Abstract
We construct the D3-brane dual to a k-quark of \( \mathcal{N}=4 \) super-Yang-Mills theory in the totally symmetric representation of SU(N ), undergoing arbitrary motion. Our method of construction generalizes previous work by Mikhailov, and proceeds by shooting light rays inward from the anti-de Sitter boundary, to trace out the brane embedding. We expect this method to have wider relevance, and provide evidence for this by showing that it correctly reproduces the known D5-brane embeddings dual to totally antisymmetric k-quarks. As an application of our solutions, we compute the energy of the D3-brane and extract from it the k-quark’s intrinsic energy and rate of radiation. The result matches expectations based on previous calculations, and makes contact with the exact Bremsstrahlung function for the fundamental representation.
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References
A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in \( \mathcal{N}=4 \) super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].
B. Fiol, B. Garolera and A. Lewkowycz, Exact results for static and radiative fields of a quark in \( \mathcal{N}=4 \) super Yang-Mills, JHEP 05 (2012) 093 [arXiv:1202.5292] [INSPIRE].
A. Lewkowycz and J. Maldacena, Exact results for the entanglement entropy and the energy radiated by a quark, JHEP 05 (2014) 025 [arXiv:1312.5682] [INSPIRE].
B. Fiol, B. Garolera and G. Torrents, Exact momentum fluctuations of an accelerated quark in \( \mathcal{N}=4 \) super Yang-Mills, JHEP 06 (2013) 011 [arXiv:1302.6991] [INSPIRE].
J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].
N. Drukker and D.J. Gross, An exact prediction of \( \mathcal{N}=4 \) SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [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].
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].
A. Mikhailov, Nonlinear waves in AdS/CFT correspondence, hep-th/0305196 [INSPIRE].
M. Chernicoff and A. Güijosa, Acceleration, energy loss and screening in strongly-coupled gauge theories, JHEP 06 (2008) 005 [arXiv:0803.3070] [INSPIRE].
M. Kruczenski, A note on twist two operators in \( \mathcal{N}=4 \) SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large-N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Vacua, propagators and holographic probes in AdS/CFT, JHEP 01 (1999) 002 [hep-th/9812007] [INSPIRE].
C.G. Callan Jr. and A. Güijosa, Undulating strings and gauge theory waves, Nucl. Phys. B 565 (2000) 157 [hep-th/9906153] [INSPIRE].
M. Chernicoff, A. Güijosa and J.F. Pedraza, The gluonic field of a heavy quark in conformal field theories at strong coupling, JHEP 10 (2011) 041 [arXiv:1106.4059] [INSPIRE].
C. Athanasiou, P.M. Chesler, H. Liu, D. Nickel and K. Rajagopal, Synchrotron radiation in strongly coupled conformal field theories, Phys. Rev. D 81 (2010) 126001 [Erratum ibid. D 84 (2011) 069901] [arXiv:1001.3880] [INSPIRE].
Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Radiation by a heavy quark in \( \mathcal{N}=4 \) SYM at strong coupling, Nucl. Phys. B 850 (2011) 31 [arXiv:1102.0232] [INSPIRE].
C.A. Agón, A. Güijosa and J.F. Pedraza, Radiation and a dynamical UV/IR connection in AdS/CFT, JHEP 06 (2014) 043 [arXiv:1402.5961] [INSPIRE].
B.-W. Xiao, On the exact solution of the accelerating string in AdS 5 space, Phys. Lett. B 665 (2008) 173 [arXiv:0804.1343] [INSPIRE].
E. Cáceres, M. Chernicoff, A. Güijosa and J.F. Pedraza, Quantum fluctuations and the Unruh effect in strongly-coupled conformal field theories, JHEP 06 (2010) 078 [arXiv:1003.5332] [INSPIRE].
S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006) 037 [hep-th/0603208] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
C.G. Callan Jr., A. Güijosa and K.G. Savvidy, Baryons and string creation from the five-brane world volume action, Nucl. Phys. B 547 (1999) 127 [hep-th/9810092] [INSPIRE].
J. Pawelczyk and S.-J. Rey, Ramond-Ramond flux stabilization of D-branes, Phys. Lett. B 493 (2000) 395 [hep-th/0007154] [INSPIRE].
S.A. Hartnoll, Two universal results for Wilson loops at strong coupling, Phys. Rev. D 74 (2006) 066006 [hep-th/0606178] [INSPIRE].
B. Fiol and B. Garolera, Energy loss of an infinitely massive half-Bogomol’nyi-Prasad-Sommerfeld particle by radiation to all orders in 1/N , Phys. Rev. Lett. 107 (2011) 151601 [arXiv:1106.5418] [INSPIRE].
B. Fiol and G. Torrents, Exact results for Wilson loops in arbitrary representations, JHEP 01 (2014) 020 [arXiv:1311.2058] [INSPIRE].
J. Gomis and F. Passerini, Wilson loops as D3-branes, JHEP 01 (2007) 097 [hep-th/0612022] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
S. Giombi, R. Ricci and D. Trancanelli, Operator product expansion of higher rank Wilson loops from D-branes and matrix models, JHEP 10 (2006) 045 [hep-th/0608077] [INSPIRE].
A. Faraggi, J.T. Liu, L.A. Pando Zayas and G. Zhang, One-loop structure of higher rank Wilson loops in AdS/CFT, Phys. Lett. B 740 (2014) 218 [arXiv:1409.3187] [INSPIRE].
M. Chernicoff, J.A. García and A. Güijosa, Generalized Lorentz-Dirac equation for a strongly-coupled gauge theory, Phys. Rev. Lett. 102 (2009) 241601 [arXiv:0903.2047] [INSPIRE].
M. Chernicoff, J.A. García and A. Güijosa, A tail of a quark in \( \mathcal{N}=4 \) SYM, JHEP 09 (2009) 080 [arXiv:0906.1592] [INSPIRE].
V.E. Hubeny, Relativistic beaming in AdS/CFT, arXiv:1011.1270 [INSPIRE].
V.E. Hubeny, Holographic dual of collimated radiation, New J. Phys. 13 (2011) 035006 [arXiv:1012.3561] [INSPIRE].
C.A. Agón, A. Güijosa and B.O. Larios, On the beaming of gluonic fields at strong coupling, JHEP 12 (2012) 101 [arXiv:1206.5005] [INSPIRE].
Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Aspects of the UV/IR correspondence: energy broadening and string fluctuations, JHEP 02 (2011) 065 [arXiv:1011.3763] [INSPIRE].
A. Güijosa and J.F. Pedraza, Early-time energy loss in a strongly-coupled SYM plasma, JHEP 05 (2011) 108 [arXiv:1102.4893] [INSPIRE].
S.S. Gubser, D.R. Gulotta, S.S. Pufu and F.D. Rocha, Gluon energy loss in the gauge-string duality, JHEP 10 (2008) 052 [arXiv:0803.1470] [INSPIRE].
P.M. Chesler, K. Jensen and A. Karch, Jets in strongly-coupled \( \mathcal{N}=4 \) super Yang-Mills theory, Phys. Rev. D 79 (2009) 025021 [arXiv:0804.3110] [INSPIRE].
P.M. Chesler, K. Jensen, A. Karch and L.G. Yaffe, Light quark energy loss in strongly-coupled \( \mathcal{N}=4 \) supersymmetric Yang-Mills plasma, Phys. Rev. D 79 (2009) 125015 [arXiv:0810.1985] [INSPIRE].
P. Arnold and D. Vaman, Jet quenching in hot strongly coupled gauge theories simplified, JHEP 04 (2011) 027 [arXiv:1101.2689] [INSPIRE].
R. Morad and W.A. Horowitz, Strong-coupling jet energy loss from AdS/CFT, JHEP 11 (2014) 017 [arXiv:1409.7545] [INSPIRE].
A. Stoffers and I. Zahed, Holographic jets in an expanding plasma, Phys. Rev. C 86 (2012) 054905 [arXiv:1110.2943] [INSPIRE].
K. Zarembo, Supersymmetric Wilson loops, Nucl. Phys. B 643 (2002) 157 [hep-th/0205160] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, On the D3-brane description of some 1/4 BPS Wilson loops, JHEP 04 (2007) 008 [hep-th/0612168] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, More supersymmetric Wilson loops, Phys. Rev. D 76 (2007) 107703 [arXiv:0704.2237] [INSPIRE].
N. Drukker, S. Giombi, R. Ricci and D. Trancanelli, Supersymmetric Wilson loops on S 3, JHEP 05 (2008) 017 [arXiv:0711.3226] [INSPIRE].
M. Chernicoff and A. Güijosa, Energy loss of gluons, baryons and k-quarks in an \( \mathcal{N}=4 \) SYM plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].
J.M. Camino, A. Paredes and A.V. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
J.A. García, A. Güijosa and E.J. Pulido, No line on the horizon: on uniform acceleration and gluonic fields at strong coupling, JHEP 01 (2013) 096 [arXiv:1210.4175] [INSPIRE].
M. Chernicoff, A. Güijosa and J.F. Pedraza, Holographic EPR pairs, wormholes and radiation, JHEP 10 (2013) 211 [arXiv:1308.3695] [INSPIRE].
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman, San Francisco U.S.A. (2002).
V.E. Hubeny and G.W. Semenoff, String worldsheet for accelerating quark, arXiv:1410.1171 [INSPIRE].
V.E. Hubeny and G.W. Semenoff, Holographic accelerated heavy quark-anti-quark pair, arXiv:1410.1172 [INSPIRE].
A. Paredes, K. Peeters and M. Zamaklar, Temperature versus acceleration: the Unruh effect for holographic models, JHEP 04 (2009) 015 [arXiv:0812.0981] [INSPIRE].
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ArXiv ePrint: 1410.0692
Work done during a sabbatical year at the Department of Physics at Princeton University (Alberto Güijosa).
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Fiol, B., Güijosa, A. & Pedraza, J.F. Branes from light: embeddings and energetics for symmetric k-quarks in \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2015, 149 (2015). https://doi.org/10.1007/JHEP01(2015)149
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DOI: https://doi.org/10.1007/JHEP01(2015)149