Abstract
We formulate and close the boundary state bootstrap for factorizing K-matrices in AdS/CFT. We found that there are no boundary degrees of freedom in the boundary bound states, merely the boundary parameters are shifted. We use this family of boundary bound states to describe the D3-D5 system for higher dimensional matrix product states and provide their asymptotic overlap formulas. In doing so we generalize the nesting for overlaps of matrix product states and Bethe states.
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S. Ghoshal and A.B. Zamolodchikov, Boundary S matrix and boundary state in two-dimensional integrable quantum field theory, Int. J. Mod. Phys. A 9 (1994) 3841 [Erratum ibid. 9 (1994) 4353] [hep-th/9306002] [INSPIRE].
J.-S. Caux and F.H.L. Essler, Time evolution of local observables after quenching to an integrable model, Phys. Rev. Lett. 110 (2013) 257203 [arXiv:1301.3806] [INSPIRE].
L. Piroli, E. Vernier, P. Calabrese and B. Pozsgay, Integrable quenches in nested spin chains I: the exact steady states, J. Stat. Mech. 1906 (2019) 063103 [arXiv:1811.00432] [INSPIRE].
L. Piroli, E. Vernier, P. Calabrese and B. Pozsgay, Integrable quenches in nested spin chains II: fusion of boundary transfer matrices, J. Stat. Mech. 1906 (2019) 063104 [arXiv:1812.05330] [INSPIRE].
B. Pozsgay, L. Piroli and E. Vernier, Integrable Matrix Product States from boundary integrability, SciPost Phys. 6 (2019) 062 [arXiv:1812.11094] [INSPIRE].
M. de Leeuw, Coordinate Bethe Ansatz for the String S-matrix, J. Phys. A 40 (2007) 14413 [arXiv:0705.2369] [INSPIRE].
M. de Leeuw, C. Kristjansen and K. Zarembo, One-point Functions in Defect CFT and Integrability, JHEP 08 (2015) 098 [arXiv:1506.06958] [INSPIRE].
I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen and K. Zarembo, One-point Functions in AdS/dCFT from Matrix Product States, JHEP 02 (2016) 052 [arXiv:1512.02532] [INSPIRE].
M. de Leeuw, C. Kristjansen and G. Linardopoulos, One-point functions of non-protected operators in the SO(5) symmetric D3–D7 dCFT, J. Phys. A 50 (2017) 254001 [arXiv:1612.06236] [INSPIRE].
I. Buhl-Mortensen, M. de Leeuw, A.C. Ipsen, C. Kristjansen and M. Wilhelm, One-loop one-point functions in gauge-gravity dualities with defects, Phys. Rev. Lett. 117 (2016) 231603 [arXiv:1606.01886] [INSPIRE].
M. de Leeuw, C. Kristjansen and S. Mori, AdS/dCFT one-point functions of the SU(3) sector, Phys. Lett. B 763 (2016) 197 [arXiv:1607.03123] [INSPIRE].
I. Buhl-Mortensen, M. de Leeuw, A.C. Ipsen, C. Kristjansen and M. Wilhelm, Asymptotic One-Point Functions in Gauge-String Duality with Defects, Phys. Rev. Lett. 119 (2017) 261604 [arXiv:1704.07386] [INSPIRE].
M. De Leeuw, C. Kristjansen and G. Linardopoulos, Scalar one-point functions and matrix product states of AdS/dCFT, Phys. Lett. B 781 (2018) 238 [arXiv:1802.01598] [INSPIRE].
M. De Leeuw, T. Gombor, C. Kristjansen, G. Linardopoulos and B. Pozsgay, Spin Chain Overlaps and the Twisted Yangian, JHEP 01 (2020) 176 [arXiv:1912.09338] [INSPIRE].
G. Linardopoulos, Solving holographic defects, PoS(CORFU2019)141 [arXiv:2005.02117] [INSPIRE].
C. Kristjansen, D. Müller and K. Zarembo, Integrable boundary states in D3-D5 dCFT: beyond scalars, JHEP 08 (2020) 103 [arXiv:2005.01392] [INSPIRE].
S. Komatsu and Y. Wang, Non-perturbative defect one-point functions in planar \( \mathcal{N} \) = 4 super-Yang-Mills, Nucl. Phys. B 958 (2020) 115120 [arXiv:2004.09514] [INSPIRE].
T. Gombor and Z. Bajnok, Boundary states, overlaps, nesting and bootstrapping AdS/dCFT, JHEP 10 (2020) 123 [arXiv:2004.11329] [INSPIRE].
P. Dorey, R. Tateo and G. Watts, Generalizations of the Coleman-Thun mechanism and boundary reflection factors, Phys. Lett. B 448 (1999) 249 [hep-th/9810098] [INSPIRE].
P. Mattsson and P. Dorey, Boundary spectrum in the sine-Gordon model with Dirichlet boundary conditions, J. Phys. A 33 (2000) 9065 [hep-th/0008071] [INSPIRE].
Z. Bajnok, L. Palla and G. Takács, Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition, Nucl. Phys. B 614 (2001) 405 [hep-th/0106069] [INSPIRE].
Z. Bajnok, L. Palla, G. Takács and G.Z. Toth, The Spectrum of boundary states in sine-Gordon model with integrable boundary conditions, Nucl. Phys. B 622 (2002) 548 [hep-th/0106070] [INSPIRE].
Z. Bajnok, G. Bohm and G. Takács, On perturbative quantum field theory with boundary, Nucl. Phys. B 682 (2004) 585 [hep-th/0309119] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS5 × S5 Superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
G. Arutyunov and S. Frolov, On String S-matrix, Bound States and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568] [INSPIRE].
L. Piroli, B. Pozsgay and E. Vernier, What is an integrable quench?, Nucl. Phys. B 925 (2017) 362 [arXiv:1709.04796] [INSPIRE].
M. Brockmann, J. De Nardis, B. Wouters and J.-S. Caux, A Gaudin-like determinant for overlaps of Ńeel and XXZ Bethe states, J. Phys. A 47 (2014) 145003.
M. Brockmann, J. De Nardis, B. Wouters and J.-S. Caux, Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit, J. Phys. A 47 (2014) 345003.
B. Pozsgay, Overlaps with arbitrary two-site states in the XXZ spin chain, J. Stat. Mech. 1805 (2018) 053103 [arXiv:1801.03838] [INSPIRE].
Y. Jiang and B. Pozsgay, On exact overlaps in integrable spin chains, JHEP 06 (2020) 022 [arXiv:2002.12065] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Structure constants in \( \mathcal{N} \) = 4 SYM at finite coupling as worldsheet g-function, JHEP 07 (2020) 037 [arXiv:1906.07733] [INSPIRE].
Y. Jiang, S. Komatsu and E. Vescovi, Exact Three-Point Functions of Determinant Operators in Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 123 (2019) 191601 [arXiv:1907.11242] [INSPIRE].
I. Kostov, D. Serban and D.-L. Vu, Boundary TBA, trees and loops, Nucl. Phys. B 949 (2019) 114817 [arXiv:1809.05705] [INSPIRE].
D.-L. Vu, I. Kostov and D. Serban, Boundary entropy of integrable perturbed SU(2)k WZNW, JHEP 08 (2019) 154 [arXiv:1906.01909] [INSPIRE].
I. Kostov, Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz, JHEP 02 (2020) 043 [arXiv:1911.07343] [INSPIRE].
J. Caetano and S. Komatsu, Functional equations and separation of variables for exact g-function, JHEP 09 (2020) 180 [arXiv:2004.05071] [INSPIRE].
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ArXiv ePrint: 2006.16151
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Gombor, T., Bajnok, Z. Boundary state bootstrap and asymptotic overlaps in AdS/dCFT. J. High Energ. Phys. 2021, 222 (2021). https://doi.org/10.1007/JHEP03(2021)222
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DOI: https://doi.org/10.1007/JHEP03(2021)222