Abstract
We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.S. Bianchi, L. Griguolo, M. Leoni, S. Penati and D. Seminara, BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis, JHEP 06 (2014) 123 [arXiv:1402.4128] [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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [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].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
A. Kapustin, B. Willett and I. Yaakov, Exact results for Wilson loops in superconformal Chern-Simons theories with matter, JHEP 03 (2010) 089 [arXiv:0909.4559] [INSPIRE].
J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in 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 N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
D. Correa, J. Henn, J. Maldacena and A. Sever, An exact formula for the radiation of a moving quark in N = 4 super Yang-Mills, JHEP 06 (2012) 048 [arXiv:1202.4455] [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 V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
N. Gromov, V. Kazakov, A. Kozak and P. Vieira, Exact spectrum of anomalous dimensions of planar N = 4 supersymmetric Yang-Mills theory: TBA and excited states, Lett. Math. Phys. 91 (2010) 265 [arXiv:0902.4458] [INSPIRE].
G. Arutyunov and S. Frolov, Thermodynamic Bethe ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].
N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
N. Gromov and A. Sever, Analytic solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Analytic solution of Bremsstrahlung TBA II: turning on the sphere angle, JHEP 10 (2013) 036 [arXiv:1305.1944] [INSPIRE].
M. Bonini, L. Griguolo, M. Preti and D. Seminara, Bremsstrahlung function, leading Lüscher correction at weak coupling and localization, JHEP 02 (2016) 172 [arXiv:1511.05016] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for planar N = 4 super-Yang-Mills theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CF T 4, JHEP 09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in N = 4 SYM, JHEP 04 (2016) 134 [arXiv:1510.02098] [INSPIRE].
B. Fiol, E. Gerchkovitz and Z. Komargodski, Exact Bremsstrahlung function in N = 2 superconformal field theories, Phys. Rev. Lett. 116 (2016) 081601 [arXiv:1510.01332] [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].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M 2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
D. Berenstein and D. Trancanelli, Three-dimensional N = 6 SCFT’s and their membrane dynamics, Phys. Rev. D 78 (2008) 106009 [arXiv:0808.2503] [INSPIRE].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [INSPIRE].
B. Chen and J.-B. Wu, Supersymmetric Wilson loops in N = 6 super Chern-Simons-matter theory, Nucl. Phys. B 825 (2010) 38 [arXiv:0809.2863] [INSPIRE].
S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson loops in superconformal Chern-Simons theory and fundamental strings in anti-de Sitter supergravity dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [INSPIRE].
N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].
L. Griguolo, D. Marmiroli, G. Martelloni and D. Seminara, The generalized cusp in ABJ(M) N = 6 super Chern-Simons theories, JHEP 05 (2013) 113 [arXiv:1208.5766] [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].
M. Mariño and P. Putrov, Exact results in ABJM theory from topological strings, JHEP 06 (2010) 011 [arXiv:0912.3074] [INSPIRE].
N. Drukker, M. Mariño and P. Putrov, From weak to strong coupling in ABJM theory, Commun. Math. Phys. 306 (2011) 511 [arXiv:1007.3837] [INSPIRE].
V. Forini, V.G.M. Puletti and O. Ohlsson Sax, The generalized cusp in AdS 4 × CP 3 and more one-loop results from semiclassical strings, J. Phys. A 46 (2013) 115402 [arXiv:1204.3302] [INSPIRE].
J. Aguilera-Damia, D.H. Correa and G.A. Silva, Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM, JHEP 03 (2015) 002 [arXiv:1412.4084] [INSPIRE].
D.H. Correa, J. Aguilera-Damia and G.A. Silva, Strings in AdS 4 × CP 3 Wilson loops in N = 6 super Chern-Simons-matter and Bremsstrahlung functions, JHEP 06 (2014) 139 [arXiv:1405.1396] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
J.-L. Gervais and A. Neveu, The slope of the leading Regge trajectory in quantum chromodynamics, Nucl. Phys. B 163 (1980) 189 [INSPIRE].
V.S. Dotsenko and S.N. Vergeles, Renormalizability of phase factors in the non-Abelian gauge theory, Nucl. Phys. B 169 (1980) 527 [INSPIRE].
I. Ya. Arefeva, Quantum contour field equations, Phys. Lett. B 93 (1980) 347 [INSPIRE].
J.G.M. Gatheral, Exponentiation of eikonal cross-sections in non-Abelian gauge theories, Phys. Lett. B 133 (1983) 90 [INSPIRE].
A. Klemm, M. Mariño, M. Schiereck and M. Soroush, Aharony-Bergman-Jafferis-Maldacena Wilson loops in the Fermi gas approach, Z. Naturforsch. A 68 (2013) 178 [arXiv:1207.0611] [INSPIRE].
M.S. Bianchi, L. Griguolo, M. Leoni, A. Mauri, S. Penati and D. Seminara, Framing and localization in Chern-Simons theories with matter, JHEP 06 (2016) 133 [arXiv:1604.00383] [INSPIRE].
M.S. Bianchi, L. Griguolo, M. Leoni, A. Mauri, S. Penati and D. Seminara, The quantum 1/2 BPS Wilson loop in N = 4 Chern-Simons-matter theories, JHEP 09 (2016) 009 [arXiv:1606.07058] [INSPIRE].
K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, New approach to evaluation of multiloop Feynman integrals: the Gegenbauer polynomial × space technique, Nucl. Phys. B 174 (1980) 345 [INSPIRE].
A. Mauri, A. Santambrogio and S. Scoleri, The leading order dressing phase in ABJM theory, JHEP 04 (2013) 146 [arXiv:1301.7732] [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, Three loop cusp anomalous dimension in QCD, Phys. Rev. Lett. 114 (2015) 062006 [arXiv:1409.0023] [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP 01 (2016) 140 [arXiv:1510.07803] [INSPIRE].
W. Siegel, Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett. B 84 (1979) 193 [INSPIRE].
M.S. Bianchi, G. Giribet, M. Leoni and S. Penati, The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details, JHEP 10 (2013) 085 [arXiv:1307.0786] [INSPIRE].
L. Griguolo, G. Martelloni, M. Poggi and D. Seminara, Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 super Chern-Simons theories, JHEP 09 (2013) 157 [arXiv:1307.0787] [INSPIRE].
M.S. Bianchi, G. Giribet, M. Leoni and S. Penati, Light-like Wilson loops in ABJM and maximal transcendentality, JHEP 08 (2013) 111 [arXiv:1304.6085] [INSPIRE].
A.G. Grozin, Calculating three loop diagrams in heavy quark effective theory with integration by parts recurrence relations, JHEP 03 (2000) 013 [hep-ph/0002266] [INSPIRE].
K.G. Chetyrkin and A.G. Grozin, Three loop anomalous dimension of the heavy light quark current in HQET, Nucl. Phys. B 666 (2003) 289 [hep-ph/0303113] [INSPIRE].
F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
S. Laporta and E. Remiddi, The analytical value of the electron (g − 2) at order α 3 in QED, Phys. Lett. B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
A.V. Smirnov and V.A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun. 184 (2013) 2820 [arXiv:1302.5885] [INSPIRE].
A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
K.-M. Lee and S. Lee, 1/2-BPS Wilson loops and vortices in ABJM model, JHEP 09 (2010) 004 [arXiv:1006.5589] [INSPIRE].
M. Lietti, A. Mauri, S. Penati and J.-J. Zhang, String theory duals of Wilson loops from Higgsing, arXiv:1705.02322 [INSPIRE].
H. Dorn, Renormalization of path ordered phase factors and related hadron operators in gauge field theories, Fortsch. Phys. 34 (1986) 11 [INSPIRE].
N.S. Craigie and H. Dorn, On the renormalization and short distance properties of hadronic operators in QCD, Nucl. Phys. B 185 (1981) 204 [INSPIRE].
S. Aoyama, The renormalization of the string operator in QCD, Nucl. Phys. B 194 (1982) 513 [INSPIRE].
D. Knauss and K. Scharnhorst, Two loop renormalization of nonsmooth string operators in Yang-Mills theory, Annalen Phys. 41 (1984) 331 [INSPIRE].
M. Preti, WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory, arXiv:1707.08108 [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in N = 4 SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum spectral curve of the N = 6 supersymmetric Chern-Simons theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
D. Bombardelli, A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, The full quantum spectral curve for AdS 4 /CF T 3, arXiv:1701.00473 [INSPIRE].
T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
G. Grignani, T. Harmark and M. Orselli, The SU(2) × SU(2) sector in the string dual of N = 6 superconformal Chern-Simons theory, Nucl. Phys. B 810 (2009) 115 [arXiv:0806.4959] [INSPIRE].
D. Gaiotto, S. Giombi and X. Yin, Spin chains in N = 6 superconformal Chern-Simons-matter theory, JHEP 04 (2009) 066 [arXiv:0806.4589] [INSPIRE].
N. Gromov and G. Sizov, Exact slope and interpolating functions in N = 6 supersymmetric Chern-Simons theory, Phys. Rev. Lett. 113 (2014) 121601 [arXiv:1403.1894] [INSPIRE].
M. Bonini, L. Griguolo, M. Preti and D. Seminara, Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension, JHEP 05 (2016) 180 [arXiv:1603.00541] [INSPIRE].
M.S. Bianchi and M. Leoni, An exact limit of the Aharony-Bergman-Jafferis-Maldacena theory, Phys. Rev. D 94 (2016) 045011 [arXiv:1605.02745] [INSPIRE].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, On the exact interpolating function in ABJ theory, JHEP 12 (2016) 086 [arXiv:1605.04888] [INSPIRE].
J.M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [arXiv:1304.1806] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1705.10780
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bianchi, M.S., Griguolo, L., Mauri, A. et al. Towards the exact Bremsstrahlung function of ABJM theory. J. High Energ. Phys. 2017, 22 (2017). https://doi.org/10.1007/JHEP08(2017)022
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)022