Quantum Spectral Curve for AdS3/CFT2: a proposal

Journal of High Energy Physics - 2021
Andrea Cavaglià1, Nikolay Gromov1, Bogdan Stefański2, Алессандро Торриелли3
1Mathematics Department, King's College London, The Strand, London, WC2R 2LS, UK
2Centre for Mathematical Science, City, University of London, Northampton Square, London, EC1V 0HB, UK
3Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK

Tóm tắt

Abstract We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.

Từ khóa


Tài liệu tham khảo

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].

N. Gromov, F. Levkovich-Maslyuk, G. Sizov and S. Valatka, Quantum spectral curve at work: from small spin to strong coupling in $$ \mathcal{N} $$ = 4 SYM, JHEP 07 (2014) 156 [arXiv:1402.0871] [INSPIRE].

N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4, JHEP 06 (2016) 036 [arXiv:1504.06640] [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].

N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Pomeron Eigenvalue at Three Loops in $$ \mathcal{N} $$ = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 115 (2015) 251601 [arXiv:1507.04010] [INSPIRE].

C. Marboe and D. Volin, Quantum spectral curve as a tool for a perturbative quantum field theory, Nucl. Phys. B 899 (2015) 810 [arXiv:1411.4758] [INSPIRE].

C. Marboe and D. Volin, The full spectrum of AdS5/CFT4 II: Weak coupling expansion via the quantum spectral curve, J. Phys. A 54 (2021) 055201 [arXiv:1812.09238] [INSPIRE].

M. Alfimov, N. Gromov and V. Kazakov, QCD Pomeron from AdS/CFT Quantum Spectral Curve, JHEP 07 (2015) 164 [arXiv:1408.2530] [INSPIRE].

M. Alfimov, N. Gromov and V. Kazakov, N = 4 SYM Quantum Spectral Curve in BFKL regime, arXiv:2003.03536 [INSPIRE].

M. Alfimov, N. Gromov and G. Sizov, BFKL spectrum of $$ \mathcal{N} $$ = 4: non-zero conformal spin, JHEP 07 (2018) 181 [arXiv:1802.06908] [INSPIRE].

N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in $$ \mathcal{N} $$ = 4 SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].

A. Cavaglià, D. Fioravanti, N. Gromov and R. Tateo, Quantum Spectral Curve of the $$ \mathcal{N} $$ = 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 AdS4/CFT3, JHEP 09 (2017) 140 [arXiv:1701.00473] [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].

L. Anselmetti, D. Bombardelli, A. Cavaglià and R. Tateo, 12 loops and triple wrapping in ABJM theory from integrability, JHEP 10 (2015) 117 [arXiv:1506.09089] [INSPIRE].

D. Bombardelli, A. Cavaglià, R. Conti and R. Tateo, Exploring the spectrum of planar AdS4/CFT3 at finite coupling, JHEP 04 (2018) 117 [arXiv:1803.04748] [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].

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].

A. Cavaglià, N. Gromov, J. Julius and M. Preti, Integrability and Conformal Bootstrap: One Dimensional Defect CFT, arXiv:2107.08510 [INSPIRE].

N. Gromov, Introduction to the Spectrum of N = 4 SYM and the Quantum Spectral Curve, arXiv:1708.03648 [INSPIRE].

A. Babichenko, B. Stefański Jr. and K. Zarembo, Integrability and the AdS3/CFT2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [INSPIRE].

O. Ohlsson Sax and B. Stefański Jr., Integrability, spin-chains and the AdS3/CFT2 correspondence, JHEP 08 (2011) 029 [arXiv:1106.2558] [INSPIRE].

A. Cagnazzo and K. Zarembo, B-field in AdS3/CFT2 Correspondence and Integrability, JHEP 11 (2012) 133 [Erratum ibid. 04 (2013) 003] [arXiv:1209.4049] [INSPIRE].

J.R. David and B. Sahoo, Giant magnons in the D1-D5 system, JHEP 07 (2008) 033 [arXiv:0804.3267] [INSPIRE].

J.R. David and B. Sahoo, S-matrix for magnons in the D1-D5 system, JHEP 10 (2010) 112 [arXiv:1005.0501] [INSPIRE].

R. Borsato, O. Ohlsson Sax and A. Sfondrini, A dynamic su(1|1)2 S-matrix for AdS3 /CFT2, JHEP 04 (2013) 113 [arXiv:1211.5119] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański Jr. and A. Torrielli, The all-loop integrable spin-chain for strings on AdS3 × S3 × T4: the massive sector, JHEP 08 (2013) 043 [arXiv:1303.5995] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., Towards the All-Loop Worldsheet S Matrix for AdS3 × S3 × T4, Phys. Rev. Lett. 113 (2014) 131601 [arXiv:1403.4543] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., The complete AdS3 × S3 × T4 worldsheet S matrix, JHEP 10 (2014) 066 [arXiv:1406.0453] [INSPIRE].

T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., The complete worldsheet S matrix of superstrings on AdS3 × S3 × T4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., The AdS3 × S3 × S3 × S1 worldsheet S matrix, J. Phys. A 48 (2015) 415401 [arXiv:1506.00218] [INSPIRE].

N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].

R.A. Janik, The AdS5 × S5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [INSPIRE].

C. Gomez and R. Hernandez, The Magnon kinematics of the AdS/CFT correspondence, JHEP 11 (2006) 021 [hep-th/0608029] [INSPIRE].

J. Plefka, F. Spill and A. Torrielli, On the Hopf algebra structure of the AdS/CFT S-matrix, Phys. Rev. D 74 (2006) 066008 [hep-th/0608038] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański Jr. and A. Torrielli, Dressing phases of AdS3/CFT2, Phys. Rev. D 88 (2013) 066004 [arXiv:1306.2512] [INSPIRE].

R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., On the spectrum of AdS3 × S3 × T4 strings with Ramond-Ramond flux, J. Phys. A 49 (2016) 41LT03 [arXiv:1605.00518] [INSPIRE].

N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].

M. Beccaria, F. Levkovich-Maslyuk, G. Macorini and A.A. Tseytlin, Quantum corrections to spinning superstrings in AdS3 × S3 × M4: determining the dressing phase, JHEP 04 (2013) 006 [arXiv:1211.6090] [INSPIRE].

O. Ohlsson Sax and B. Stefański Jr., On the singularities of the RR AdS3 × S3 × T4 S matrix, J. Phys. A 53 (2020) 155402 [arXiv:1912.04320] [INSPIRE].

N. Dorey, D.M. Hofman and J.M. Maldacena, On the Singularities of the Magnon S-matrix, Phys. Rev. D 76 (2007) 025011 [hep-th/0703104] [INSPIRE].

A. Fontanella and A. Torrielli, Geometry of Massless Scattering in Integrable Superstring, JHEP 06 (2019) 116 [arXiv:1903.10759] [INSPIRE].

A. Fontanella, O. Ohlsson Sax, B. Stefański and A. Torrielli, The effectiveness of relativistic invariance in AdS3, JHEP 07 (2019) 105 [arXiv:1905.00757] [INSPIRE].

A. Cavaglià, M. Cornagliotto, M. Mattelliano and R. Tateo, A Riemann-Hilbert formulation for the finite temperature Hubbard model, JHEP 06 (2015) 015 [arXiv:1501.04651] [INSPIRE].

S. Ekhammar and D. Volin, Mondromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2, arXiv:2109.06164 [INSPIRE].

P. Vieira and D. Volin, Review of AdS/CFT Integrability, Chapter III.3: The Dressing factor, Lett. Math. Phys. 99 (2012) 231 [arXiv:1012.3992] [INSPIRE].

R. Hernandez and E. Lopez, Quantum corrections to the string Bethe ansatz, JHEP 07 (2006) 004 [hep-th/0603204] [INSPIRE].

Z. Bajnok, Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz, Lett. Math. Phys. 99 (2012) 299 [arXiv:1012.3995] [INSPIRE].

M.C. Abbott and I. Aniceto, Integrable field theories with an interacting massless sector, Phys. Rev. D 103 (2021) 086017 [arXiv:2002.12060] [INSPIRE].

D. Bombardelli, B. Stefański and A. Torrielli, The low-energy limit of AdS3/CFT2 and its TBA, JHEP 10 (2018) 177 [arXiv:1807.07775] [INSPIRE].

M.C. Abbott and I. Aniceto, Massless Lüscher terms and the limitations of the AdS3 asymptotic Bethe ansatz, Phys. Rev. D 93 (2016) 106006 [arXiv:1512.08761] [INSPIRE].

A. Dei and A. Sfondrini, Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model, JHEP 02 (2019) 072 [arXiv:1812.08195] [INSPIRE].

A. Babichenko, A. Dekel and O. Ohlsson Sax, Finite-gap equations for strings on AdS3 × S3 × T4 with mixed 3-form flux, JHEP 11 (2014) 122 [arXiv:1405.6087] [INSPIRE].

O. Ohlsson Sax and B. Stefański Jr., Closed strings and moduli in AdS3/CFT2, JHEP 05 (2018) 101 [arXiv:1804.02023] [INSPIRE].

O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., Integrability and the Conformal Field Theory of the Higgs branch, JHEP 06 (2015) 103 [arXiv:1411.3676] [INSPIRE].

A. Cavaglià, D. Fioravanti and R. Tateo, Extended Y-system for the AdS5/CFT4 correspondence, Nucl. Phys. B 843 (2011) 302 [arXiv:1005.3016] [INSPIRE].

N. Gromov, V. Kazakov, S. Leurent and D. Volin, Solving the AdS/CFT Y-system, JHEP 07 (2012) 023 [arXiv:1110.0562] [INSPIRE].

J. de Boer, Six-dimensional supergravity on S3 × AdS3 and 2-D conformal field theory, Nucl. Phys. B 548 (1999) 139 [hep-th/9806104] [INSPIRE].

J. de Boer, Large N elliptic genus and AdS/CFT correspondence, JHEP 05 (1999) 017 [hep-th/9812240] [INSPIRE].

M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, JHEP 07 (2012) 137 [arXiv:1203.1036] [INSPIRE].

M. Baggio, O. Ohlsson Sax, A. Sfondrini, B. Stefański and A. Torrielli, Protected string spectrum in AdS3/CFT2 from worldsheet integrability, JHEP 04 (2017) 091 [arXiv:1701.03501] [INSPIRE].

S. Majumder, O.O. Sax, B. Stefański and A. Torrielli, Protected states in AdS3 backgrounds from integrability, arXiv:2103.16972 [INSPIRE].

A. Varga, Semiclassical quantization of the mixed-flux AdS3 giant magnon, JHEP 09 (2020) 107 [arXiv:2006.12080] [INSPIRE].

O. Ohlsson Sax and B. Stefański Jr., to appear.

B. Hoare, A. Pittelli and A. Torrielli, Integrable S-matrices, massive and massless modes and the AdS2 * S2 superstring, JHEP 11 (2014) 051 [arXiv:1407.0303] [INSPIRE].

Thông tin
Thông tin xuất bản

Journal of High Energy Physics

Thông tin tác giả