Bianchi, Massimo; Freedman, Daniel Z.; Skenderis, Kostas Holographic renormalization. (English) Zbl 0995.81075 Nucl. Phys., B 631, No. 1-2, 159-194 (2002). Summary: We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector. Cited in 212 Documents MSC: 81T17 Renormalization group methods applied to problems in quantum field theory Keywords:RG flows; asymptotically AdS domain walls; local boundary counterterms PDFBibTeX XMLCite \textit{M. Bianchi} et al., Nucl. Phys., B 631, No. 1--2, 159--194 (2002; Zbl 0995.81075) Full Text: DOI arXiv References: [1] Maldacena, J., Adv. Theor. Math. Phys., 2, 231-252 (1998) [2] Witten, E., Adv. Theor. Math. Phys., 2, 253-291 (1998) [3] Gubser, S.; Klebanov, I.; Polyakov, A., Phys. Lett. B, 428, 105-114 (1998) [4] Freedman, D. Z.; Gubser, S. S.; Pilch, K.; Warner, N. P., Adv. Theor. Math. Phys., 3, 363 (1999) [5] Freedman, D. Z.; Gubser, S. S.; Pilch, K.; Warner, N. P., JHEP, 0007, 038 (2000) [6] Brandhuber, A.; Sfetsos, K., Adv. Theor. Math. Phys., 3, 851 (1999) [7] Girardello, L.; Petrini, M.; Porrati, M.; Zaffaroni, A., Nucl. Phys. B, 569, 451-469 (2000) [8] Porrati, M.; Starinets, A., Phys. Lett. B, 454, 77 (1999) · Zbl 1009.83523 [9] Petrini, M.; Zaffaroni, A., The holographic RG flow to conformal and nonconformal theory [10] Pilch, K.; Warner, N. P., Nucl. Phys. B, 594, 209 (2001) · Zbl 0971.83513 [11] Freedman, D. Z.; Henry-Labordere, P., Field theory insight from the AdS/CFT correspondence, and references therein [12] Freedman, D. Z.; Mathur, S. D.; Matusis, A.; Rastelli, L., Nucl. Phys. B, 546, 96 (1999) [13] Henningson, M.; Skenderis, K., Fortsch. Phys., 48, 125 (2000) [14] de Haro, S.; Solodukhin, S. N.; Skenderis, K., Commun. Math. Phys., 217, 595 (2001) [15] Bianchi, M.; Freedman, D. Z.; Skenderis, K., JHEP, 0108, 041 (2001) [16] Mück, W., Correlation functions in holographic renormalization group flows · Zbl 0988.81081 [17] Arutyunov, G.; Frolov, S.; Theisen, S., Phys. Lett. B, 484, 295 (2000) [18] Bianchi, M.; DeWolfe, O.; Freedman, D. Z.; Pilch, K., JHEP, 0101, 021 (2001) [19] Brandhuber, A.; Sfetsos, K., JHEP, 0012, 014 (2000) [20] DeWolfe, O.; Freedman, D. Z., Notes on fluctuations and correlation functions in holographic renormalization group flows [21] Boonstra, H. J.; Skenderis, K.; Townsend, P. K., JHEP, 9901, 003 (1999) [22] Skenderis, K.; Townsend, P. K., Phys. Lett. B, 468, 46 (1999) [23] DeWolfe, O.; Freedman, D. Z.; Gubser, S. S.; Karch, A., Phys. Rev. D, 62, 046008 (2000) [24] Townsend, P. K., Phys. Lett., 148B, 55 (1984) [25] de Boer, J.; Verlinde, E.; Verlinde, H., JHEP, 0008, 003 (2000) [26] Berg, M.; Samtleben, H., An exact holographic RG flow between 2d conformal fixed points [27] Fefferman, C.; Graham, C. R., Conformal invariants, (Elie Cartan et les Mathématiques d’aujourd’hui (1985), Astérisque), 95 · Zbl 0602.53007 [28] Imbimbo, C.; Schwimmer, A.; Theisen, S.; Yankielowicz, S., Class. Quantum Grav., 17, 1129-1138 (2000) [29] Skenderis, K., Int. J. Mod. Phys. A, 16, 740 (2001) [30] Erdmenger, J., Phys. Rev. D, 64, 085012 (2001) [31] Brown, J. D.; York, J. W., Phys. Rev. D, 47, 1407 (1993) [32] Balasubramanian, V.; Kraus, P., Commun. Math. Phys., 208, 413 (1999) [33] Klebanov, I. R.; Witten, E., Nucl. Phys. B, 556, 89-114 (1999) [34] Petkou, A.; Skenderis, K., Nucl. Phys. B, 561, 100 (1999) [35] Kalkkinen, J.; Martelli, D.; Mück, W., JHEP, 0104, 036 (2001) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.