Abstract
We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.
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A. Cavaglià, N. Gromov, J. Julius and M. Preti, Integrability and conformal bootstrap: One dimensional defect conformal field theory, Phys. Rev. D 105 (2022) L021902 [arXiv:2107.08510] [INSPIRE].
A. Cavaglià, N. Gromov, J. Julius and M. Preti, Bootstrability in defect CFT: integrated correlators and sharper bounds, JHEP 05 (2022) 164 [arXiv:2203.09556] [INSPIRE].
S. Caron-Huot, F. Coronado, A.-K. Trinh and Z. Zahraee, Bootstrapping \( \mathcal{N} \) = 4 sYM correlators using integrability, JHEP 02 (2023) 083 [arXiv:2207.01615] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N} \) = 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 AdS5/CFT4, JHEP 09 (2015) 187 [arXiv:1405.4857] [INSPIRE].
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
S. El-Showk et al., Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [INSPIRE].
S.M. Chester, Weizmann Lectures on the Numerical Conformal Bootstrap, arXiv:1907.05147 [INSPIRE].
N.B. Agmon, S.M. Chester and S.S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [arXiv:1711.07343] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 4 Superconformal Bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, More \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. D 96 (2017) 046014 [arXiv:1612.02363] [INSPIRE].
S.M. Chester, R. Dempsey and S.S. Pufu, Bootstrapping \( \mathcal{N} \) = 4 super-Yang-Mills on the conformal manifold, JHEP 01 (2023) 038 [arXiv:2111.07989] [INSPIRE].
O. Aharony, L.F. Alday, A. Bissi and E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036 [arXiv:1612.03891] [INSPIRE].
L.F. Alday and A. Bissi, Loop Corrections to Supergravity on AdS5 × S5, Phys. Rev. Lett. 119 (2017) 171601 [arXiv:1706.02388] [INSPIRE].
L.F. Alday, T. Hansen and J.A. Silva, AdS Virasoro-Shapiro from dispersive sum rules, JHEP 10 (2022) 036 [arXiv:2204.07542] [INSPIRE].
L.F. Alday, T. Hansen and J.A. Silva, AdS Virasoro-Shapiro from single-valued periods, JHEP 12 (2022) 010 [arXiv:2209.06223] [INSPIRE].
N. Kiryu and S. Komatsu, Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization, JHEP 02 (2019) 090 [arXiv:1812.04593] [INSPIRE].
P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 104 (2021) L081703 [arXiv:2103.10440] [INSPIRE].
D.J. Binder, S.M. Chester, S.S. Pufu and Y. Wang, \( \mathcal{N} \) = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization, JHEP 12 (2019) 119 [arXiv:1902.06263] [INSPIRE].
H. Paul, E. Perlmutter and H. Raj, Integrated correlators in \( \mathcal{N} \) = 4 SYM via SL(2, ℤ) spectral theory, JHEP 01 (2023) 149 [arXiv:2209.06639] [INSPIRE].
D. Dorigoni, M.B. Green and C. Wen, Novel Representation of an Integrated Correlator in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 126 (2021) 161601 arXiv:2102.08305] [INSPIRE].
D. Dorigoni, M.B. Green and C. Wen, Exact properties of an integrated correlator in \( \mathcal{N} \) = 4 SU(N) SYM, JHEP 05 (2021) 089 [arXiv:2102.09537] [INSPIRE].
D. Dorigoni, M.B. Green and C. Wen, Exact results for duality-covariant integrated correlators in \( \mathcal{N} \) = 4 SYM with general classical gauge groups, SciPost Phys. 13 (2022) 092 [arXiv:2202.05784] [INSPIRE].
N. Drukker, Z. Kong and G. Sakkas, Broken Global Symmetries and Defect Conformal Manifolds, Phys. Rev. Lett. 129 (2022) 201603 [arXiv:2203.17157] [INSPIRE].
J. Barrat, P. Liendo, G. Peveri and J. Plefka, Multipoint correlators on the supersymmetric Wilson line defect CFT, JHEP 08 (2022) 067 [arXiv:2112.10780] [INSPIRE].
J. Barrat, P. Liendo and G. Peveri, Multipoint correlators on the supersymmetric Wilson line defect CFT II: Unprotected operators, arXiv:2210.14916 [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [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].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev. D 60 (1999) 125006 [hep-th/9904191] [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].
K. Zarembo, Supersymmetric Wilson loops, Nucl. Phys. B 643 (2002) 157 [hep-th/0205160] [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].
M. Gunaydin and R.J. Scalise, Unitary Lowest Weight Representations of the Noncompact Supergroup Osp(2m∗/2n), J. Math. Phys. 32 (1991) 599 [INSPIRE].
P. Liendo and C. Meneghelli, Bootstrap equations for \( \mathcal{N} \) = 4 SYM with defects, JHEP 01 (2017) 122 [arXiv:1608.05126] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [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].
D. Grabner, N. Gromov and J. Julius, Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve, JHEP 07 (2020) 042 [arXiv:2001.11039] [INSPIRE].
J. Julius, Modern techniques for solvable models, Ph.D. thesis, King’s College London, London, U.K. (2021) [INSPIRE].
N.B. Agmon and Y. Wang, Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines, arXiv:2009.06650 [INSPIRE].
N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].
A.M. Polyakov and V.S. Rychkov, Gauge field strings duality and the loop equation, Nucl. Phys. B 581 (2000) 116 [hep-th/0002106] [INSPIRE].
G.W. Semenoff and D. Young, Wavy Wilson line and AdS/CFT, Int. J. Mod. Phys. A 20 (2005) 2833 [hep-th/0405288] [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].
A. Cavaglià, D. Grabner, N. Gromov and A. Sever, Colour-twist operators. Part I. Spectrum and wave functions, JHEP 06 (2020) 092 [arXiv:2001.07259] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Loop Space Formalism and Renormalization Group for the Infrared Asymptotics of QCD, Phys. Lett. B 171 (1986) 459 [INSPIRE].
N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [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 F. Levkovich-Maslyuk, Quantum Spectral Curve for a cusped Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 04 (2016) 134 [arXiv:1510.02098] [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].
N. Drukker, 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model, JHEP 09 (2006) 004 [hep-th/0605151] [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].
G. Sizov and S. Valatka, Algebraic Curve for a Cusped Wilson Line, JHEP 05 (2014) 149 [arXiv:1306.2527] [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].
A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in \( \mathcal{N} \) = 4 SYM: cusps in the ladder limit, JHEP 10 (2018) 060 [arXiv:1802.04237] [INSPIRE].
H. Dorn, On anomalous conformal Ward identities for Wilson loops on polygon-like contours with circular edges, JHEP 03 (2020) 166 [arXiv:2001.03391] [INSPIRE].
J.L. Cardy, Scaling and renormalization in statistical physics, (1996) [INSPIRE].
A.B. Zamolodchikov, Renormalization Group and Perturbation Theory Near Fixed Points in Two-Dimensional Field Theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [INSPIRE].
A. Zamolodchikov, Integrable field theory from conformal field theory, in Integrable Sys Quantum Field Theory, M. Jimbo, T. Miwa and A. Tsuchiya eds, Academic Press, San Diego (1989), pp. 641–674.
D. Kutasov, Geometry on the Space of Conformal Field Theories and Contact Terms, Phys. Lett. B 220 (1989) 153 [INSPIRE].
K. Ranganathan, H. Sonoda and B. Zwiebach, Connections on the state space over conformal field theories, Nucl. Phys. B 414 (1994) 405 [hep-th/9304053] [INSPIRE].
M.R. Gaberdiel, A. Konechny and C. Schmidt-Colinet, Conformal perturbation theory beyond the leading order, J. Phys. A 42 (2009) 105402 [arXiv:0811.3149] [INSPIRE].
A. Amoretti and N. Magnoli, Conformal perturbation theory, Phys. Rev. D 96 (2017) 045016 [arXiv:1705.03502] [INSPIRE].
C. Behan, Conformal manifolds: ODEs from OPEs, JHEP 03 (2018) 127 [arXiv:1709.03967] [INSPIRE].
M. Baggio, V. Niarchos and K. Papadodimas, Aspects of Berry phase in QFT, JHEP 04 (2017) 062 [arXiv:1701.05587] [INSPIRE].
B. Gabai, A. Sever and D.-L. Zhong, Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions, Phys. Rev. Lett. 129 (2022) 121604 [arXiv:2204.05262] [INSPIRE].
D. Maitre, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [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].
L. Bianchi, M. Preti and E. Vescovi, Exact Bremsstrahlung functions in ABJM theory, JHEP 07 (2018) 060 [arXiv:1802.07726] [INSPIRE].
L. Bianchi et al., Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1, JHEP 08 (2020) 143 [arXiv:2004.07849] [INSPIRE].
N. Gorini et al., Constant primary operators and where to find them: the strange case of BPS defects in ABJ(M) theory, JHEP 02 (2023) 013 [arXiv:2209.11269] [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. 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 et al., 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 AdS4 × 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., Towards the exact Bremsstrahlung function of ABJM theory, JHEP 08 (2017) 022 [arXiv:1705.10780] [INSPIRE].
N. Drukker et al., Roadmap on Wilson loops in 3d Chern-Simons-matter theories, J. Phys. A 53 (2020) 173001 [arXiv:1910.00588] [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 et al., The full Quantum Spectral Curve for AdS4/CFT3, JHEP 09 (2017) 140 [arXiv:1701.00473] [INSPIRE].
J.K. Erickson, G.W. Semenoff, R.J. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].
A.B. Zamolodchikov, “Fishing-net” diagrams as a completely integrable system, Phys. Lett. B 97 (1980) 63 [INSPIRE].
Ö. Gürdoğan and V. Kazakov, New Integrable 4D Quantum Field Theories from Strongly Deformed Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 117 (2016) 201602 [Addendum ibid. 117 (2016) 259903] [arXiv:1512.06704] [INSPIRE].
J. Caetano, Ö. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP 03 (2018) 077 [arXiv:1612.05895] [INSPIRE].
V. Kazakov, E. Olivucci and M. Preti, Generalized fishnets and exact four-point correlators in chiral CFT4, JHEP 06 (2019) 078 [arXiv:1901.00011] [INSPIRE].
A. Pittelli and M. Preti, Integrable fishnet from γ-deformed \( \mathcal{N} \) = 2 quivers, Phys. Lett. B 798 (2019) 134971 [arXiv:1906.03680] [INSPIRE].
N. Gromov, J. Julius and N. Primi, Open fishchain in N = 4 Supersymmetric Yang-Mills Theory, JHEP 07 (2021) 127 [arXiv:2101.01232] [INSPIRE].
G. Cuomo, Z. Komargodski and M. Mezei, Localized magnetic field in the O(N) model, JHEP 02 (2022) 134 [arXiv:2112.10634] [INSPIRE].
A. Gimenez-Grau, E. Lauria, P. Liendo and P. van Vliet, Bootstrapping line defects with O(2) global symmetry, JHEP 11 (2022) 018 [arXiv:2208.11715] [INSPIRE].
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Cavaglià, A., Gromov, N., Julius, J. et al. Integrated correlators from integrability: Maldacena-Wilson line in \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2023, 26 (2023). https://doi.org/10.1007/JHEP04(2023)026
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DOI: https://doi.org/10.1007/JHEP04(2023)026