Abstract
We find new type II backgrounds with non-relativistic symmetries via non-Abelian T-duality. First we consider geometries with Galilean symmetries in type IIA, which have been identified as non-relativistic generalizations of the ABJM background and massive IIA supergravities. We then consider the non-Abelian T-duality transformation on the backgrounds with Lifshitz symmetry constructed by Donos and Gauntlett. Using gauge/gravity duality we study aspects of the field theory dual to these backgrounds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
P. Anderson, Basic Notions Of Condensed Matter Physics, Advanced Books Classics Series, Westview Press, (2008).
S. Sachdev, Quantum Phase Transitions, Troisième Cycle de la Physique, Cambridge University Press, (2011).
Y. Nishida and D.T. Son, Nonrelativistic conformal field theories, Phys. Rev. D 76 (2007) 086004 [arXiv:0706.3746] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: A geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [INSPIRE].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].
A. Donos and J.P. Gauntlett, Lifshitz Solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].
N. Bobev, A. Kundu and K. Pilch, Supersymmetric IIB Solutions with Schrödinger Symmetry, JHEP 07 (2009) 107 [arXiv:0905.0673] [INSPIRE].
A. Donos and J.P. Gauntlett, Supersymmetric solutions for non-relativistic holography, JHEP 03 (2009) 138 [arXiv:0901.0818] [INSPIRE].
A. Donos and J.P. Gauntlett, Solutions of type IIB and D = 11 supergravity with Schrödinger(z) symmetry, JHEP 07 (2009) 042 [arXiv:0905.1098] [INSPIRE].
H. Ooguri and C.-S. Park, Supersymmetric non-relativistic geometries in M-theory, Nucl. Phys. B 824 (2010) 136 [arXiv:0905.1954] [INSPIRE].
A. Donos and J.P. Gauntlett, Schrödinger invariant solutions of type IIB with enhanced supersymmetry, JHEP 10 (2009) 073 [arXiv:0907.1761] [INSPIRE].
H. Singh, Galilean type IIA backgrounds and a map, Mod. Phys. Lett. A 26 (2011) 1443 [arXiv:1007.0866] [INSPIRE].
J. Jeong, H.-C. Kim, S. Lee, E. O Colgain and H. Yavartanoo, Schrödinger invariant solutions of M-theory with Enhanced Supersymmetry, JHEP 03 (2010) 034 [arXiv:0911.5281] [INSPIRE].
R. Gregory, S.L. Parameswaran, G. Tasinato and I. Zavala, Lifshitz solutions in supergravity and string theory, JHEP 12 (2010) 047 [arXiv:1009.3445] [INSPIRE].
S.M. Ko, C. Melby-Thompson, R. Meyer and J.-H. Park, Dynamics of Perturbations in Double Field Theory and Non-Relativistic String Theory, arXiv:1508.01121 [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS backgrounds in string and M-theory, hep-th/0411194 [INSPIRE].
U. Gran, G. Papadopoulos and D. Roest, Systematics of M-theory spinorial geometry, Class. Quant. Grav. 22 (2005) 2701 [hep-th/0503046] [INSPIRE].
C.I. Lazaroiu and E.-M. Babalic, Geometric algebra and M-theory compactifications, Rom. J. Phys. 58 (2013) 5 [arXiv:1301.5094] [INSPIRE].
T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].
A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé, J.L.F. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, An Introduction to T duality in string theory, Nucl. Phys. Proc. Suppl. 41 (1995) 1 [hep-th/9410237] [INSPIRE].
X.C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].
A. Giveon and M. Roček, On nonAbelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].
M. Gasperini, R. Ricci and G. Veneziano, A problem with nonAbelian duality?, Phys. Lett. B 319 (1993) 438 [hep-th/9308112] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On nonAbelian duality, Nucl. Phys. B 424 (1994) 155 [hep-th/9403155] [INSPIRE].
K. Sfetsos and D.C. Thompson, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B 846 (2011) 21 [arXiv:1012.1320] [INSPIRE].
Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond Fields and Coset Geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, Non-Abelian T-duality and the AdS/CFT correspondence:new N = 1 backgrounds, Nucl. Phys. B 873 (2013) 1 [arXiv:1301.6755] [INSPIRE].
Ö. Kelekci, Y. Lozano, N.T. Macpherson and E. Ó Colgáin, Supersymmetry and non-Abelian T-duality in type-II supergravity, Class. Quant. Grav. 32 (2015) 035014 [arXiv:1409.7406] [INSPIRE].
Y. Lozano, E. Ó Colgáin, D. Rodríguez-Gómez and K. Sfetsos, Supersymmetric AdS6 via T Duality, Phys. Rev. Lett. 110 (2013) 231601 [arXiv:1212.1043] [INSPIRE].
G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, On Non-Abelian T-duality and new N = 1 backgrounds, Phys. Lett. B 721 (2013) 342 [arXiv:1212.4840] [INSPIRE].
Y. Lozano, E. Ó Colgáin and D. Rodríguez-Gómez, Hints of 5d Fixed Point Theories from Non-Abelian T-duality, JHEP 05 (2014) 009 [arXiv:1311.4842] [INSPIRE].
E. Caceres, N.T. Macpherson and C. Núñez, New Type IIB Backgrounds and Aspects of Their Field Theory Duals, JHEP 08 (2014) 107 [arXiv:1402.3294] [INSPIRE].
Y. Lozano and N.T. Macpherson, A new AdS 4 /CFT 3 dual with extended SUSY and a spectral flow, JHEP 11 (2014) 115 [arXiv:1408.0912] [INSPIRE].
T.R. Araujo and H. Nastase, \( \mathcal{N}=1 \) SUSY backgrounds with an AdS factor from non-Abelian T duality, Phys. Rev. D 91 (2015) 126015 [arXiv:1503.00553] [INSPIRE].
Y. Bea et al., Compactifications of the Klebanov-Witten CFT and new AdS 3 backgrounds, JHEP 05 (2015) 062 [arXiv:1503.07527] [INSPIRE].
N.T. Macpherson, Non-Abelian T-duality, G 2 -structure rotation and holographic duals of N = 1 Chern-Simons theories, JHEP 11 (2013) 137 [arXiv:1310.1609] [INSPIRE].
A. Barranco, J. Gaillard, N.T. Macpherson, C. Núñez and D.C. Thompson, G-structures and Flavouring non-Abelian T-duality, JHEP 08 (2013) 018 [arXiv:1305.7229] [INSPIRE].
J. Gaillard, N.T. Macpherson, C. Núñez and D.C. Thompson, Dualising the Baryonic Branch: Dynamic SU(2) and confining backgrounds in IIA, Nucl. Phys. B 884 (2014) 696 [arXiv:1312.4945] [INSPIRE].
K.S. Kooner and S. Zacarías, Non-Abelian T-Dualizing the Resolved Conifold with Regular and Fractional D3-branes, JHEP 08 (2015) 143 [arXiv:1411.7433] [INSPIRE].
Y. Lozano, N.T. Macpherson, J. Montero and E. Ó Colgáin, New AdS 3 × S 2 T-duals with \( \mathcal{N}=\left(0,4\right) \) supersymmetry, JHEP 08 (2015) 121 [arXiv:1507.02659] [INSPIRE].
Y. Lozano, N.T. Macpherson and J. Montero, A \( \mathcal{N}=2 \) supersymmetric AdS 4 solution in M-theory with purely magnetic flux, JHEP 10 (2015) 004 [arXiv:1507.02660] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
T. Nishioka and T. Takayanagi, On Type IIA Penrose Limit and N = 6 Chern-Simons Theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Consistent warped space Kaluza-Klein reductions, half maximal gauged supergravities and CP n constructions, Nucl. Phys. B 597 (2001) 172 [hep-th/0007109] [INSPIRE].
E. Gevorgyan and G. Sarkissian, Defects, Non-abelian T-duality and the Fourier-Mukai transform of the Ramond-Ramond fields, JHEP 03 (2014) 035 [arXiv:1310.1264] [INSPIRE].
N.T. Macpherson, C. Núñez, L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Type IIB supergravity solutions with AdS 5 from Abelian and non-Abelian T dualities, JHEP 02 (2015) 040 [arXiv:1410.2650] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S 2 × S 3, Adv. Theor. Math. Phys. 8 (2004) 711 [hep-th/0403002] [INSPIRE].
C.M. Hull, Massive string theories from M-theory and F-theory, JHEP 11 (1998) 027 [hep-th/9811021] [INSPIRE].
A. Smilga, Lectures on Quantum Chromodynamics, World Scientific, (2001).
H. Nastase, Introduction to the AdS/CFT Correspondence, Cambridge University Press, (2015).
J. Erdmenger and M. Ammon, Gauge/gravity duality. Foundations and applications, Cambridge University Press, (2015).
H. Nastase, Introduction to AdS-CFT, arXiv:0712.0689 [INSPIRE].
J. Sonnenschein, What does the string/gauge correspondence teach us about Wilson loops?, hep-th/0003032 [INSPIRE].
C. Núñez, M. Piai and A. Rago, Wilson Loops in string duals of Walking and Flavored Systems, Phys. Rev. D 81 (2010) 086001 [arXiv:0909.0748] [INSPIRE].
T.R. Araujo and H. Nastase, Comments on the T-dual of the gravity dual of D5-branes on S 3, JHEP 04 (2015) 081 [arXiv:1409.7333] [INSPIRE].
U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [INSPIRE].
J. Kluson, Open String in Non-Relativistic Background, Phys. Rev. D 81 (2010) 106006 [arXiv:0912.4587] [INSPIRE].
K.B. Fadafan, Drag force in asymptotically Lifshitz spacetimes, arXiv:0912.4873 [INSPIRE].
H.M. Siahaan, On non-relativistic \( Q\overline{Q} \) potential via Wilson loop in Galilean space-time, Mod. Phys. Lett. A 26 (2011) 1719 [arXiv:1106.5008] [INSPIRE].
K.B. Fadafan and F. Saiedi, On Holographic Non-relativistic Schwinger Effect, arXiv:1504.02432 [INSPIRE].
C. Bachas, Convexity of the Quarkonium Potential, Phys. Rev. D 33 (1986) 2723 [INSPIRE].
R.E. Arias and G.A. Silva, Wilson loops stability in the gauge/string correspondence, JHEP 01 (2010) 023 [arXiv:0911.0662] [INSPIRE].
A. Jeffrey and D. Zwillinger, Table of Integrals, Series, and Products, Elsevier Science, (2000).
P. Byrd and M. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists, Grundlehren der mathematischen Wissenschaften, Springer Berlin Heidelberg, (2013).
K. Sfetsos and D.C. Thompson, New \( \mathcal{N}=1 \) supersymmetric AdS 5 backgrounds in Type IIA supergravity, JHEP 11 (2014) 006 [arXiv:1408.6545] [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: 1508.06568
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
Araujo, T.R., Nastase, H. Non-Abelian T-duality for nonrelativistic holographic duals. J. High Energ. Phys. 2015, 203 (2015). https://doi.org/10.1007/JHEP11(2015)203
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)203