×

Worldsheet realization of the refined topological string. (English) Zbl 1282.81139

Summary: A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized \(N=2\) F-terms of the form \(F_{g,n}W^{2g}Y^{2n}\) in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield Y defined as an \(N=2\) chiral projection of a particular anti-chiral \(\bar{T}\)-vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold \(K3 {\times} T^2\), T is the usual Kähler modulus of the \(T^2\) torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an \(SU(2)\) enhancement point of the string moduli space. The two deformation parameters \(\epsilon\)- and \(\epsilon^+\) of the \(\Omega\) supergravity background are then identified with the constant field strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the \(\bar{T}\) vector multiplet, respectively.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E50 Supergravity
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Nekrasov, N. A., Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys., 7, 831 (2004) · Zbl 1056.81068
[2] Losev, A. S.; Marshakov, A.; Nekrasov, N. A., Small instantons, little strings and free fermions, (Shifman, M.; etal., From Fields to Strings, vol. 1 (2003)), 581-621 · Zbl 1081.81103
[3] Nekrasov, N.; Okounkov, A., Seiberg-Witten theory and random partitions · Zbl 1233.14029
[4] Iqbal, A.; Kashani-Poor, A.-K., Instanton counting and Chern-Simons theory, Adv. Theor. Math. Phys., 7, 457 (2004) · Zbl 1044.32022
[5] Iqbal, A.; Kashani-Poor, A.-K., \(SU(N)\) geometries and topological string amplitudes, Adv. Theor. Math. Phys., 10, 1 (2006) · Zbl 1101.81088
[6] Witten, E., Topological sigma models, Commun. Math. Phys., 118, 411 (1988) · Zbl 0674.58047
[7] 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 (1994) · Zbl 0815.53082
[8] Gopakumar, R.; Vafa, C., M theory and topological strings. 1
[9] Gopakumar, R.; Vafa, C., M theory and topological strings. 2
[10] Hollowood, T. J.; Iqbal, A.; Vafa, C., Matrix models, geometric engineering and elliptic genera, JHEP, 0803, 069 (2008)
[11] Dijkgraaf, R.; Vafa, C.; Verlinde, E., M-theory and a topological string duality
[12] Awata, H.; Kanno, H., Instanton counting, Macdonald functions and the moduli space of D-branes, JHEP, 0505, 039 (2005)
[13] Iqbal, A.; Kozcaz, C.; Vafa, C., The refined topological vertex, JHEP, 0910, 069 (2009)
[14] Dijkgraaf, R.; Vafa, C., Toda theories, matrix models, topological strings, and \(N = 2\) gauge systems
[15] Lockhart, G.; Vafa, C., Superconformal partition functions and non-perturbative topological strings · Zbl 1402.81248
[16] Antoniadis, I.; Gava, E.; Narain, K. S.; Taylor, T. R., Topological amplitudes in string theory, Nucl. Phys. B, 413, 162 (1994) · Zbl 1007.81522
[17] 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 (1995) · Zbl 0925.81158
[18] Antoniadis, I.; Gava, E.; Narain, K. S.; Taylor, T. R., Topological amplitudes in heterotic superstring theory, Nucl. Phys. B, 476, 133 (1996) · Zbl 0925.81184
[19] Lerche, W.; Stieberger, S., 1/4 BPS states and nonperturbative couplings in \(N = 4\) string theories, Adv. Theor. Math. Phys., 3, 1539 (1999) · Zbl 1055.81607
[20] Antoniadis, I.; Narain, K. S.; Taylor, T. R., Open string topological amplitudes and gaugino masses, Nucl. Phys. B, 729, 235 (2005)
[21] Antoniadis, I.; Hohenegger, S.; Narain, K. S., \(N = 4\) topological amplitudes and string effective action, Nucl. Phys. B, 771, 40 (2007) · Zbl 1117.81111
[22] Antoniadis, I.; Hohenegger, S.; Narain, K. S.; Sokatchev, E., Harmonicity in \(N = 4\) supersymmetry and its quantum anomaly, Nucl. Phys. B, 794, 348 (2008) · Zbl 1273.81200
[23] Antoniadis, I.; Hohenegger, S.; Narain, K. S.; Sokatchev, E., A new class of \(N = 2\) topological amplitudes, Nucl. Phys. B, 823, 448 (2009) · Zbl 1196.83032
[24] Antoniadis, I.; Hohenegger, S.; Narain, K. S.; Sokatchev, E., Generalized \(N = 2\) topological amplitudes and holomorphic anomaly equation, Nucl. Phys. B, 856, 360 (2012) · Zbl 1246.81198
[25] Hohenegger, S.; Stieberger, S., BPS saturated string amplitudes: K3 elliptic genus and Igusa cusp form, Nucl. Phys. B, 856, 413 (2012) · Zbl 1246.81261
[26] 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
[27] Nakayama, Y.; Ooguri, H., Comments on worldsheet description of the omega background · Zbl 1246.81288
[28] Morales, J. F.; Serone, M., Higher derivative \(F\) terms in \(N = 2\) strings, Nucl. Phys. B, 481, 389 (1996) · Zbl 1049.81608
[29] Moore, G. W.; Nekrasov, N.; Shatashvili, S., Integrating over Higgs branches, Commun. Math. Phys., 209, 97 (2000) · Zbl 0981.53082
[30] Losev, A.; Nekrasov, N.; Shatashvili, S. L., Testing Seiberg-Witten solution, in: Strings, Branes and Dualities, Cargese, 1997, pp. 359-372 · Zbl 1053.81547
[31] Verlinde, E. P.; Verlinde, H. L., Chiral bosonization, determinants and the string partition function, Nucl. Phys. B, 288, 357 (1987)
[32] Polchinski, J., Evaluation of the one loop string path integral, Commun. Math. Phys., 104, 37 (1986) · Zbl 0606.58014
[33] Gava, E.; Jayaraman, T.; Narain, K. S.; Sarmadi, M. H., D-branes and the conifold singularity, Phys. Lett. B, 388, 29-34 (1996)
[34] Bianchi, M.; Sagnotti, A., Twist symmetry and open string Wilson lines, Nucl. Phys. B, 361, 519 (1991)
[35] Pradisi, G.; Sagnotti, A., Open string orbifolds, Phys. Lett. B, 216, 59 (1989)
[36] Angelantonj, C.; Sagnotti, A., Phys. Rept., 376, 339 (2003), Erratum · Zbl 0999.83056
[37] Krefl, D.; Walcher, J., Extended holomorphic anomaly in gauge theory, Lett. Math. Phys., 95, 67 (2011) · Zbl 1205.81118
[38] Krefl, D.; Walcher, J., Shift versus extension in refined partition functions
[39] Huang, M.-x.; Kashani-Poor, A.-K.; Klemm, A., The Omega deformed B-model for rigid \(N = 2\) theories · Zbl 1272.81119
[40] Hellerman, S.; Orlando, D.; Reffert, S., String theory of the Omega deformation, JHEP, 1201, 148 (2012) · Zbl 1306.81110
[41] Reffert, S., General Omega deformations from closed string backgrounds, JHEP, 1204, 059 (2012) · Zbl 1348.81383
[42] Hellerman, S.; Orlando, D.; Reffert, S., The Omega deformation from string and M-theory, JHEP, 1207, 061 (2012)
[43] Hellerman, S.; Orlando, D.; Reffert, S., BPS states in the duality web of the Omega deformation · Zbl 1342.81290
[44] Billo, M.; Frau, M.; Fucito, F.; Lerda, A., Instanton calculus in R-R background and the topological string, JHEP, 0611, 012 (2006)
[45] Billo, M.; Ferro, L.; Frau, M.; Gallot, L.; Lerda, A.; Pesando, I., Exotic instanton counting and heterotic/type I-prime duality, JHEP, 0907, 092 (2009)
[46] Nekrasov, N. A.; Shatashvili, S. L., Quantization of integrable systems and four dimensional gauge theories · Zbl 1214.83049
[47] Nekrasov, N. A.; Shatashvili, S. L., Quantum integrability and supersymmetric vacua, Prog. Theor. Phys. Suppl., 177, 105 (2009) · Zbl 1173.81325
[48] Nekrasov, N. A.; Shatashvili, S. L., Supersymmetric vacua and Bethe ansatz, Nucl. Phys. B (Proc. Suppl.), 192-193, 91 (2009) · Zbl 1180.81125
[49] Gerasimov, A. A.; Shatashvili, S. L., Two-dimensional gauge theories and quantum integrable systems · Zbl 1153.81532
[50] Nekrasov, N.; Rosly, A.; Shatashvili, S., Darboux coordinates, Yang-Yang functional, and gauge theory, Nucl. Phys. B (Proc. Suppl.), 216, 69 (2011)
[51] Angelantonj, C.; Florakis, I.; Pioline, B., A new look at one-loop integrals in string theory, Commun. Num. Theor. Phys., 6, 159 (2012) · Zbl 1270.81147
[52] Angelantonj, C.; Florakis, I.; Pioline, B., One-loop BPS amplitudes as BPS-state sums, JHEP, 1206, 070 (2012) · Zbl 1397.81211
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.