Abstract
We compute the holographic entanglement entropy contribution from planar two-dimensional defects in six-dimensional \( \mathcal{N}=\left(2,0\right) \) superconformal field theory, holographically dual to probe M2- and M5-branes in AdS7 × S4. In particular, we test the viability of the universal contribution of the defect to entanglement entropy as a candidate C-function. We find that this coefficient is not monotonic under defect renormalization group flows triggered by the vacuum expectation value of a marginal operator. Another candidate C-function, the on-shell action inside the entanglement wedge, monotonically decreases under the flows we study.
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References
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].
J. Bagger and N. Lambert, Modeling multiple M 2’s, Phys. Rev. D 75 (2007) 045020 [hep-th/0611108] [INSPIRE].
A. Gustavsson, Algebraic structures on parallel M 2-branes, Nucl. Phys. B 811 (2009) 6 [arXiv:0709.1260] [INSPIRE].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M 2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [INSPIRE].
J. Bagger and N. Lambert, Comments on multiple M 2-branes, JHEP 02 (2008) 105 [arXiv:0712.3738] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M 2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Strominger, Open p-branes, Phys. Lett. B 383 (1996) 44 [hep-th/9512059] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [INSPIRE].
D. Freed, J.A. Harvey, R. Minasian and G.W. Moore, Gravitational anomaly cancellation for M-theory five-branes, Adv. Theor. Math. Phys. 2 (1998) 601 [hep-th/9803205] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
J.A. Harvey, R. Minasian and G.W. Moore, Non-Abelian tensor multiplet anomalies, JHEP 09 (1998) 004 [hep-th/9808060] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
W. Nahm, Supersymmetries and their representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
N. Wyllard, A N − 1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [INSPIRE].
O. Lunin, 1/2-BPS states in M-theory and defects in the dual CFTs, JHEP 10 (2007) 014 [arXiv:0704.3442] [INSPIRE].
B. Chen, W. He, J.-B. Wu and L. Zhang, M 5-branes and Wilson surfaces, JHEP 08 (2007) 067 [arXiv:0707.3978] [INSPIRE].
H. Mori and S. Yamaguchi, M5-branes and Wilson surfaces in AdS 7 /CFT 6 correspondence, Phys. Rev. D 90 (2014) 026005 [arXiv:1404.0930] [INSPIRE].
S.A. Gentle, M. Gutperle and C. Marasinou, Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory, JHEP 08 (2015) 019 [arXiv:1506.00052] [INSPIRE].
J. Estes et al., Wilson surface central charge from holographic entanglement entropy, arXiv:1812.00923 [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
H. Casini and M. Huerta, A c-theorem for the entanglement entropy, J. Phys. A 40 (2007) 7031 [cond-mat/0610375] [INSPIRE].
N. Kobayashi, T. Nishioka, Y. Sato and K. Watanabe, Towards a C-theorem in defect CFT, JHEP 01 (2019) 039 [arXiv:1810.06995] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-theorem: N = 2 field theories on the three-sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-theorem without supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
S.P. Kumar and D. Silvani, Holographic flows and thermodynamics of Polyakov loop impurities, JHEP 03 (2017) 107 [arXiv:1611.06033] [INSPIRE].
S.P. Kumar and D. Silvani, Entanglement of heavy quark impurities and generalized gravitational entropy, JHEP 01 (2018) 052 [arXiv:1711.01554] [INSPIRE].
J.M. Camino, A. Paredes and A.V. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].
A. Karch, B. Robinson and C.F. Uhlemann, Precision test of gauge-gravity duality with flavor, Phys. Rev. Lett. 115 (2015) 261601 [arXiv:1509.00013] [INSPIRE].
B. Robinson and C.F. Uhlemann, Supersymmetric D3/D5 for massive defects on curved space, JHEP 12 (2017) 143 [arXiv:1709.08650] [INSPIRE].
E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and eleven-dimensional supergravity, Phys. Lett. B 189 (1987) 75 [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [INSPIRE].
I.A. Bandos et al., Covariant action for the superfive-brane of M-theory, Phys. Rev. Lett. 78 (1997) 4332 [hep-th/9701149] [INSPIRE].
M. Aganagic, J. Park, C. Popescu and J.H. Schwarz, World volume action of the M-theory five-brane, Nucl. Phys. B 496 (1997) 191 [hep-th/9701166] [INSPIRE].
P.K. Townsend, D-branes from M-branes, Phys. Lett. B 373 (1996) 68 [hep-th/9512062] [INSPIRE].
J.H. Schwarz, Coupling a selfdual tensor to gravity in six-dimensions, Phys. Lett. B 395 (1997) 191 [hep-th/9701008] [INSPIRE].
S.-L. Ko, D. Sorokin and P. Vanichchapongjaroen, The M 5-brane action revisited, JHEP 11 (2013) 072 [arXiv:1308.2231] [INSPIRE].
I.A. Bandos et al., On the equivalence of different formulations of the M-theory five-brane, Phys. Lett. B 408 (1997) 135 [hep-th/9703127] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
J. Gomis and F. Passerini, Wilson loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].
K. Jensen and A. O’Bannon, Holography, entanglement entropy and conformal field theories with boundaries or defects, Phys. Rev. D 88 (2013) 106006 [arXiv:1309.4523] [INSPIRE].
A. Karch and C.F. Uhlemann, Generalized gravitational entropy of probe branes: flavor entanglement holographically, JHEP 05 (2014) 017 [arXiv:1402.4497] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
A. Rényi, On measures of entropy and information, in the proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability , June 20-July 30, Berkeley U.S.A. (1961).
J.C. Baez, Renyi entropy and free energy, arXiv:1102.2098.
L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic calculations of Renyi entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [INSPIRE].
D.S. Berman and J.A. Harvey, The self-dual string and anomalies in the M 5-brane, JHEP 11 (2004) 015 [hep-th/0408198] [INSPIRE].
C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021] [INSPIRE].
J. Gomis, A.V. Ramallo, J. Simon and P.K. Townsend, Supersymmetric baryonic branes, JHEP 11 (1999) 019 [hep-th/9907022] [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].
A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [INSPIRE].
D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative entropy and holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
P.S. Howe, N.D. Lambert and P.C. West, The selfdual string soliton, Nucl. Phys. B 515 (1998) 203 [hep-th/9709014] [INSPIRE].
J.P. Gauntlett et al., Finite energy Dirac-Born-Infeld monopoles and string junctions, Phys. Rev. D 60 (1999) 045004 [hep-th/9903156] [INSPIRE].
B. Chen, The self-dual string soliton in AdS 4 × S 7 spacetime, Eur. Phys. J. C 54 (2008) 489 [arXiv:0710.2593] [INSPIRE].
S. Kobayashi et al., Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS 7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [INSPIRE].
D. Gaiotto and A. Tomasiello, Holography for (1, 0) theories in six dimensions, JHEP 12 (2014) 003 [arXiv:1404.0711] [INSPIRE].
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Rodgers, R. Holographic entanglement entropy from probe M-theory branes. J. High Energ. Phys. 2019, 92 (2019). https://doi.org/10.1007/JHEP03(2019)092
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DOI: https://doi.org/10.1007/JHEP03(2019)092