Abstract
We consider the Bremsstrahlung function associated to a 1/6-BPS Wilson loop in ABJM theory, with a cusp in the couplings to scalar fields. We non-trivially extend its recent four-loop computation at weak coupling to include non-planar corrections. We have recently proposed a conjecture relating this object to supersymmetric circular Wilson loops with multiple windings, which can be computed via localization. We find agreement between this proposal and the perturbative computation of the Bremsstrahlung function, including color sub-leading corrections. This supports the conjecture and hints at its validity beyond the planar approximation.
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O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N} \) = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [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].
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].
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].
D. Berenstein and D. Trancanelli, Three-dimensional \( \mathcal{N} \) = 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].
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].
M.S. Bianchi and A. Mauri, ABJM θ-Bremsstrahlung at four loops and beyond, arXiv:1709.01089 [INSPIRE].
A. Grozin, J. Henn and M. Stahlhofen, On the Casimir scaling violation in the cusp anomalous dimension at small angle, JHEP 10 (2017) 052 [arXiv:1708.01221] [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].
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, A. Mauri, S. Penati, M. Preti and D. Seminara, Towards the exact Bremsstrahlung function of ABJM theory, JHEP 08 (2017) 022 [arXiv:1705.10780] [INSPIRE].
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].
D.H. Correa, J. Aguilera-Damia and G.A. Silva, Strings in \( Ad{S}_4\times \mathbb{C}{\mathrm{\mathbb{P}}}^3 \) Wilson loops in \( \mathcal{N} \) = 6 super Chern-Simons-matter and bremsstrahlung functions, JHEP 06 (2014) 139 [arXiv:1405.1396] [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].
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].
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].
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].
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].
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, 1/2 BPS Wilson loop in N = 6 superconformal Chern-Simons theory at two loops, Phys. Rev. D 88 (2013) 026009 [arXiv:1303.6939] [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, 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, A note on multiply wound BPS Wilson loops in ABJM, JHEP 09 (2016) 047 [arXiv:1605.01025] [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].
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].
N. Gromov and F. Levkovich-Maslyuk, Quantum Spectral Curve for a cusped Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 04 (2016) 134[arXiv:1510.02098][INSPIRE].
A.G. Grozin, Lectures on multiloop calculations, Int. J. Mod. Phys. A 19 (2004) 473 [hep-ph/0307297] [INSPIRE].
K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, New Approach to Evaluation of Multiloop Feynman Integrals: The Gegenbauer Polynomial x Space Technique, Nucl. Phys. B 174 (1980) 345 [INSPIRE].
D. Young, ABJ(M) Chiral Primary Three-Point Function at Two-loops, JHEP 07 (2014) 120 [arXiv:1404.1117] [INSPIRE].
J.A. Minahan, O. Ohlsson Sax and C. Sieg, Anomalous dimensions at four loops in N = 6 superconformal Chern-Simons theories, Nucl. Phys. B 846 (2011) 542 [arXiv:0912.3460] [INSPIRE].
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Bianchi, M.S., Mauri, A. ABJM θ-Bremsstrahlung at four loops and beyond: non-planar corrections. J. High Energ. Phys. 2017, 166 (2017). https://doi.org/10.1007/JHEP11(2017)166
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DOI: https://doi.org/10.1007/JHEP11(2017)166