53082 |
| [2] | Antoniadis, I.; Gava, E.; Narain, K. S.; Taylor, T. R., Topological amplitudes in string theory, Nucl. Phys. B, 413, 162-184 (1994) · Zbl 1007.81522 |
| [3] | Gopakumar, R.; Vafa, C., M theory and topological strings. 2 · Zbl 0922.32015 |
| [4] | Ooguri, H.; Strominger, A.; Vafa, C., Black hole attractors and the topological string, Phys. Rev. D, 70, 106007 (2004) |
| [5] | Nekrasov, N. A., Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys., 7, 831-864 (2004) · Zbl 1056.81068 |
| [6] | Losev, A. S.; Marshakov, A.; Nekrasov, N. A., Small instantons, little strings and free fermions, (Shifman, M.; etal., From Fields to Strings: Circumnavigating Theoretical Physics, vol. 1 (2005), World Scientific: World Scientific Singapore), 581-621 · Zbl 1081.81103 |
| [7] | Nekrasov, N.; Okounkov, A., Seiberg-Witten theory and random partitions · Zbl 1233.14029 |
| [8] | Awata, H.; Kanno, H., Instanton counting, Macdonald functions and the moduli space of D-branes, JHEP, 0505, 039 (2005) |
| [9] | Iqbal, A.; Kozcaz, C.; Vafa, C., The refined topological vertex, JHEP, 0910, 069 (2009) |
| [10] | Dijkgraaf, R.; Vafa, C., Toda theories, matrix models, topological strings, and \(N = 2\) Gauge systems |
| [11] | Antoniadis, I.; Hohenegger, S.; Narain, K. S.; Taylor, T. R., Deformed Topological Partition Function and Nekrasov Backgrounds, Nucl. Phys. B, 838, 253-265 (2010) · Zbl 1206.81093 |
| [12] | Morales, J. F.; Serone, M., Higher derivative F terms in \(N = 2\) strings, Nucl. Phys. B, 481, 389-402 (1996) · Zbl 0925.81218 |
| [13] | de Wit, B.; Katmadas, S.; van Zalk, M., New supersymmetric higher-derivative couplings: full \(N = 2\) superspace does not count!, JHEP, 1101, 007 (2011) · Zbl 1214.83043 |
| [14] | Ito, K.; Nakajima, H.; Saka, T.; Sasaki, S., JHEP, 1011, 093 (2010) |
| [15] | Antoniadis, I.; Gava, E.; Narain, K. S.; Taylor, T. R., \(N = 2\) type II heterotic duality and higher derivative F terms, Nucl. Phys. B, 455, 109-130 (1995) · Zbl 0925.81158 |
| [16] | Aganagic, M.; Klemm, A.; Marino, M.; Vafa, C., The topological vertex, Commun. Math. Phys., 254, 425 (2005) · Zbl 1114.81076 |
| [17] | de Wit, B.; Lauwers, P. G.; Van Proeyen, A., Lagrangians of \(N = 2\) supergravity-matter systems, Nucl. Phys. B, 255, 569 (1985) |
| [18] | Andrianopoli, L.; Bertolini, M.; Ceresole, A.; DʼAuria, R.; Ferrara, S.; Fre, P.; Magri, T., \(N = 2\) supergravity and \(N = 2\) super Yang-Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map, J. Geom. Phys., 23, 111-189 (1997) · Zbl 0899.53073 |
| [19] | Ooguri, H.; Vafa, C., The C deformation of gluino and nonplanar diagrams, Adv. Theor. Math. Phys., 7, 53-85 (2003) |
| [20] | Berkovits, N.; Seiberg, N., Superstrings in graviphoton background and \(N = 1 / 2 + 3 / 2\) supersymmetry, JHEP, 0307, 010 (2003) |
| [21] | Martelli, D.; Sparks, J.; Yau, S.-T., Sasaki-Einstein manifolds and volume minimisation, Commun. Math. Phys., 280, 611-673 (2008) · Zbl 1161.53029 |
| [22] | Nekrasov, N. A.; Shatashvili, S. L., Quantization of integrable systems and four dimensional gauge theories · Zbl 1317.81201 |
| [23] | Nakayama, Y., Refined Cigar and Omega-deformed conifold, JHEP, 1007, 054 (2010) · Zbl 1290.81130 |
| [24] | Huang, M.-X.; Klemm, A., Direct integration for general \(Ω\) backgrounds · Zbl 1276.81098 |
| [25] | Hollowood, T. J.; Iqbal, A.; Vafa, C., JHEP, 0803, 069 (2008) |
| [26] | Krefl, D.; Walcher, J., Shift versus extension in refined partition functions |
| [27] | Lawrence, A.; McGreevy, J., Local string models of soft supersymmetry breaking, JHEP, 0406, 007 (2004) |
| [28] | Aganagic, M.; Beem, C., Geometric transitions and D-term SUSY breaking, Nucl. Phys. B, 796, 44-65 (2008) · Zbl 1219.81205 |
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