Abstract
We consider scalar QED with Nf flavors in AdSD. For D < 4 the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large Nf. We then apply this result to compute the boundary four-point function of the charged operators at leading order in 1/Nf and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large Nf, in integer dimension D = 3 an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.
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References
C.G. Callan Jr. and F. Wilczek, Infrared behavior at negative curvature, Nucl. Phys. B 340 (1990) 366 [INSPIRE].
J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].
S.B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].
M. Gary and S.B. Giddings, The Flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev. D 80 (2009) 046008 [arXiv:0904.3544] [INSPIRE].
M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].
A.L. Fitzpatrick, E. Katz, D. Poland and D. Simmons-Duffin, Effective Conformal Theory and the Flat-Space Limit of AdS, JHEP 07 (2011) 023 [arXiv:1007.2412] [INSPIRE].
T. Okuda and J. Penedones, String scattering in flat space and a scaling limit of Yang-Mills correlators, Phys. Rev. D 83 (2011) 086001 [arXiv:1002.2641] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the Holographic S-Matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
M.F. Paulos et al., The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
E. Hijano, Flat space physics from AdS/CFT, JHEP 07 (2019) 132 [arXiv:1905.02729] [INSPIRE].
S. Komatsu, M.F. Paulos, B.C. Van Rees and X. Zhao, Landau diagrams in AdS and S-matrices from conformal correlators, JHEP 11 (2020) 046 [arXiv:2007.13745] [INSPIRE].
E. Hijano and D. Neuenfeld, Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT, JHEP 11 (2020) 009 [arXiv:2005.03667] [INSPIRE].
Y.-Z. Li, Notes on flat-space limit of AdS/CFT, JHEP 09 (2021) 027 [arXiv:2106.04606] [INSPIRE].
A. Gadde and T. Sharma, A scattering amplitude for massive particles in AdS, JHEP 09 (2022) 157 [arXiv:2204.06462] [INSPIRE].
B.C. van Rees and X. Zhao, Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms, Phys. Rev. Lett. 130 (2023) 191601 [arXiv:2210.15683] [INSPIRE].
S. Duary, E. Hijano and M. Patra, Towards an IR finite S-matrix in the flat limit of AdS/CFT, arXiv:2211.13711 [INSPIRE].
M.F. Paulos et al., The S-matrix bootstrap II: two dimensional amplitudes, JHEP 11 (2017) 143 [arXiv:1607.06110] [INSPIRE].
M.F. Paulos et al., The S-matrix bootstrap. Part III: higher dimensional amplitudes, JHEP 12 (2019) 040 [arXiv:1708.06765] [INSPIRE].
D. Mazac, Analytic bounds and emergence of AdS2 physics from the conformal bootstrap, JHEP 04 (2017) 146 [arXiv:1611.10060] [INSPIRE].
D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices, JHEP 02 (2019) 162 [arXiv:1803.10233] [INSPIRE].
D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part II. Natural bases for the crossing equation, JHEP 02 (2019) 163 [arXiv:1811.10646] [INSPIRE].
M.F. Paulos, Analytic functional bootstrap for CFTs in d > 1, JHEP 04 (2020) 093 [arXiv:1910.08563] [INSPIRE].
W. Knop and D. Mazac, Dispersive sum rules in AdS2, JHEP 10 (2022) 038 [arXiv:2203.11170] [INSPIRE].
D. Carmi, L. Di Pietro and S. Komatsu, A Study of Quantum Field Theories in AdS at Finite Coupling, JHEP 01 (2019) 200 [arXiv:1810.04185] [INSPIRE].
M. Hogervorst, M. Meineri, J. Penedones and K.S. Vaziri, Hamiltonian truncation in Anti-de Sitter spacetime, JHEP 08 (2021) 063 [arXiv:2104.10689] [INSPIRE].
A. Antunes et al., Towards bootstrapping RG flows: sine-Gordon in AdS, JHEP 12 (2021) 094 [arXiv:2109.13261] [INSPIRE].
L. Córdova, Y. He and M.F. Paulos, From conformal correlators to analytic S-matrices: CFT1/QFT2, JHEP 08 (2022) 186 [arXiv:2203.10840] [INSPIRE].
N. Levine and M.F. Paulos, Bootstrapping bulk locality. Part I: Sum rules for AdS form factors, arXiv:2305.07078 [INSPIRE].
M. Meineri, J. Penedones and T. Spirig, Renormalization group flows in AdS and the bootstrap program, arXiv:2305.11209 [INSPIRE].
A. Kakkar and S. Sarkar, On partition functions and phases of scalars in AdS, JHEP 07 (2022) 089 [arXiv:2201.09043] [INSPIRE].
A. Kakkar and S. Sarkar, Phases of theories with fermions in AdS, JHEP 06 (2023) 009 [arXiv:2303.02711] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Correlators on non-supersymmetric Wilson line in \( \mathcal{N} \) = 4 SYM and AdS2/CFT1, JHEP 05 (2019) 122 [arXiv:1903.04365] [INSPIRE].
M. Beccaria and A.A. Tseytlin, On boundary correlators in Liouville theory on AdS2, JHEP 07 (2019) 008 [arXiv:1904.12753] [INSPIRE].
M. Beccaria, H. Jiang and A.A. Tseytlin, Non-abelian Toda theory on AdS2 and AdS2/\( {CFT}_2^{1/2} \) duality, JHEP 09 (2019) 036 [arXiv:1907.01357] [INSPIRE].
M. Beccaria, H. Jiang and A.A. Tseytlin, Supersymmetric Liouville theory in AdS2 and AdS/CFT, JHEP 11 (2019) 051 [arXiv:1909.10255] [INSPIRE].
M. Beccaria, H. Jiang and A.A. Tseytlin, Boundary correlators in WZW model on AdS2, JHEP 05 (2020) 099 [arXiv:2001.11269] [INSPIRE].
S. Giombi, E. Helfenberger, Z. Ji and H. Khanchandani, Monodromy defects from hyperbolic space, JHEP 02 (2022) 041 [arXiv:2102.11815] [INSPIRE].
C.P. Herzog and I. Shamir, On Marginal Operators in Boundary Conformal Field Theory, JHEP 10 (2019) 088 [arXiv:1906.11281] [INSPIRE].
S. Giombi and H. Khanchandani, CFT in AdS and boundary RG flows, JHEP 11 (2020) 118 [arXiv:2007.04955] [INSPIRE].
S. Giombi, E. Helfenberger and H. Khanchandani, Fermions in AdS and Gross-Neveu BCFT, JHEP 07 (2022) 018 [arXiv:2110.04268] [INSPIRE].
O. Aharony, M. Berkooz, D. Tong and S. Yankielowicz, Confinement in Anti-de Sitter Space, JHEP 02 (2013) 076 [arXiv:1210.5195] [INSPIRE].
M.S. Costa, V. Gonçalves and J. Penedones, Spinning AdS Propagators, JHEP 09 (2014) 064 [arXiv:1404.5625] [INSPIRE].
M. Loparco, J. Penedones, K. Salehi Vaziri and Z. Sun, The Källén-Lehmann representation in de Sitter spacetime, arXiv:2306.00090 [INSPIRE].
J. Ren, One-dimensional holographic superconductor from AdS3/CFT2 correspondence, JHEP 11 (2010) 055 [arXiv:1008.3904] [INSPIRE].
T. Faulkner and N. Iqbal, Friedel oscillations and horizon charge in 1D holographic liquids, JHEP 07 (2013) 060 [arXiv:1207.4208] [INSPIRE].
S.R. Coleman, R. Jackiw and H.D. Politzer, Spontaneous Symmetry Breaking in the O(N) Model for Large N*, Phys. Rev. D 10 (1974) 2491 [INSPIRE].
L. Di Pietro, E. Lauria and P. Niro, Vacuum stability, fixed points, and phases of QED3 at large Nf, arXiv:2301.04611 [INSPIRE].
V. Gorbenko, S. Rychkov and B. Zan, Walking, Weak first-order transitions, and Complex CFTs, JHEP 10 (2018) 108 [arXiv:1807.11512] [INSPIRE].
M. Shifman, Advanced Topics in Quantum Field Theory, Cambridge University Press (2022) [https://doi.org/10.1017/9781108885911] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Lattice Abelian-Higgs model with noncompact gauge fields, Phys. Rev. B 103 (2021) 085104 [arXiv:2010.06311] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Breaking of Gauge Symmetry in Lattice Gauge Theories, Phys. Rev. Lett. 127 (2021) 091601 [arXiv:2104.09892] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Lattice gauge theories in the presence of a linear gauge-symmetry breaking, Phys. Rev. E 104 (2021) 014140 [arXiv:2106.02503] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Breaking the gauge symmetry in lattice gauge-invariant models, PoS LATTICE2021 (2022) 101 [arXiv:2110.07941] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory, Phys. Rev. B 105 (2022) 085112 [arXiv:2201.01082] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, Three-dimensional monopole-free CPN−1 models: behavior in the presence of a quartic potential, J. Stat. Mech. 2206 (2022) 063206 [arXiv:2202.04614] [INSPIRE].
C. Bonati, A. Pelissetto and E. Vicari, The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing, arXiv:2305.15236 [INSPIRE].
M. Correia, A. Sever and A. Zhiboedov, An analytical toolkit for the S-matrix bootstrap, JHEP 03 (2021) 013 [arXiv:2006.08221] [INSPIRE].
G. Galati and M. Serone, Cancellation of IR divergences in 3d Abelian gauge theories, JHEP 02 (2022) 123 [arXiv:2111.02124] [INSPIRE].
S.S. Pufu and S. Sachdev, Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry, JHEP 09 (2013) 127 [arXiv:1303.3006] [INSPIRE].
E. Dyer, M. Mezei, S.S. Pufu and S. Sachdev, Scaling dimensions of monopole operators in the \( {\mathbbm{CP}}^{N_b-1} \) theory in 2 + 1 dimensions, JHEP 06 (2015) 037 [Erratum ibid. 03 (2016) 111] [arXiv:1504.00368] [INSPIRE].
S.M. Chester, É. Dupuis and W. Witczak-Krempa, Evidence for web of dualities from monopole operators, Phys. Rev. D 108 (2023) L021701 [arXiv:2210.12370] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
D.M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].
A.J. Bray and M.A. Moore, Critical Behavior of a Semiinfinite System: n Vector Model in the Large n Limit, Phys. Rev. Lett. 38 (1977) 735 [INSPIRE].
K. Ohno and Y. Okabe, The 1/n Expansion for the n-Vector Model in the Semi-infinite Space, Prog. Theor. Phys. 70 (1983) 1226 [INSPIRE].
S. Jain et al., Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter, JHEP 04 (2015) 129 [arXiv:1404.6373] [INSPIRE].
B. Gabai, J. Sandor and X. Yin, Anyon scattering from lightcone Hamiltonian: the singlet channel, JHEP 09 (2022) 145 [arXiv:2205.09144] [INSPIRE].
U. Mehta et al., Crossing Symmetry in Matter Chern-Simons Theories at finite N and k, arXiv:2210.07272 [INSPIRE].
S. Duary, AdS correction to the Faddeev-Kulish state: migrating from the flat peninsula, JHEP 05 (2023) 079 [arXiv:2212.09509] [INSPIRE].
Y.-C. He, J. Rong, N. Su and A. Vichi, Non-Abelian currents bootstrap, arXiv:2302.11585 [INSPIRE].
D. Carmi, Loops in AdS: From the Spectral Representation to Position Space, JHEP 06 (2020) 049 [arXiv:1910.14340] [INSPIRE].
D. Carmi, Loops in AdS: from the spectral representation to position space. Part II, JHEP 07 (2021) 186 [arXiv:2104.10500] [INSPIRE].
Acknowledgments
We thank Christian Copetti, Riccardo Ciccone, Fabiana de Cesare, Victor Gorbenko, Shota Komatsu, Ziming Ji, Manuel Loparco, Veronica Sacchi and Marco Serone for useful discussions and/or collaboration on related topics. We also thank the organizers of the workshops “S-matrix bootstrap IV” in Heraklion and “Conformal Bootstrap, CFTs and Gravity” at LITP, Haifa where this work was presented. A. thanks ICTP for funding his doctoral scholarship. A. and L.D. are partially supported by the INFN “Iniziativa Specifica ST&FI”. L.D. also acknowledges support by the program “Rita Levi Montalcini” for young researchers.
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Ankur, Carmi, D. & Di Pietro, L. Scalar QED in AdS. J. High Energ. Phys. 2023, 89 (2023). https://doi.org/10.1007/JHEP10(2023)089
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DOI: https://doi.org/10.1007/JHEP10(2023)089