Abstract
We compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the AdS 4 × ℂℙ3 action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the AdS 4 radius, with the cusp anomaly of \( \mathcal{N} \) = 4 SYM, and extract the two-loop contribution to the non-trivial integrable coupling h(λ) of ABJM theory. It coincides with the strong coupling expansion of the exact expression for h(λ) recently conjectured by Gromov and Sizov. Our work provides thus a non-trivial perturbative check for the latter, as well as evidence for two-loop UV-finiteness and quantum integrability of the Type IIA AdS 4 × ℂℙ3 superstring in this gauge.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for superconformal Chern-Simons, JHEP 09 (2008) 040 [arXiv:0806.3951] [INSPIRE].
N. Gromov and P. Vieira, The all loop AdS4/CFT3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [INSPIRE].
T. Klose, Review of AdS/CFT Integrability, Chapter IV.3: N = 6 Chern-Simons and Strings on AdS 4 × CP 3, Lett. Math. Phys. 99 (2012) 401 [arXiv:1012.3999] [INSPIRE].
A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, The Quantum Spectral Curve of the ABJM theory, Phys. Rev. Lett. 113 (2014) 021601 [arXiv:1403.1859] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semi-classical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
M. Kruczenski, A note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [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. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant Magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
T. Klose, T. McLoughlin, J.A. Minahan and K. Zarembo, World-sheet scattering in AdS 5 × S 5 at two loops, JHEP 08 (2007) 051 [arXiv:0704.3891] [INSPIRE].
D. Berenstein and D. Trancanelli, S-duality and the giant magnon dispersion relation, Eur. Phys. J. C 74 (2014) 2925 [arXiv:0904.0444] [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 \( \mathcal{N} \) = 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].
A.V. Belitsky, A.S. Gorsky and G.P. Korchemsky, Logarithmic scaling in gauge/string correspondence, Nucl. Phys. B 748 (2006) 24 [hep-th/0601112] [INSPIRE].
M. Kruczenski, R. Roiban, A. Tirziu and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS 5 × S 5, Nucl. Phys. B 791 (2008) 93 [arXiv:0707.4254] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
T. McLoughlin and R. Roiban, Spinning strings at one-loop in AdS 4 × CP 3, JHEP 12 (2008) 101 [arXiv:0807.3965] [INSPIRE].
L.F. Alday, G. Arutyunov and D. Bykov, Semiclassical Quantization of Spinning Strings in AdS 4 × CP 3, JHEP 11 (2008) 089 [arXiv:0807.4400] [INSPIRE].
C. Krishnan, AdS 4 /CFT 3 at One Loop, JHEP 09 (2008) 092 [arXiv:0807.4561] [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].
N. Gromov and V. Mikhaylov, Comment on the Scaling Function in AdS 4 × CP 3, JHEP 04 (2009) 083 [arXiv:0807.4897] [INSPIRE].
D. Astolfi, V.G.M. Puletti, G. Grignani, T. Harmark and M. Orselli, Finite-size corrections in the SU(2) × SU(2) sector of type IIA string theory on AdS 4 × CP 3, Nucl. Phys. B 810 (2009) 150 [arXiv:0807.1527] [INSPIRE].
M.A. Bandres and A.E. Lipstein, One-Loop Corrections to Type IIA String Theory in AdS 4 × CP 3, JHEP 04 (2010) 059 [arXiv:0911.4061] [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].
M.C. Abbott and P. Sundin, The Near-Flat-Space and BMN Limits for Strings in AdS 4 × CP 3 at One Loop, J. Phys. A 45 (2012) 025401 [arXiv:1106.0737] [INSPIRE].
D. Astolfi, V.G.M. Puletti, G. Grignani, T. Harmark and M. Orselli, Finite-size corrections for quantum strings on AdS 4 × CP 3, JHEP 05 (2011) 128 [arXiv:1101.0004] [INSPIRE].
D. Astolfi, G. Grignani, E. Ser-Giacomi and A.V. Zayakin, Strings in AdS 4 × CP 3 : finite size spectrum vs. Bethe Ansatz, JHEP 04 (2012) 005 [arXiv:1111.6628] [INSPIRE].
C. Lopez-Arcos and H. Nastase, Eliminating ambiguities for quantum corrections to strings moving in AdS 4 × CP 3, Int. J. Mod. Phys. A 28 (2013) 1350058 [arXiv:1203.4777] [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].
I. Shenderovich, Giant magnons in AdS 4 /CFT 3 : Dispersion, quantization and finite-size corrections, arXiv:0807.2861 [INSPIRE].
B. Stefanski Jr., Green-Schwarz action for Type IIA strings on AdS 4 × CP 3, Nucl. Phys. B 808 (2009) 80 [arXiv:0806.4948] [INSPIRE].
G. Arutyunov and S. Frolov, Superstrings on AdS 4 × CP 3 as a Coset σ-model, JHEP 09 (2008) 129 [arXiv:0806.4940] [INSPIRE].
J. Gomis, D. Sorokin and L. Wulff, The Complete AdS 4 × CP 3 superspace for the type IIA superstring and D-branes, JHEP 03 (2009) 015 [arXiv:0811.1566] [INSPIRE].
S. Giombi, R. Ricci, R. Roiban, A.A. Tseytlin and C. Vergu, Quantum AdS 5 × S 5 superstring in the AdS light-cone gauge, JHEP 03 (2010) 003 [arXiv:0912.5105] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
A. Cagnazzo, D. Sorokin and L. Wulff, String instanton in AdS 4 × CP 3, JHEP 05 (2010) 009 [arXiv:0911.5228] [INSPIRE].
D.V. Uvarov, AdS 4 × CP 3 superstring in the light-cone gauge, Nucl. Phys. B 826 (2010) 294 [arXiv:0906.4699] [INSPIRE].
D.V. Uvarov, Light-cone gauge Hamiltonian for AdS 4 × CP 3 superstring, Mod. Phys. Lett. A 25 (2010) 1251 [arXiv:0912.1044] [INSPIRE].
P.A. Grassi, D. Sorokin and L. Wulff, Simplifying superstring and D-brane actions in AdS 4 × CP 3 superbackground, JHEP 08 (2009) 060 [arXiv:0903.5407] [INSPIRE].
B. de Wit, K. Peeters, J. Plefka and A. Sevrin, The M-theory two-brane in AdS 4 × S 7 and AdS 7 × S 4, Phys. Lett. B 443 (1998) 153 [hep-th/9808052] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Superstring action in AdS 5 × S 5 . Kappa symmetry light cone gauge, Phys. Rev. D 63 (2001) 046002 [hep-th/0007036] [INSPIRE].
R.R. Metsaev, C.B. Thorn and A.A. Tseytlin, Light cone superstring in AdS space-time, Nucl. Phys. B 596 (2001) 151 [hep-th/0009171] [INSPIRE].
R. Roiban, A. Tirziu and A.A. Tseytlin, Two-loop world-sheet corrections in AdS 5 × S 5 superstring, JHEP 07 (2007) 056 [arXiv:0704.3638] [INSPIRE].
S. Giombi, R. Ricci, R. Roiban, A.A. Tseytlin and C. Vergu, Generalized scaling function from light-cone gauge AdS 5 × S 5 superstring, JHEP 06 (2010) 060 [arXiv:1002.0018] [INSPIRE].
S. Giombi, R. Ricci, R. Roiban and A.A. Tseytlin, Two-loop AdS 5 × S 5 superstring: testing asymptotic Bethe ansatz and finite size corrections, J. Phys. A 44 (2011) 045402 [arXiv:1010.4594] [INSPIRE].
O.T. Engelund, R.W. McKeown and R. Roiban, Generalized unitarity and the worldsheet S matrix in AdS n × S n × M 10−2n, JHEP 08 (2013) 023 [arXiv:1304.4281] [INSPIRE].
L. Bianchi, V. Forini and B. Hoare, Two-dimensional S-matrices from unitarity cuts, JHEP 07 (2013) 088 [arXiv:1304.1798] [INSPIRE].
L. Bianchi and B. Hoare, AdS 3 × S 3 × M 4 string S-matrices from unitarity cuts, JHEP 08 (2014) 097 [arXiv:1405.7947] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
D. Sorokin and L. Wulff, Evidence for the classical integrability of the complete AdS 4 × CP 3 superstring, JHEP 11 (2010) 143 [arXiv:1009.3498] [INSPIRE].
L. Wulff, Superisometries and integrability of superstrings, arXiv:1402.3122 [INSPIRE].
M. Beccaria, G.V. Dunne, V. Forini, M. Pawellek and A.A. Tseytlin, Exact computation of one-loop correction to energy of spinning folded string in AdS 5 × S 5, J. Phys. A 43 (2010) 165402 [arXiv:1001.4018] [INSPIRE].
V. Forini, Quark-antiquark potential in AdS at one loop, JHEP 11 (2010) 079 [arXiv:1009.3939] [INSPIRE].
N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].
R. Roiban and A.A. Tseytlin, Spinning superstrings at two loops: Strong-coupling corrections to dimensions of large-twist SYM operators, Phys. Rev. D 77 (2008) 066006 [arXiv:0712.2479] [INSPIRE].
O. Bergman and S. Hirano, Anomalous radius shift in AdS 4 /CFT 3, JHEP 07 (2009) 016 [arXiv:0902.1743] [INSPIRE].
O. Aharony, O. Bergman and D.L. Jafferis, Fractional M2-branes, JHEP 11 (2008) 043 [arXiv:0807.4924] [INSPIRE].
N. Gromov and G. Sizov, Exact Slope and Interpolating Functions in ABJM Theory, arXiv:1403.1894 [INSPIRE].
B. Basso, An exact slope for AdS/CFT, arXiv:1109.3154 [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].
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.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 AdS 4 × CP 3 Wilson loops in \( \mathcal{N} \) =6 super Chern-Simons-matter and bremsstrahlung functions, JHEP 06 (2014) 139 [arXiv:1405.1396] [INSPIRE].
K. Zarembo, Worldsheet spectrum in AdS 4 /CFT 3 correspondence, JHEP 04 (2009) 135 [arXiv:0903.1747] [INSPIRE].
D.V. Uvarov, AdS 4 × CP 3 superstring and D = 3 N = 6 superconformal symmetry, Phys. Rev. D 79 (2009) 106007 [arXiv:0811.2813] [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].
R. Roiban and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly from quantum superstring, JHEP 11 (2007) 016 [arXiv:0709.0681] [INSPIRE].
R.W. McKeown and R. Roiban, The quantum AdS 5 × S 5 superstring at finite coupling, arXiv:1308.4875 [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: 1407.4788
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, L., Bianchi, M.S., Brès, A. et al. Two-loop cusp anomaly in ABJM at strong coupling. J. High Energ. Phys. 2014, 13 (2014). https://doi.org/10.1007/JHEP10(2014)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2014)013