Abstract
We consider a \( \frac{1}{2} \)-BPS solution for a D3 brane probe in AdS5 × S5 that has world-volume geometry of AdS3 × S1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary \( \mathcal{N} \) = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a \( \frac{1}{2} \)-BPS M5 brane probe solution in AdS7 × S4 with the world-volume geometry of AdS5 × S1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N2 term in a-anomaly of the supersymmetric S4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S4 defect a-anomaly coefficient.
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N. Andrei et al., Boundary and Defect CFT: Open Problems and Applications, J. Phys. A 53 (2020) 453002 [arXiv:1810.05697] [INSPIRE].
K. Jensen, A. O’Bannon, B. Robinson and R. Rodgers, From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects, Phys. Rev. Lett. 122 (2019) 241602 [arXiv:1812.08745] [INSPIRE].
A. Chalabi, A. O’Bannon, B. Robinson and J. Sisti, Central charges of 2d superconformal defects, JHEP 05 (2020) 095 [arXiv:2003.02857] [INSPIRE].
Y. Wang, Defect a-theorem and a-maximization, JHEP 02 (2022) 061 [arXiv:2101.12648] [INSPIRE].
N. Drukker, S. Giombi, A.A. Tseytlin and X. Zhou, Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7×S4, JHEP 07 (2020) 101 [arXiv:2004.04562] [INSPIRE].
A. Chalabi et al., Weyl anomalies of four dimensional conformal boundaries and defects, JHEP 02 (2022) 166 [arXiv:2111.14713] [INSPIRE].
N. Drukker, O. Shahpo and M. Trépanier, Quantum holographic surface anomalies, J. Phys. A 57 (2024) 085402 [arXiv:2311.14797] [INSPIRE].
P. Capuozzo, J. Estes, B. Robinson and B. Suzzoni, Holographic Weyl anomalies for 4d defects in 6d SCFTs, JHEP 04 (2024) 120 [arXiv:2310.17447] [INSPIRE].
N.R. Constable, J. Erdmenger, Z. Guralnik and I. Kirsch, Intersecting D-3 branes and holography, Phys. Rev. D 68 (2003) 106007 [hep-th/0211222] [INSPIRE].
N. Drukker, J. Gomis and S. Matsuura, Probing N = 4 SYM With Surface Operators, JHEP 10 (2008) 048 [arXiv:0805.4199] [INSPIRE].
E. D’Hoker et al., Half-BPS supergravity solutions and superalgebras, JHEP 12 (2008) 047 [arXiv:0810.1484] [INSPIRE].
N. Drukker, J. Gomis and D. Young, Vortex Loop Operators, M2-branes and Holography, JHEP 03 (2009) 004 [arXiv:0810.4344] [INSPIRE].
M. Gutperle and C.F. Uhlemann, Janus on the Brane, JHEP 07 (2020) 243 [arXiv:2003.12080] [INSPIRE].
V. Gupta, Holographic M5 branes in AdS7 × S4, JHEP 12 (2021) 032 [Erratum ibid. 02 (2023) 026] [arXiv:2109.08551] [INSPIRE].
N. Drukker and O. Shahpo, Vortex loop operators and quantum M2-branes, arXiv:2312.17091 [INSPIRE].
O. Lunin, 1/2-BPS states in M theory and defects in the dual CFTs, JHEP 10 (2007) 014 [arXiv:0704.3442] [INSPIRE].
S. Giombi and A.A. Tseytlin, Wilson Loops at Large N and the Quantum M2-Brane, Phys. Rev. Lett. 130 (2023) 201601 [arXiv:2303.15207] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Instanton contributions to the ABJM free energy from quantum M2 branes, JHEP 10 (2023) 029 [arXiv:2307.14112] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, (2,0) theory on S5 × S1 and quantum M2 branes, Nucl. Phys. B 998 (2024) 116400 [arXiv:2309.10786] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Large N expansion of superconformal index of k = 1 ABJM theory and semiclassical M5 brane partition function, Nucl. Phys. B 1001 (2024) 116507 [arXiv:2312.01917] [INSPIRE].
M. Sakaguchi, H. Shin and K. Yoshida, Semiclassical Analysis of M2-brane in AdS4 × S7/Zk, JHEP 12 (2010) 012 [arXiv:1007.3354] [INSPIRE].
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
R. Camporesi and A. Higuchi, The Plancherel measure for p-forms in real hyperbolic spaces, J. Geom. Phys. 15 (1994) 57.
S. Giombi, A. Maloney and X. Yin, One-loop Partition Functions of 3D Gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].
S. Giombi et al., AdS Description of Induced Higher-Spin Gauge Theory, JHEP 10 (2013) 016 [arXiv:1306.5242] [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
S. Giombi, I.R. Klebanov and B.R. Safdi, Higher Spin AdSd+1/CFTd at One Loop, Phys. Rev. D 89 (2014) 084004 [arXiv:1401.0825] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP 11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
K. Skenderis and M. Taylor, Branes in AdS and p p wave space-times, JHEP 06 (2002) 025 [hep-th/0204054] [INSPIRE].
A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].
E.I. Buchbinder and A.A. Tseytlin, 1/N correction in the D3-brane description of a circular Wilson loop at strong coupling, Phys. Rev. D 89 (2014) 126008 [arXiv:1404.4952] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
L. Martucci, J. Rosseel, D. Van den Bleeken and A. Van Proeyen, Dirac actions for D-branes on backgrounds with fluxes, Class. Quant. Grav. 22 (2005) 2745 [hep-th/0504041] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Supersymmetric D3-brane action in AdS5 × S5, Phys. Lett. B 436 (1998) 281 [hep-th/9806095] [INSPIRE].
O. Aharony, M. Berkooz, A. Karasik and T. Vaknin, Supersymmetric field theories on AdSp × Sq, JHEP 04 (2016) 066 [arXiv:1512.04698] [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.S. Howe, E. Sezgin, P.C. West and M. Dine, Covariant field equations of the M-theory five-brane, Phys. Lett. B 399 (1997) 49 [hep-th/9702008] [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].
L. Santilli and C.F. Uhlemann, 3d defects in 5d: RG flows and defect F-maximization, JHEP 06 (2023) 136 [arXiv:2305.01004] [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].
P. Claus, Super M-brane actions in AdS4 × S7 and AdS7 × S4, Phys. Rev. D 59 (1999) 066003 [hep-th/9809045] [INSPIRE].
P. Claus, R. Kallosh and A. Van Proeyen, M five-brane and superconformal (0,2) tensor multiplet in six-dimensions, Nucl. Phys. B 518 (1998) 117 [hep-th/9711161] [INSPIRE].
B. de Wit, K. Peeters, J. Plefka and A. Sevrin, The M theory two-brane in AdS4 × S7 and AdS7 × S4, Phys. Lett. B 443 (1998) 153 [hep-th/9808052] [INSPIRE].
M. Sakaguchi and K. Yoshida, Open M-branes on AdS4/7 × S7/4 revisited, Nucl. Phys. B 714 (2005) 51 [hep-th/0405109] [INSPIRE].
E. Cremmer and B. Julia, The SO(8) Supergravity, Nucl. Phys. B 159 (1979) 141 [INSPIRE].
Y.N. Obukhov, The geometric approach to antisymmetric tensor field theory, Phys. Lett. B 109 (1982) 195 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Quantum Properties of Higher Dimensional and Dimensionally Reduced Supersymmetric Theories, Nucl. Phys. B 227 (1983) 252 [INSPIRE].
F. Bastianelli, S. Frolov and A.A. Tseytlin, Conformal anomaly of (2,0) tensor multiplet in six-dimensions and AdS/CFT correspondence, JHEP 02 (2000) 013 [hep-th/0001041] [INSPIRE].
J.R. David and J. Mukherjee, Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms, JHEP 01 (2021) 202 [arXiv:2005.08402] [INSPIRE].
J.R. David and J. Mukherjee, Partition functions of p-forms from Harish-Chandra characters, JHEP 09 (2021) 094 [arXiv:2105.03662] [INSPIRE].
R.R. Metsaev, Lowest eigenvalues of the energy operator for totally (anti)symmetric massless fields of the n-dimensional anti-de Sitter group, Class. Quant. Grav. 11 (1994) L141 [INSPIRE].
R.R. Metsaev, Massive totally symmetric fields in AdSd, Phys. Lett. B 590 (2004) 95 [hep-th/0312297] [INSPIRE].
R.R. Metsaev, Fermionic fields in the d-dimensional anti-de Sitter space-time, Phys. Lett. B 419 (1998) 49 [hep-th/9802097] [INSPIRE].
S. Gukov, Comments on N = 2 AdS orbifolds, Phys. Lett. B 439 (1998) 23 [hep-th/9806180] [INSPIRE].
O. Aharony, M. Berkooz and S.-J. Rey, Rigid holography and six-dimensional \( \mathcal{N} \) = (2, 0) theories on AdS5 × 𝕊1, JHEP 03 (2015) 121 [arXiv:1501.02904] [INSPIRE].
H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP 05 (2013) 144 [arXiv:1206.6339] [INSPIRE].
M. Beccaria and A. Cabo-Bizet, Large N Schur index of N = 4 SYM from semiclassical D3 brane, JHEP 04 (2024) 110 [arXiv:2402.12172].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
H. Lu, C.N. Pope and J. Rahmfeld, A Construction of Killing spinors on Sn, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [INSPIRE].
E. Bergshoeff, R. Kallosh, T. Ortin and G. Papadopoulos, Kappa symmetry, supersymmetry and intersecting branes, Nucl. Phys. B 502 (1997) 149 [hep-th/9705040] [INSPIRE].
J. Simon, Brane Effective Actions, Kappa-Symmetry and Applications, Living Rev. Rel. 15 (2012) 3 [arXiv:1110.2422] [INSPIRE].
Acknowledgments
We are grateful to M. Beccaria, N. Drukker, S. Giombi, C. Herzog and R. Metsaev for useful discussions and comments, and also thank O. Aharony, A. Chalabi and D. Sorokin for related correspondence. This work was supported in part by the STFC Consolidated Grant ST/T000791/1.
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ArXiv ePrint: 2402.07881
Arkady A. Tseytlin is also at Institute for Theoretical and Mathematical Physics (ITMP) of Moscow University and Lebedev Institute, Moscow, Russia
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Jiang, H., Tseytlin, A.A. On co-dimension 2 defect anomalies in \( \mathcal{N} \) = 4 SYM and (2,0) theory via brane probes in AdS/CFT. J. High Energ. Phys. 2024, 280 (2024). https://doi.org/10.1007/JHEP07(2024)280
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DOI: https://doi.org/10.1007/JHEP07(2024)280