Abstract
We introduce and study renormalization group interfaces between two holographic conformal theories which are related by deformation by a scalar double trace operator. At leading order in the 1/N expansion, we derive expressions for the two point correlation functions of the scalar, as well as the spectrum of operators living on the interface. We also compute the interface contribution to the sphere partition function, which in two dimensions gives the boundary g factor. Checks of our proposal include reproducing the g factor and some defect overlap coefficients of Gaiotto’s RG interfaces at large N , and the two-point correlation function whenever conformal perturbation theory is valid.
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References
I. Brunner and D. Roggenkamp, Defects and bulk perturbations of boundary Landau-Ginzburg orbifolds, JHEP 04 (2008) 001 [arXiv:0712.0188] [INSPIRE].
A. Konechny and C. Schmidt-Colinet, Entropy of conformal perturbation defects, J. Phys. A 47 (2014) 485401 [arXiv:1407.6444] [INSPIRE].
I. Brunner and C. Schmidt-Colinet, Reflection and transmission of conformal perturbation defects, J. Phys. A 49 (2016) 195401 [arXiv:1508.04350] [INSPIRE].
F. Gliozzi, P. Liendo, M. Meineri and A. Rago, Boundary and Interface CFTs from the Conformal Bootstrap, JHEP 05 (2015) 036 [arXiv:1502.07217] [INSPIRE].
D. Gaiotto, Domain Walls for Two-Dimensional Renormalization Group Flows, JHEP 12 (2012) 103 [arXiv:1201.0767] [INSPIRE].
T. Dimofte, D. Gaiotto and R. van der Veen, RG Domain Walls and Hybrid Triangulations, Adv. Theor. Math. Phys. 19 (2015) 137 [arXiv:1304.6721] [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, A dilatonic deformation of AdS 5 and its field theory dual, JHEP 05 (2003) 072 [hep-th/0304129] [INSPIRE].
E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Exact Half-BPS Flux Solutions in M-theory. I: Local Solutions, JHEP 08 (2008) 028 [arXiv:0806.0605] [INSPIRE].
E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Janus solutions in M-theory, JHEP 06 (2009) 018 [arXiv:0904.3313] [INSPIRE].
T. Nishioka and H. Tanaka, Lifshitz-like Janus Solutions, JHEP 02 (2011) 023 [arXiv:1010.6075] [INSPIRE].
D. Bak, M. Gutperle and R.A. Janik, Janus Black Holes, JHEP 10 (2011) 056 [arXiv:1109.2736] [INSPIRE].
M. Chiodaroli, J. Estes and Y. Korovin, Holographic two-point functions for Janus interfaces in the D1/D5 CFT, JHEP 04 (2017) 145 [arXiv:1612.08916] [INSPIRE].
N. Bobev, K. Pilch and N.P. Warner, Supersymmetric Janus Solutions in Four Dimensions, JHEP 06 (2014) 058 [arXiv:1311.4883] [INSPIRE].
P. Karndumri and K. Upathambhakul, Supersymmetric RG flows and Janus from type-II orbifold compactification, Eur. Phys. J. C 77 (2017) 455 [arXiv:1704.00538] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].
I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory, North Holland, (1966).
O. Aharony, O. DeWolfe, D.Z. Freedman and A. Karch, Defect conformal field theory and locally localized gravity, JHEP 07 (2003) 030 [hep-th/0303249] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [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].
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].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
D. Bak, A. Gustavsson and S.-J. Rey, Conformal Janus on Euclidean Sphere, JHEP 12 (2016) 025 [arXiv:1605.00857] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
C.P. Herzog, K.-W. Huang and K. Jensen, Universal Entanglement and Boundary Geometry in Conformal Field Theory, JHEP 01 (2016) 162 [arXiv:1510.00021] [INSPIRE].
D. Fursaev, Conformal anomalies of CFT’s with boundaries, JHEP 12 (2015) 112 [arXiv:1510.01427] [INSPIRE].
S.N. Solodukhin, Boundary terms of conformal anomaly, Phys. Lett. B 752 (2016) 131 [arXiv:1510.04566] [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
R. Jost, The General Theory of Quantized Fields, AMS, Providence, RI, U.S.A. (1965).
M.R. Gaberdiel and R. Gopakumar, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
C. Ahn, The Large-N ’t Hooft Limit of Coset Minimal Models, JHEP 10 (2011) 125 [arXiv:1106.0351] [INSPIRE].
C. Ahn, The Large-N ’t Hooft Limit of Kazama-Suzuki Model, JHEP 08 (2012) 047 [arXiv:1206.0054] [INSPIRE].
D. Roggenkamp and K. Wendland, Limits and degenerations of unitary conformal field theories, Commun. Math. Phys. 251 (2004) 589 [hep-th/0308143] [INSPIRE].
I. Runkel and G.M.T. Watts, A nonrational CFT with c = 1 as a limit of minimal models, JHEP 09 (2001) 006 [hep-th/0107118] [INSPIRE].
M.R. Gaberdiel and P. Suchanek, Limits of Minimal Models and Continuous Orbifolds, JHEP 03 (2012) 104 [arXiv:1112.1708] [INSPIRE].
S. Fredenhagen and C. Restuccia, The large level limit of Kazama-Suzuki models, JHEP 04 (2015) 015 [arXiv:1408.0416] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
D. Altschuler, M. Bauer and H. Saleur, Level rank duality in nonunitary coset theories, J. Phys. A 23 (1990) L789 [INSPIRE].
C. Ahn, D. Bernard and A. LeClair, Fractional Supersymmetries in Perturbed Coset CFTs and Integrable Soliton Theory, Nucl. Phys. B 346 (1990) 409 [INSPIRE].
S. Giombi and I.R. Klebanov, One Loop Tests of Higher Spin AdS/CFT, JHEP 12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
C. Crnkovic, R. Paunov, G.M. Sotkov and M. Stanishkov, Fusions of Conformal Models, Nucl. Phys. B 336 (1990) 637 [INSPIRE].
A. Recknagel, Permutation branes, JHEP 04 (2003) 041 [hep-th/0208119] [INSPIRE].
H. Ishikawa, Boundary states in coset conformal field theories, Nucl. Phys. B 629 (2002) 209 [hep-th/0111230] [INSPIRE].
T. Quella and V. Schomerus, Symmetry breaking boundary states and defect lines, JHEP 06 (2002) 028 [hep-th/0203161] [INSPIRE].
T. Quella, I. Runkel and G.M.T. Watts, Reflection and transmission for conformal defects, JHEP 04 (2007) 095 [hep-th/0611296] [INSPIRE].
P. Bouwknegt and K. Schoutens, W symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Springer New York (1997), [https://doi.org/10.1007/978-1-4612-2256-9].
V.S. Dotsenko and V.A. Fateev, Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models, Nucl. Phys. B 240 (1984) 312 [INSPIRE].
C.-M. Chang and X. Yin, Correlators in W N Minimal Model Revisited, JHEP 10 (2012) 050 [arXiv:1112.5459] [INSPIRE].
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFT d, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, A Mellin space approach to the conformal bootstrap, JHEP 05 (2017) 027 [arXiv:1611.08407] [INSPIRE].
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical tables, Wiley-Interscience, New York U.S.A., (1972).
H. Weyl, Über gewönliche lineare Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen, Göttinger Nachrichten (1910) 442-467, reprinted in H. Weyl, Gessamelte Abhandlungen I, Springer, (1968), pp. 222-247.
E.C. Titchmarsh, Eigenfunction expansions with second-order differential operators, Oxford, Clarendon Press, (1946).
M.N. Olevskii, On the representation of an arbitrary function in the form of an integral with a kernel containing a hypergeometric function (in Russian), Doklady Akad. Nauk SSSR (N.S.) 69 (1949) 11.
Y.A. Neretin, Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces, Sbornik Math. 192 (2001) 403 [math/0104035].
A. Erdélyi ed., Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York U.S.A., (1953).
A. Ebisu and K. Iwasaki, Three-Term Relations for 3F2(1), arXiv:1604.00480.
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Melby-Thompson, C.M., Schmidt-Colinet, C. Double trace interfaces. J. High Energ. Phys. 2017, 110 (2017). https://doi.org/10.1007/JHEP11(2017)110
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DOI: https://doi.org/10.1007/JHEP11(2017)110