Abstract
In this paper we study the Bremsstrahlung functions for the \( \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} \) and the \( \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} \) Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric (B φ1/6 ) and R-symmetry (B θ1/6 ) deformations of the \( \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} \) Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for B θ1/6 based on a known result for B φ1/6 . Subsequently, we explore the consequences of this relation for the \( \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} \) Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function h(λ). During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.
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References
V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [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].
M. Cooke, A. Dekel and N. Drukker, The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines, J. Phys. A 50 (2017) 335401 [arXiv:1703.03812] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS 2 /CFT 1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
B. Fiol, B. Garolera and A. Lewkowycz, Exact results for static and radiative fields of a quark in N = 4 super Yang-Mills, JHEP 05 (2012) 093 [arXiv:1202.5292] [INSPIRE].
V. Pestun, Localization of the four-dimensional N = 4 SYM to a two-sphere and 1/8 BPS Wilson loops, JHEP 12 (2012) 067 [arXiv:0906.0638] [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].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [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].
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].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [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].
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].
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].
T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
J.A. Minahan, O. Ohlsson Sax and C. Sieg, Magnon dispersion to four loops in the ABJM and ABJ models, J. Phys. A 43 (2010) 275402 [arXiv:0908.2463] [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].
M. Leoni et al., Superspace calculation of the four-loop spectrum in N = 6 supersymmetric Chern-Simons theories, JHEP 12 (2010) 074 [arXiv:1010.1756] [INSPIRE].
T. McLoughlin, R. Roiban and A.A. Tseytlin, Quantum spinning strings in AdS 4 × CP 3 : testing the Bethe ansatz proposal, JHEP 11 (2008) 069 [arXiv:0809.4038] [INSPIRE].
M.C. Abbott, I. Aniceto and D. Bombardelli, Quantum strings and the AdS 4 /CFT 3 interpolating function, JHEP 12 (2010) 040 [arXiv:1006.2174] [INSPIRE].
C. Lopez-Arcos and H. Nastase, Eliminating ambiguities for quantum corrections to strings moving in AdS 4 × ℂℙ3, Int. J. Mod. Phys. A 28 (2013) 1350058 [arXiv:1203.4777] [INSPIRE].
L. Bianchi et al., Two-loop cusp anomaly in ABJM at strong coupling, JHEP 10 (2014) 013 [arXiv:1407.4788] [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. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [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].
N. Drukker and D. Trancanelli, A supermatrix model for N = 6 super Chern-Simons-matter theory, JHEP 02 (2010) 058 [arXiv:0912.3006] [INSPIRE].
V. Cardinali, L. Griguolo, G. Martelloni and D. Seminara, New supersymmetric Wilson loops in ABJ(M) theories, Phys. Lett. B 718 (2012) 615 [arXiv:1209.4032] [INSPIRE].
A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [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].
L. Griguolo et al., The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories, JHEP 05 (2013) 113 [arXiv:1208.5766] [INSPIRE].
D.H. Correa, J. Aguilera-Damia and G.A. Silva, Strings in AdS 4 × ℂℙ3 Wilson loops in \( \mathcal{N}=6 \) super Chern-Simons-matter and bremsstrahlung functions,JHEP 06(2014) 139 [arXiv:1405.1396] [INSPIRE].
M.S. Bianchi et al., BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis, JHEP 06 (2014) 123 [arXiv:1402.4128] [INSPIRE].
M.S. Bianchi et al., Towards the exact Bremsstrahlung function of ABJM theory, JHEP 08 (2017) 022 [arXiv:1705.10780] [INSPIRE].
L. Bianchi, L. Griguolo, M. Preti and D. Seminara, Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation, JHEP 10 (2017) 050 [arXiv:1706.06590] [INSPIRE].
M.S. Bianchi et al., Framing and localization in Chern-Simons theories with matter, JHEP 06 (2016) 133 [arXiv:1604.00383] [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. 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].
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 and A. Mauri, ABJM θ-Bremsstrahlung at four loops and beyond, JHEP 11 (2017) 173 [arXiv:1709.01089] [INSPIRE].
M.S. Bianchi and A. Mauri, ABJM θ-Bremsstrahlung at four loops and beyond: non-planar corrections, JHEP 11 (2017) 166 [arXiv:1709.10092] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, Multiplets of superconformal symmetry in diverse dimensions, arXiv:1612.00809 [INSPIRE].
P. Liendo and C. Meneghelli, Bootstrap equations for \( \mathcal{N}=4 \) SYM with defects, JHEP 01 (2017) 122 [arXiv:1608.05126] [INSPIRE].
R. Blumenhagen, N = 2 supersymmetric W algebras, Nucl. Phys. B 405 (1993) 744 [hep-th/9208069] [INSPIRE].
P. Di Vecchia, J.L. Petersen and H.B. Zheng, N = 2 extended superconformal theories in two-dimensions, Phys. Lett. B 162 (1985) 327.
G. Mussardo, G. Sotkov and M. Stanishkov, N = 2 superconformal minimal models, Int. J. Mod. Phys. A 4 (1989) 1135 [INSPIRE].
M. Cornagliotto, M. Lemos and V. Schomerus, Long multiplet bootstrap, JHEP 10 (2017) 119 [arXiv:1702.05101] [INSPIRE].
A.L. Fitzpatrick et al., Covariant approaches to superconformal blocks, JHEP 08 (2014) 129 [arXiv:1402.1167] [INSPIRE].
M.A. Bandres, A.E. Lipstein and J.H. Schwarz, Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry, JHEP 09 (2008) 027 [arXiv:0807.0880] [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].
K.-M. Lee and S. Lee, 1/2-BPS Wilson loops and vortices in ABJM model, JHEP 09 (2010) 004 [arXiv:1006.5589] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
N. Gromov and P. Vieira, The all loop AdS 4 /CFT 3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [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. Preti, WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory, Comput. Phys. Commun. 227 (2018) 126 [arXiv:1707.08108] [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].
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].
L. Bianchi, M. Meineri, R.C. Myers and M. Smolkin, Rényi entropy and conformal defects, JHEP 07 (2016) 076 [arXiv:1511.06713] [INSPIRE].
L. Bianchi et al., Shape dependence of holographic Rényi entropy in general dimensions, JHEP 11 (2016) 180 [arXiv:1607.07418] [INSPIRE].
M. Lemos, P. Liendo, M. Meineri and S. Sarkar, Universality at large transverse spin in defect CFT, arXiv:1712.08185 [INSPIRE].
S. Balakrishnan, T. Faulkner, Z.U. Khandker and H. Wang, A general proof of the quantum null energy condition, arXiv:1706.09432 [INSPIRE].
X. Dong, Shape dependence of holographic Rényi entropy in conformal field theories, Phys. Rev. Lett. 116 (2016) 251602 [arXiv:1602.08493] [INSPIRE].
S. Balakrishnan, S. Dutta and T. Faulkner, Gravitational dual of the Rényi twist displacement operator, Phys. Rev. D 96 (2017) 046019 [arXiv:1607.06155] [INSPIRE].
C.P. Herzog and K.-W. Huang, Boundary conformal field theory and a boundary central charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [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].
M.S. Bianchi, A note on multiply wound BPS Wilson loops in ABJM, JHEP 09 (2016) 047 [arXiv:1605.01025] [INSPIRE].
M.S. Bianchi et al., A matrix model for the latitude Wilson loop in ABJM theory, arXiv:1802.07742 [INSPIRE].
M. Mariño, Chern-Simons theory, matrix integrals and perturbative three manifold invariants, Commun. Math. Phys. 253 (2004) 25 [hep-th/0207096] [INSPIRE].
I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, Academic Press, U.S.A. (2007).
E. Vescovi, Perturbative and non-perturbative approaches to string sigma-models in AdS/CFT, Springer, Germany (2017).
B. Basso, An exact slope for AdS/CFT, arXiv:1109.3154 [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum Spectral Curve of the \( \mathcal{N}=6 \) Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
D. Bombardelli, D. Fioravanti and R. Tateo, TBA and Y-system for planar AdS 4 /CFT 3, Nucl. Phys. B 834 (2010) 543 [arXiv:0912.4715] [INSPIRE].
N. Gromov and F. Levkovich-Maslyuk, Y-system, TBA and quasi-classical strings in AdS 4 × CP 3, JHEP 06 (2010) 088 [arXiv:0912.4911] [INSPIRE].
D. Bombardelli et al., The full Quantum Spectral Curve for AdS 4 /CFT 3, JHEP 09 (2017) 140 [arXiv:1701.00473] [INSPIRE].
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Bianchi, L., Preti, M. & Vescovi, E. Exact Bremsstrahlung functions in ABJM theory. J. High Energ. Phys. 2018, 60 (2018). https://doi.org/10.1007/JHEP07(2018)060
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DOI: https://doi.org/10.1007/JHEP07(2018)060