Abstract
We find explicit solutions for giant magnons and spiky strings living on the Schrödinger space Schr5 × T1,1 and compute dispersion relations. The holographic dual field theory is conjectured to be a non-local dipole-deformed CFT at strong coupling. We find that the dependence between conserved charges in the dispersion relations is transcen- dental, which is quite different from the most symmetric case of spherical internal space. Keeping the squashing parameter b general allows us to take some limits and to compare our results to known cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for superconformal deformations of N = 4 super Yang-Mills theory, JHEP 07 (2005) 045 [hep-th/0503192] [INSPIRE].
L.F. Alday, G. Arutyunov and S. Frolov, Green-Schwarz strings in TsT-transformed backgrounds, JHEP 06 (2006) 018 [hep-th/0512253] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
H. Dimov and R.C. Rashkov, On the anatomy of multi-spin magnon and single spike string solutions, Nucl. Phys. B 799 (2008) 255 [arXiv:0709.4231] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
U. Gürsoy and C. Núñez, Dipole deformations of N = 1 SYM and supergravity backgrounds with U(1) × U(1) global symmetry, Nucl. Phys. B 725 (2005) 45 [hep-th/0505100] [INSPIRE].
D.Z. Freedman and U. Gürsoy, Comments on the beta-deformed N = 4 SYM theory, JHEP 11 (2005) 042 [hep-th/0506128] [INSPIRE].
U. Gürsoy, Probing universality in the gravity duals of N = 1 SYM by gamma-deformations, JHEP 05 (2006) 014 [hep-th/0602215] [INSPIRE].
C.-S. Chu, G. Georgiou and V.V. Khoze, Magnons, classical strings and β-deformations, JHEP 11 (2006) 093 [hep-th/0606220] [INSPIRE].
N.P. Bobev and R.C. Rashkov, Multispin giant magnons, Phys. Rev. D 74 (2006) 046011 [hep-th/0607018] [INSPIRE].
N.P. Bobev and R.C. Rashkov, Spiky strings, giant magnons and β-deformations, Phys. Rev. D 76 (2007) 046008 [arXiv:0706.0442] [INSPIRE].
N.P. Bobev, H. Dimov and R.C. Rashkov, Semiclassical strings in Lunin-Maldacena background, Bulg. J. Phys. 35 (2008) 274 [hep-th/0506063] [INSPIRE].
D.V. Bykov and S. Frolov, Giant magnons in TsT-transformed AdS5 × S5 , JHEP 07 (2008) 071 [arXiv:0805.1070] [INSPIRE].
H. Dimov, M. Michalcik and R.C. Rashkov, Strings on the deformed T1,1: giant magnon and single spike solutions, JHEP 10 (2009) 019 [arXiv:0908.3065] [INSPIRE].
M. Michalcik and R.C. Rashkov, On finite size corrections to the dispersion relations of giant magnon and single spike on γ-deformed T1,1 , Eur. Phys. J. C 73 (2013) 2312 [arXiv:1208.0698] [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].
A. Adams, K. Balasubramanian and J. McGreevy, Hot spacetimes for cold atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
V.K. Dobrev, Non-relativistic holography — a group-theoretical perspective, Int. J. Mod. Phys. A 29 (2014) 1430001 [arXiv:1312.0219] [INSPIRE].
C. Duval, M. Hassaine and P.A. Horvathy, The geometry of Schrödinger symmetry in gravity background/non-relativistic CFT, Annals Phys. 324 (2009) 1158 [arXiv:0809.3128] [INSPIRE].
A. Akhavan, M. Alishahiha, A. Davody and A. Vahedi, Non-relativistic CFT and semi-classical strings, JHEP 03 (2009) 053 [arXiv:0811.3067] [INSPIRE].
N. Bobev and A. Kundu, Deformations of holographic duals to non-relativistic CFTs, JHEP 07 (2009) 098 [arXiv:0904.2873] [INSPIRE].
S.J. van Tongeren, Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory, Nucl. Phys. B 904 (2016) 148 [arXiv:1506.01023] [INSPIRE].
M. Guica, F. Levkovich-Maslyuk and K. Zarembo, Integrability in dipole-deformed N = 4 super Yang-Mills, J. Phys. A 50 (2017) 39 [arXiv:1706.07957] [INSPIRE].
C. Ahn and P. Bozhilov, Giant magnon-like solution in Sch5 × S5 , Phys. Rev. D 98 (2018) 106005 [arXiv:1711.09252] [INSPIRE].
G. Georgiou and D. Zoakos, Giant magnons and spiky strings in the Schrödinger/dipole-deformed CFT correspondence, JHEP 02 (2018) 173 [arXiv:1712.03091] [INSPIRE].
H. Ouyang, Semiclassical spectrum for BMN string in Sch5 × S5, JHEP 12 (2017) 126 [arXiv:1709.06844] [INSPIRE].
G. Georgiou and D. Zoakos, Holographic three-point correlators in the Schrödinger/dipole CFT correspondence, JHEP 09 (2018) 026 [arXiv:1806.08181] [INSPIRE].
H. Dimov, M. Radomirov, R.C. Rashkov and T. Vetsov, On pulsating strings in Schrödinger backgrounds, JHEP 10 (2019) 094 [arXiv:1903.07444] [INSPIRE].
G. Georgiou, K. Sfetsos and D. Zoakos, String theory on the Schrödinger pp-wave background, JHEP 08 (2019) 093 [arXiv:1906.08269] [INSPIRE].
G. Georgiou and D. Zoakos, Giant gravitons on the Schrödinger pp-wave geometry, JHEP 03 (2020) 185 [arXiv:2002.05460] [INSPIRE].
D. Zoakos, Finite size effects in classical string solutions of the Schrödinger geometry, arXiv:2006.02285 [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S2 × S3, Adv. Theor. Math. Phys. 8 (2004) 711 [hep-th/0403002] [INSPIRE].
M. Cvetič, H. Lü, D.N. Page and C.N. Pope, New Einstein-Sasaki spaces in five and higher dimensions, Phys. Rev. Lett. 95 (2005) 071101 [hep-th/0504225] [INSPIRE].
S. Benvenuti and E. Tonni, Giant magnons and spiky strings on the conifold, JHEP 02 (2009) 041 [arXiv:0811.0145] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
N. Itzhaki, I.R. Klebanov and S. Mukhi, PP wave limit and enhanced supersymmetry in gauge theories, JHEP 03 (2002) 048 [hep-th/0202153] [INSPIRE].
J. Gomis and H. Ooguri, Penrose limit of N = 1 gauge theories, Nucl. Phys. B 635 (2002) 106 [hep-th/0202157] [INSPIRE].
L.A. Pando Zayas and J. Sonnenschein, On Penrose limits and gauge theories, JHEP 05 (2002) 010 [hep-th/0202186] [INSPIRE].
P. Basu and L.A. Pando Zayas, Chaos rules out integrability of strings on AdS5 × T1,1, Phys. Lett. B 700 (2011) 243 [arXiv:1103.4107] [INSPIRE].
K.L. Panigrahi and M. Samal, Chaos in classical string dynamics in \( \hat{\upgamma} \) deformed AdS5 × T1,1, Phys. Lett. B 761 (2016) 475 [arXiv:1605.05638] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.13802
Rights and permissions
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.
About this article
Cite this article
Golubtsova, A., Dimov, H., Iliev, I. et al. More on Schrödinger holography. J. High Energ. Phys. 2020, 90 (2020). https://doi.org/10.1007/JHEP08(2020)090
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2020)090