Abstract
The equations of motion of a super non-Abelian T-dual sigma model on the Lie supergroup (C 11 + A) in the curved background are explicitly solved by the super Poisson-Lie T-duality. To find the solution of the flat model we use the transformation of supercoordinates, transforming the metric into a constant one, which is shown to be a supercanonical transformation. Then, using the super Poisson-Lie T-duality transformations and the dual decomposition of elements of Drinfel’d superdouble, the solution of the equations of motion for the dual sigma model is obtained. The general form of the dilaton fields satisfying the vanishing β−function equations of the sigma models is found. In this respect, conformal invariance of the sigma models built on the Drinfel’d superdouble ((C 11 + A), I (2|2)) is guaranteed up to one-loop, at least.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Henneaux and L. Mezincescu, A σ-model interpretation of Green-Schwarz covariant superstring action, Phys. Lett. B 152 (1985) 340 [INSPIRE].
N. Read and H. Saleur, Exact spectra of conformal supersymmetric nonlinear σ-models in two-dimensions, Nucl. Phys. B 613 (2001) 409 [hep-th/0106124] [INSPIRE].
S. Guruswamy, A. LeClair and A.W.W. Ludwig, gl(N|N) super-current algebras for disordered Dirac fermions in two-dimensions, Nucl. Phys. B 583 (2000) 475 [cond-mat/9909143] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
N. Berkovits, C. Vafa and E. Witten, Conformal field theory of AdS background with Ramond-Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098] [INSPIRE].
M. Bershadsky, S. Zhukov and A. Vaintrob, PSL(n|n) σ-model as a conformal field theory, Nucl. Phys. B 559 (1999) 205 [hep-th/9902180] [INSPIRE].
N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS 2 × S 2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [INSPIRE].
J. de Boer and S.L. Shatashvili, Two-dimensional conformal field theories on AdS(2d + 1) backgrounds, JHEP 06 (1999) 013 [hep-th/9905032] [INSPIRE].
D. Kagan and C.A.S. Young, Conformal σ-models on supercoset targets, Nucl. Phys. B 745 (2006) 109 [hep-th/0512250] [INSPIRE].
T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].
T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
M.J. Duff, Duality rotations in string theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [INSPIRE].
E. Kiritsis, Exact duality symmetries in CFT and string theory, Nucl. Phys. B 405 (1993) 109 [hep-th/9302033] [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
X.C. de la Ossa and F. Quevedo, Duality symmetries from non-Abelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
C. Klimčík and P. Ševera, Dual non-Abelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
V.G. Drinfeld, Quantum groups, in the Proceedings of the International Congress of Mathematicians, Berkeley U.S.A. (1986), American Mathematical Society, New York U.S.A. (1987), pg. 798.
L. Hlavaty, Classical solution of a σ-model in curved background, Phys. Lett. B 625 (2005) 285 [hep-th/0506188] [INSPIRE].
L. Hlavaty, J. Hybl and M. Turek, Classical solutions of σ-models in curved backgrounds by the Poisson-Lie T-plurality, Int. J. Mod. Phys. A 22 (2007) 1039 [hep-th/0608069] [INSPIRE].
L. Hlavatý and L. Šnobl, Poisson-Lie T-plurality of three-dimensional conformally invariant σ-models. II. Nondiagonal metrics and dilaton puzzle, JHEP 10 (2004) 045 [hep-th/0408126] [INSPIRE].
L. Hlavatý and M. Turek, Flat coordinates and dilaton fields for three-dimensional conformal sigma models, JHEP 06 (2006) 003 [hep-th/0512082] [INSPIRE].
L. Hlavatý, Dilatons in curved backgrounds by the Poisson-Lie transformation, hep-th/0601172 [INSPIRE].
A. Eghbali and A. Rezaei-Aghdam, Poisson-Lie T-dual σ-models on supermanifolds, JHEP 09 (2009) 094 [arXiv:0901.1592] [INSPIRE].
A. Eghbali and A. Rezaei-Aghdam, String cosmology from Poisson-Lie T-dual σ-models on supermanifolds, JHEP 01 (2012) 151 [arXiv:1107.2041] [INSPIRE].
A. Eghbali and A. Rezaei-Aghdam, WZW models as mutual super Poisson-Lie T-dual σ-models, JHEP 07 (2013) 134 [arXiv:1303.4069] [INSPIRE].
A. Eghbali and A. Rezaei-Aghdam, Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions, Nucl. Phys. B 866 (2013) 26 [arXiv:1207.2304] [INSPIRE].
N. Backhouse, A classification of four-dimensional Lie superalgebras, J. Math. Phys. 19 (1978) 2400 [INSPIRE].
B. DeWitt, Supermanifolds, Cambridge University Press, Cambridge U.K. (1992).
A. Eghbali, A. Rezaei-Aghdam and F. Heidarpour, Classification of four and six dimensional Drinfel’d superdoubles, J. Math. Phys. 51 (2010) 103503 [arXiv:0911.1760] [INSPIRE].
A. Eghbali, A. Rezaei-Aghdam and F. Heidarpour, Classification of two and three dimensional Lie super-bialgebras, J. Math. Phys. 51 (2010) 073503 [arXiv:0901.4471] [INSPIRE].
C. Klimčík and P. Ševera, Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett. B 372 (1996) 65 [hep-th/9512040] [INSPIRE].
C. Klimčík and P. Ševera, Poisson Lie T duality: open strings and D-branes, Phys. Lett. B 376 (1996) 82 [hep-th/9512124] [INSPIRE].
T. Tokunaga, String theories on flat supermanifolds, Report Number YITP-05-47, [hep-th/0509198] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1409.3933
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Eghbali, A. Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality. J. High Energ. Phys. 2015, 25 (2015). https://doi.org/10.1007/JHEP02(2015)025
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)025