Abstract
We study various perturbations and their holographic interpretation for non-Abelian T-dual of AdS5 × S5 where the T-duality is applied along the SU(2) of AdS5. This paper focuses on two types of perturbations, namely the scalar and the vector fields on NATD of AdS5 × S5. For scalar perturbations, the corresponding solutions could be categorised into two classes. For one of these classes of solutions, we build up the associated holographic dictionary where the asymptotic radial mode sources scalar operators for the (0 + 1)d matrix model. These scalar operators correspond to either a marginal or an irrelevant deformation of the dual matrix model at strong coupling. We calculate the two point correlation between these scalar operators and explore their high as well as low frequency behaviour. We also discuss the completion of these geometries by setting an upper cut-off along the holographic axis and discuss the corresponding corrections to the scalar correlators in the dual matrix model. Finally, we extend our results for vector perturbations where we obtain asymptotic solutions for a particular class of modes. These are further used to calculate the boundary charge density at finite chemical potential.
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, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
O. Aharony et al., Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
A.V. Ramallo, Introduction to the AdS/CFT correspondence, Springer Proc. Phys. 161 (2015) 411 [arXiv:1310.4319] [INSPIRE].
M. Natsuume, AdS/CFT Duality User Guide, Lect. Notes Phys. 903 (2015) 1 [arXiv:1409.3575] [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].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].
Y. Lozano, C. Núñez and S. Zacarías, BMN Vacua, Superstars and Non-Abelian T-duality, JHEP 09 (2017) 008 [arXiv:1703.00417] [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].
E. Alvarez, L. Alvarez-Gaume, 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. Alvarez-Gaume 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, Y. Lozano, E. O Colgain and K. Sfetsos, Non-Abelian T-duality and consistent truncations in type-II supergravity, JHEP 08 (2012) 132 [arXiv:1205.2274] [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].
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].
R.A. Reid-Edwards and B. Stefanski, On type IIA geometries dual to N = 2 SCFTs, Nucl. Phys. B 849 (2011) 549 [arXiv:1011.0216] [INSPIRE].
O. Aharony, L. Berdichevsky and M. Berkooz, 4d N = 2 superconformal linear quivers with type IIA duals, JHEP 08 (2012) 131 [arXiv:1206.5916] [INSPIRE].
A. Barranco et al., G-structures and Flavouring non-Abelian T-duality, JHEP 08 (2013) 018 [arXiv:1305.7229] [INSPIRE].
N.T. Macpherson et al., Type IIB supergravity solutions with AdS5 from Abelian and non-Abelian T dualities, JHEP 02 (2015) 040 [arXiv:1410.2650] [INSPIRE].
Y. Lozano and C. Núñez, Field theory aspects of non-Abelian T-duality and 𝒩 = 2 linear quivers, JHEP 05 (2016) 107 [arXiv:1603.04440] [INSPIRE].
D. Roychowdhury, Fragmentation and defragmentation of strings in type IIA and their holographic duals, JHEP 08 (2021) 030 [arXiv:2104.11953] [INSPIRE].
C. Núñez, D. Roychowdhury and D.C. Thompson, Integrability and non-integrability in 𝒩 = 2 SCFTs and their holographic backgrounds, JHEP 07 (2018) 044 [arXiv:1804.08621] [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].
T.R. Araujo and H. Nastase, Non-Abelian T-duality for nonrelativistic holographic duals, JHEP 11 (2015) 203 [arXiv:1508.06568] [INSPIRE].
G. Itsios, J.M. Penín and S. Zacarías, Spin-2 excitations in Gaiotto-Maldacena solutions, JHEP 10 (2019) 231 [arXiv:1903.11613] [INSPIRE].
C. Núñez, D. Roychowdhury, S. Speziali and S. Zacarías, Holographic aspects of four dimensional 𝒩 = 2 SCFTs and their marginal deformations, Nucl. Phys. B 943 (2019) 114617 [arXiv:1901.02888] [INSPIRE].
J. van Gorsel and S. Zacarías, A Type IIB Matrix Model via non-Abelian T-dualities, JHEP 12 (2017) 101 [arXiv:1711.03419] [INSPIRE].
D. Roychowdhury, Matrix models and non-Abelian T dual of AdS5 × S5, Fortsch. Phys. 71 (2023) 2300146 [arXiv:2110.05395] [INSPIRE].
S. Roychowdhury and D. Roychowdhury, Spin 2 spectrum for marginal deformations of 4d 𝒩 = 2 SCFTs, JHEP 03 (2023) 083 [arXiv:2301.12757] [INSPIRE].
D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, JHEP 10 (2012) 189 [arXiv:0904.4466] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
J.M. Maldacena, M.M. Sheikh-Jabbari and M. Van Raamsdonk, Transverse five-branes in matrix theory, JHEP 01 (2003) 038 [hep-th/0211139] [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
H. Lin, The supergravity dual of the BMN matrix model, JHEP 12 (2004) 001 [hep-th/0407250] [INSPIRE].
H. Lin and J.M. Maldacena, Fivebranes from gauge theory, Phys. Rev. D 74 (2006) 084014 [hep-th/0509235] [INSPIRE].
M. Abramowitz and I.A. Stegun, Poligamma Functions, in Handbook of Mathematical Functions, section 6.4 Dover Publications (1964) [ISBN: 978-0-486-61272-0].
Y. Asano, G. Ishiki, T. Okada and S. Shimasaki, Emergent bubbling geometries in the plane wave matrix model, JHEP 05 (2014) 075 [arXiv:1401.5079] [INSPIRE].
Y. Asano, G. Ishiki and S. Shimasaki, Emergent bubbling geometries in gauge theories with SU(2|4) symmetry, JHEP 09 (2014) 137 [arXiv:1406.1337] [INSPIRE].
Y. Asano, G. Ishiki, T. Okada and S. Shimasaki, Exact results for perturbative partition functions of theories with SU(2|4) symmetry, JHEP 02 (2013) 148 [arXiv:1211.0364] [INSPIRE].
F. Leblond, R.C. Myers and D.C. Page, Superstars and giant gravitons in M theory, JHEP 01 (2002) 026 [hep-th/0111178] [INSPIRE].
Acknowledgments
It’s a pleasure to thank Carlos Nunez for his careful reading of the draft and making several useful comments that has improved the presentation. The author is indebted to the authorities of IIT Roorkee for their unconditional support towards researches in basic sciences. The author would like to acknowledge the Mathematical Research Impact Centric Support (MATRICS) grant (MTR/2023/000005) received from SERB, India. The author also acknowledges The Royal Society, U.K. (grant no. AL/231026) for financial assistance.
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: 2310.10210
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
Roychowdhury, D. Matrix model correlators from non-Abelian T-dual of AdS5 × S5. J. High Energ. Phys. 2024, 62 (2024). https://doi.org/10.1007/JHEP02(2024)062
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)062