Abstract
In this paper we study the thermodynamics of black branes with a modulated complex scalar in the context of bulk and boundary theories. The modulation induces inhomogeneity to the dual field theory, anisotropic pressure, and brane charge to the bulk geometry. The first law of thermodynamics and the Smarr relation are obtained using the off-shell ADT and the reduced action formalisms. We discuss the prescription for the mass of black branes, which relies on relevant and marginal deformations in the dual field theory. One of the cases is the gravity dual to a ABJM model with a sinusoidal mass function depending on a spatial coordinate. This is the first study of the deformed ABJM model at finite temperature including bulk thermodynamics.
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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].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
K.K. Kim and O.-K. Kwon, Janus ABJM Models with Mass Deformation, JHEP 08 (2018) 082 [arXiv:1806.06963] [INSPIRE].
K.K. Kim, Y. Kim, O.-K. Kwon and C. Kim, Aspects of Massive ABJM Models with Inhomogeneous Mass Parameters, JHEP 12 (2019) 153 [arXiv:1910.05044] [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].
K. Hosomichi, K.-M. Lee, S. Lee, S. Lee and J. Park, N = 5, 6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds, JHEP 09 (2008) 002 [arXiv:0806.4977] [INSPIRE].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A Massive Study of M2-brane Proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].
N. Lambert and P. Richmond, M2-Branes and Background Fields, JHEP 10 (2009) 084 [arXiv:0908.2896] [INSPIRE].
B. Ahn, S. Hyun, K.K. Kim, O.-K. Kwon and S.-A. Park, AdS Q-Soliton and Inhomogeneously mass-deformed ABJM Model, arXiv:1911.05783 [INSPIRE].
B. de Wit and H. Nicolai, N = 8 Supergravity with Local SO(8) × SU(8) Invariance, Phys. Lett. 108B (1982) 285 [INSPIRE].
A. Das, M. Fischler and M. Roček, SuperHiggs Effect in a New Class of Scalar Models and a Model of Super QED, Phys. Rev. D 16 (1977) 3427 [INSPIRE].
J.P. Gauntlett and C. Rosen, Susy Q and spatially modulated deformations of ABJM theory, JHEP 10 (2018) 066 [arXiv:1808.02488] [INSPIRE].
I. Arav, J.P. Gauntlett, M. Roberts and C. Rosen, Spatially modulated and supersymmetric deformations of ABJM theory, JHEP 04 (2019) 099 [arXiv:1812.11159] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
M. Cvetič, H. Lü and C.N. Pope, Geometry of the embedding of supergravity scalar manifolds in D = 11 and D = 10, Nucl. Phys. B 584 (2000) 149 [hep-th/0002099] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
D. Kubiznak, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30 (1973) 71 [Erratum ibid. 30 (1973) 521] [INSPIRE].
L.F. Abbott and S. Deser, Stability of Gravity with a Cosmological Constant, Nucl. Phys. B 195 (1982) 76 [INSPIRE].
S. Deser and B. Tekin, Gravitational energy in quadratic curvature gravities, Phys. Rev. Lett. 89 (2002) 101101 [hep-th/0205318] [INSPIRE].
W. Kim, S. Kulkarni and S.-H. Yi, Quasilocal Conserved Charges in a Covariant Theory of Gravity, Phys. Rev. Lett. 111 (2013) 081101 [Erratum ibid. 112 (2014) 079902] [arXiv:1306.2138] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Quasilocal conserved charges and holography, Phys. Rev. D 90 (2014) 104016 [arXiv:1406.7101] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Frame-independent holographic conserved charges, Phys. Rev. D 91 (2015) 064052 [arXiv:1410.1312] [INSPIRE].
J.-J. Peng, Conserved charge of gravity theory with p-form gauge fields and its property under Kaluza-Klein reduction, Phys. Rev. D 95 (2017) 104022 [arXiv:1611.06317] [INSPIRE].
M. Bañados and S. Theisen, Scale invariant hairy black holes, Phys. Rev. D 72 (2005) 064019 [hep-th/0506025] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Scaling symmetry and scalar hairy Lifshitz black holes, JHEP 10 (2015) 105 [arXiv:1507.03574] [INSPIRE].
B. Ahn, S. Hyun, K.K. Kim, S.-A. Park and S.-H. Yi, Holography without counter terms, Phys. Rev. D 94 (2016) 024043 [arXiv:1512.09319] [INSPIRE].
T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].
W. Kim, S. Kulkarni and S.-H. Yi, Conserved quantities and Virasoro algebra in New massive gravity, JHEP 05 (2013) 041 [arXiv:1303.3691] [INSPIRE].
W. Kim, S. Kulkarni and S.-H. Yi, Quasilocal conserved charges in the presence of a gravitational Chern-Simons term, Phys. Rev. D 88 (2013) 124004 [arXiv:1310.1739] [INSPIRE].
S. Hyun, S.-A. Park and S.-H. Yi, Quasi-local charges and asymptotic symmetry generators, JHEP 06 (2014) 151 [arXiv:1403.2196] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
B. Ahn, S. Hyun, S.-A. Park and S.-H. Yi, Scaling symmetry and scalar hairy rotating AdS3 black holes, Phys. Rev. D 93 (2016) 024041 [arXiv:1508.06484] [INSPIRE].
S. Hyun, S.-A. Park and S.-H. Yi, Revisiting the thermodynamic relations in AdS/CMT models, Phys. Rev. D 95 (2017) 066012 [arXiv:1609.04351] [INSPIRE].
S. Hyun, J. Jeong, S.-A. Park and S.-H. Yi, Thermodynamic Volume and the Extended Smarr Relation, JHEP 04 (2017) 048 [arXiv:1702.06629] [INSPIRE].
K.K. Kim, K.-Y. Kim, Y. Seo and S.-J. Sin, Building Magnetic Hysteresis in Holography, JHEP 07 (2019) 158 [arXiv:1902.10929] [INSPIRE].
C. Erices, M. Riquelme and P. Rodríguez, BTZ black hole with Korteweg-de Vries-type boundary conditions: Thermodynamics revisited, Phys. Rev. D 100 (2019) 126026 [arXiv:1907.13026] [INSPIRE].
B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [INSPIRE].
M. Cvetič, G.W. Gibbons, D. Kubiznak and C.N. Pope, Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].
T. Padmanabhan, Classical and quantum thermodynamics of horizons in spherically symmetric space-times, Class. Quant. Grav. 19 (2002) 5387 [gr-qc/0204019] [INSPIRE].
D. Mateos and D. Trancanelli, Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
D. Jang, Y. Kim, O.-K. Kwon and D.D. Tolla, Mass-deformed ABJM Theory and LLM Geometries: Exact Holography, JHEP 04 (2017) 104 [arXiv:1612.05066] [INSPIRE].
D. Jang, Y. Kim, O.-K. Kwon and D.D. Tolla, Holography of Massive M2-brane Theory with Discrete Torsion, arXiv:1906.06881 [INSPIRE].
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Hyun, S., Ahn, B., Kim, K.K. et al. Thermodynamics of inhomogeneously mass-deformed ABJM model and pressure anisotropy. J. High Energ. Phys. 2020, 62 (2020). https://doi.org/10.1007/JHEP02(2020)062
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DOI: https://doi.org/10.1007/JHEP02(2020)062