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Supergravity background of \(\lambda\)-deformed model for \(\mathrm{AdS}_{2} \times S^{2}\) supercoset. (English) Zbl 1332.81170
Summary: Starting with the \(\hat{F} / G\) supercoset model corresponding to the \(\mathrm{AdS}_n \times S^n\) superstring one can define the \(\lambda\)-model of [T. Hollowood et al., “An integrable deformation of the \(\mathrm{AdS}_5\times\mathrm S_5\) superstring”, Preprint, arxiv:1409.1538] either as a deformation of the \(\hat{F} / \hat{F}\) gauged WZW model or as an integrable one-parameter generalisation of the non-abelian T-dual of the \(AdS_n \times S^n\) superstring sigma model with respect to the whole supergroup \(\hat{F}\). Here we consider the case of \(n = 2\) and find the explicit form of the 4d target space background for the \(\lambda\)-model for the \(\operatorname{PSU}(1, 1 | 2) / \operatorname{SO}(1, 1) \times \operatorname{SO}(2)\) supercoset. We show that this background represents a solution of type IIB 10d supergravity compactified on a 6-torus with only metric, dilaton {\(\Phi\)} and the RR 5-form (represented by a 2-form \(F\) in 4d) being non-trivial. This implies that the \(\lambda\)-model is Weyl invariant at the quantum level and thus defines a consistent superstring sigma model. The supergravity solution we find is different from the one in [K. Sfetsos et al., arxiv:1410.1886, 35 p. (2014)] which should correspond to a version of the \(\lambda\)-model where only the bosonic subgroup of \(\hat{F}\) is gauged. Still, the two solutions have equivalent scaling limit of [B. Hoare and the second author, arxiv:1504.07213, 28 p. (2015)] leading to the isometric background for the metric and \(e^{\Phi} F\) which is related to the \(\eta\)-deformed \(\mathrm{AdS}_2 \times S^2\) sigma model of [F. Delduc et al., “Integrable deformation of the \(\mathrm{AdS}_5\times\mathrm S_5\) superstring action”, Phys. Rev. Lett. 112, No. 5, Article ID 051601, 5 p. (2014; doi:10.1103/PhysRevLett.112.051601)]. Similar results are expected in the \(\mathrm{AdS}_3 \times S^3\) and \(\mathrm{AdS}_5 \times S^5\) cases.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
14D15 Formal methods and deformations in algebraic geometry
83E50 Supergravity
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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References:
[1] Delduc, F.; Magro, M.; Vicedo, B.; Delduc, F.; Magro, M.; Vicedo, B., Derivation of the action and symmetries of the q-deformed \(\mathit{AdS}_5 \times S^5\) superstring, Phys. Rev. Lett., J. High Energy Phys., 1410, 5, (2014) · Zbl 1333.81322
[2] Klimcik, C.; Klimcik, C.; Klimcik, C., Integrability of the bi-Yang-Baxter sigma-model, J. High Energy Phys., J. Math. Phys., Lett. Math. Phys., 104, 1095, (2014) · Zbl 1359.70102
[3] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., Integrable deformations of strings on symmetric spaces, J. High Energy Phys., 1411, (2014) · Zbl 1333.81341
[4] Hollowood, T. J.; Miramontes, J. L.; Schmidtt, D. M., An integrable deformation of the \(\mathit{AdS}_5 \times S^5\) superstring, J. Phys. A, 47, 49, 495402, (2014) · Zbl 1305.81120
[5] Sfetsos, K., Integrable interpolations: from exact CFTs to non-abelian T-duals, Nucl. Phys. B, 880, 225, (2014) · Zbl 1284.81257
[6] Tseytlin, A. A., On a “universal” class of WZW type conformal models, Nucl. Phys. B, 418, 173, (1994) · Zbl 1009.81560
[7] Arutyunov, G.; Borsato, R.; Frolov, S., S-matrix for strings on η-deformed \(\mathit{AdS}_5 \times S^5\), J. High Energy Phys., 1404, (2014)
[8] Hoare, B.; Roiban, R.; Tseytlin, A. A., On deformations of \(\mathit{AdS}_n \times S^n\) supercosets, J. High Energy Phys., 1406, (2014)
[9] Arutyunov, G.; Borsato, R.; Frolov, S., Puzzles of η-deformed \(\mathit{AdS}_5 \times S^5\), J. High Energy Phys., 1512, (2015) · Zbl 1388.83726
[10] Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable sigma-models, J. High Energy Phys., 1311, (2013) · Zbl 1342.81182
[11] Sfetsos, K.; Thompson, D. C., Spacetimes for λ-deformations, J. High Energy Phys., 1412, (2014)
[12] Demulder, S.; Sfetsos, K.; Thompson, D. C., Integrable λ-deformations: squashing coset CFTs and \(\mathit{AdS}_5 \times S^5\), J. High Energy Phys., 1507, (2015) · Zbl 1388.83790
[13] Hoare, B.; Tseytlin, A. A., On integrable deformations of superstring sigma models related to \(\mathit{AdS}_n \times S^n\) supercosets, Nucl. Phys. B, 897, 448, (2015) · Zbl 1329.81317
[14] Berkovits, N.; Maldacena, J.; Beisert, N.; Ricci, R.; Tseytlin, A. A.; Wolf, M.; Abbott, M.; Murugan, J.; Penati, S.; Pittelli, A.; Sorokin, D.; Sundin, P.; Tarrant, J.; Wolf, M.; Wulff, L., T-duality of Green-Schwarz superstrings on \(\mathit{AdS}_d \times S^d \times M^{10 - 2 d}\), J. High Energy Phys., Phys. Rev. D, J. High Energy Phys., 1512, (2015)
[15] Metsaev, R. R.; Tseytlin, A. A., Type IIB superstring action in \(\mathit{AdS}(5) \times S^5\) background, Nucl. Phys. B, 533, 109, (1998) · Zbl 0956.81063
[16] Berkovits, N.; Bershadsky, M.; Hauer, T.; Zhukov, S.; Zwiebach, B., Superstring theory on \(\mathit{AdS}(2) \times S^2\) as a coset supermanifold, Nucl. Phys. B, 567, 61, (2000) · Zbl 0951.81040
[17] Hoare, B.; Tseytlin, A. A., Type IIB supergravity solution for the T-dual of the η-deformed \(\mathit{AdS}_5 \times S^5\) superstring, J. High Energy Phys., 1510, (2015) · Zbl 1388.83824
[18] Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A., Scale invariance of the eta-deformed \(\mathit{AdS}_5 \times S^5\) superstring, T-duality and modified type II equations, Nucl. Phys. B, 903, 262, (2016) · Zbl 1332.81167
[19] Appadu, C.; Hollowood, T. J., Beta function of k deformed \(\mathit{AdS}_5 \times S^5\) string theory, J. High Energy Phys., 1511, (2015) · Zbl 1388.81195
[20] Lunin, O.; Roiban, R.; Tseytlin, A. A., Supergravity backgrounds for deformations of \(\mathit{AdS}_n \times S^n\) supercoset string models, Nucl. Phys. B, 891, 106, (2015) · Zbl 1328.81182
[21] Fateev, V. A.; Onofri, E.; Zamolodchikov, A. B., The sausage model (integrable deformations of \(O(3)\) sigma model), Nucl. Phys. B, 406, 521, (1993) · Zbl 0990.81683
[22] Sorokin, D.; Tseytlin, A.; Wulff, L.; Zarembo, K., Superstrings in \(\mathit{AdS}(2) \times S(2) \times T(6)\), J. Phys. A, 44, 275401, (2011) · Zbl 1220.81166
[23] Hull, C. M., Timelike T duality, de Sitter space, large N gauge theories and topological field theory, J. High Energy Phys., 9807, (1998) · Zbl 0958.81085
[24] Bardakci, K.; Crescimanno, M. J.; Rabinovici, E.; Witten, E., On string theory and black holes, Nucl. Phys. B, Phys. Rev. D, 44, 314, (1991)
[25] Klimcik, C.; Severa, P.; Balazs, L. K.; Balog, J.; Forgacs, P.; Mohammedi, N.; Palla, L.; Schnittger, J., Quantum equivalence of sigma models related by nonabelian duality transformations, Phys. Lett. B, Phys. Rev. D, 57, 3585, (1998)
[26] Bars, I.; Sfetsos, K., Global analysis of new gravitational singularities in string and particle theories, Phys. Rev. D, 46, 4495, (1992)
[27] Wulff, L., The type II superstring to order \(\theta^4\), J. High Energy Phys., 1307, (2013) · Zbl 1342.83436
[28] Cvetic, M.; Lu, H.; Pope, C. N.; Stelle, K. S., T duality in the Green-Schwarz formalism, and the massless/massive IIA duality map, Nucl. Phys. B, 573, 149, (2000) · Zbl 0947.81095
[29] Grisaru, M. T.; Howe, P. S.; Mezincescu, L.; Nilsson, B.; Townsend, P. K., \(N = 2\) superstrings in a supergravity background, Phys. Lett. B, 162, 116, (1985)
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