Analyticity and the holographic \(S\)-matrix. (English) Zbl 1397.81300
Summary: We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk \(S\)-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the \(S\)-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
References:
| [1] | Penedones, J., Writing CFT correlation functions as AdS scattering amplitudes, JHEP, 03, 025, (2011) · Zbl 1301.81154 · doi:10.1007/JHEP03(2011)025 |
| [2] | Fitzpatrick, AL; Kaplan, J.; Penedones, J.; Raju, S.; Rees, BC, A natural language for AdS/CFT correlators, JHEP, 11, 095, (2011) · Zbl 1306.81225 · doi:10.1007/JHEP11(2011)095 |
| [3] | Paulos, MF, Towards Feynman rules for Mellin amplitudes, JHEP, 10, 074, (2011) · Zbl 1303.81122 · doi:10.1007/JHEP10(2011)074 |
| [4] | G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE]. |
| [5] | Mack, G., D-dimensional conformal field theories with anomalous dimensions as dual resonance models, Bulg. J. Phys., 36, 214, (2009) · Zbl 1202.81190 |
| [6] | Maldacena, JM, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys., 2, 231, (1998) · Zbl 0914.53047 |
| [7] | Witten, E., Anti-de Sitter space and holography, Adv. Theor. Math. Phys., 2, 253, (1998) · Zbl 0914.53048 |
| [8] | Gubser, S.; Klebanov, IR; Polyakov, AM, Gauge theory correlators from noncritical string theory, Phys. Lett., B 428, 105, (1998) · Zbl 1355.81126 |
| [9] | A. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-Matrix, arXiv:1112.4845 [INSPIRE]. |
| [10] | J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE]. |
| [11] | L. Susskind, Holography in the flat space limit, hep-th/9901079 [INSPIRE]. · Zbl 0973.83545 |
| [12] | Gary, M.; Giddings, SB; Penedones, J., Local bulk S-matrix elements and CFT singularities, Phys. Rev., D 80, 085005, (2009) |
| [13] | A.L. Fitzpatrick and J. Kaplan, Scattering States in AdS/CFT, arXiv:1104.2597 [INSPIRE]. |
| [14] | Arkani-Hamed, N.; Dubovsky, S.; Nicolis, A.; Trincherini, E.; Villadoro, G., A measure of de Sitter entropy and eternal inflation, JHEP, 05, 055, (2007) · doi:10.1088/1126-6708/2007/05/055 |
| [15] | Giddings, SB; Porto, RA, The gravitational S-matrix, Phys. Rev., D 81, 025002, (2010) |
| [16] | Heemskerk, I.; Penedones, J.; Polchinski, J.; Sully, J., Holography from conformal field theory, JHEP, 10, 079, (2009) · doi:10.1088/1126-6708/2009/10/079 |
| [17] | Fitzpatrick, AL; Katz, E.; Poland, D.; Simmons-Duffin, D., Effective conformal theory and the flat-space limit of AdS, JHEP, 07, 023, (2011) · Zbl 1298.81212 · doi:10.1007/JHEP07(2011)023 |
| [18] | Heemskerk, I.; Polchinski, J., Holographic and Wilsonian renormalization groups, JHEP, 06, 031, (2011) · Zbl 1298.81181 · doi:10.1007/JHEP06(2011)031 |
| [19] | Heemskerk, I.; Sully, J., More holography from conformal field theory, JHEP, 09, 099, (2010) · Zbl 1291.81351 · doi:10.1007/JHEP09(2010)099 |
| [20] | Rattazzi, R.; Rychkov, VS; Tonni, E.; Vichi, A., Bounding scalar operator dimensions in 4D CFT, JHEP, 12, 031, (2008) · Zbl 1329.81324 · doi:10.1088/1126-6708/2008/12/031 |
| [21] | Dolan, F.; Osborn, H., Conformal partial waves and the operator product expansion, Nucl. Phys., B 678, 491, (2004) · Zbl 1097.81735 · doi:10.1016/j.nuclphysb.2003.11.016 |
| [22] | Costa, MS; Penedones, J.; Poland, D.; Rychkov, S., Spinning conformal correlators, JHEP, 11, 071, (2011) · Zbl 1306.81207 · doi:10.1007/JHEP11(2011)071 |
| [23] | Costa, MS; Penedones, J.; Poland, D.; Rychkov, S., Spinning conformal blocks, JHEP, 11, 154, (2011) · Zbl 1306.81148 · doi:10.1007/JHEP11(2011)154 |
| [24] | Hellerman, S., A universal inequality for CFT and quantum gravity, JHEP, 08, 130, (2011) · Zbl 1298.83051 · doi:10.1007/JHEP08(2011)130 |
| [25] | Poland, D.; Simmons-Duffin, D.; Vichi, A., Carving out the space of 4D cfts, JHEP, 05, 110, (2012) · doi:10.1007/JHEP05(2012)110 |
| [26] | S. Rychkov, Conformal Bootstrap in Three Dimensions?, arXiv:1111.2115 [INSPIRE]. · Zbl 1365.81007 |
| [27] | Belavin, A.; Polyakov, AM; Zamolodchikov, A., Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys., B 241, 333, (1984) · Zbl 0661.17013 · doi:10.1016/0550-3213(84)90052-X |
| [28] | T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE]. |
| [29] | Balasubramanian, V.; Kraus, P.; Lawrence, AE; Trivedi, SP, Holographic probes of anti-de Sitter space-times, Phys. Rev., D 59, 104021, (1999) |
| [30] | Bena, I., On the construction of local fields in the bulk of ads_{5} and other spaces, Phys. Rev., D 62, 066007, (2000) |
| [31] | D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE]. |
| [32] | Gary, M.; Giddings, SB, The flat space S-matrix from the AdS/CFT correspondence?, Phys. Rev., D 80, 046008, (2009) |
| [33] | Dusedau, DW; Freedman, DZ, Lehmann spectral representation for anti-de Sitter quantum field theory, Phys. Rev., D 33, 389, (1986) |
| [34] | S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press, Cambridge, U.K. (1995). · Zbl 0959.81002 |
| [35] | Dolan, F.; Osborn, H., Conformal four point functions and the operator product expansion, Nucl. Phys., B 599, 459, (2001) · Zbl 1097.81734 · doi:10.1016/S0550-3213(01)00013-X |
| [36] | Amati, D.; Ciafaloni, M.; Veneziano, G., Superstring collisions at Planckian energies, Phys. Lett., B 197, 81, (1987) |
| [37] | S.B. Giddings, The gravitational S-matrix: Erice lectures, arXiv:1105.2036 [INSPIRE]. |
| [38] | R. Sundrum, From Fixed Points to the Fifth Dimension, arXiv:1106.4501 [INSPIRE]. · Zbl 1060.81622 |
| [39] | Adams, A.; Arkani-Hamed, N.; Dubovsky, S.; Nicolis, A.; Rattazzi, R., Causality, analyticity and an IR obstruction to UV completion, JHEP, 10, 014, (2006) · doi:10.1088/1126-6708/2006/10/014 |
| [40] | Skenderis, K., Lecture notes on holographic renormalization, Class. Quant. Grav., 19, 5849, (2002) · Zbl 1044.83009 · doi:10.1088/0264-9381/19/22/306 |
| [41] | Arkani-Hamed, N.; Cachazo, F.; Kaplan, J., What is the simplest quantum field theory?, JHEP, 09, 016, (2010) · Zbl 1291.81356 · doi:10.1007/JHEP09(2010)016 |
| [42] | Arkani-Hamed, N.; Cachazo, F.; Cheung, C.; Kaplan, J., A duality for the S matrix, JHEP, 03, 020, (2010) · Zbl 1271.81098 · doi:10.1007/JHEP03(2010)020 |
| [43] | Britto, R.; Cachazo, F.; Feng, B., New recursion relations for tree amplitudes of gluons, Nucl. Phys., B 715, 499, (2005) · Zbl 1207.81088 · doi:10.1016/j.nuclphysb.2005.02.030 |
| [44] | Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94, 181602, (2005) · doi:10.1103/PhysRevLett.94.181602 |
| [45] | Bern, Z.; Dixon, LJ; Roiban, R., Is N = 8 supergravity ultraviolet finite?, Phys. Lett., B 644, 265, (2007) · Zbl 1248.83136 |
| [46] | Bern, Z.; Carrasco, J.; Dixon, LJ; Johansson, H.; Roiban, R., The ultraviolet behavior of N =8 supergravity at four loops, Phys. Rev. Lett., 103, 081301, (2009) · doi:10.1103/PhysRevLett.103.081301 |
| [47] | Arkani-Hamed, N.; Kaplan, J., On tree amplitudes in gauge theory and gravity, JHEP, 04, 076, (2008) · Zbl 1246.81103 · doi:10.1088/1126-6708/2008/04/076 |
| [48] | Drummond, J.; Henn, J.; Korchemsky, G.; Sokatchev, E., Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys., B 828, 317, (2010) · Zbl 1203.81112 · doi:10.1016/j.nuclphysb.2009.11.022 |
| [49] | Banks, T.; Fischler, W.; Shenker, S.; Susskind, L., M theory as a matrix model: A conjecture, Phys. Rev., D 55, 5112, (1997) |
| [50] | Fitzpatrick, AL; Shih, D., Anomalous dimensions of non-chiral operators from AdS/CFT, JHEP, 10, 113, (2011) · Zbl 1303.81188 · doi:10.1007/JHEP10(2011)113 |
| [51] | Weinberg, S., Six-dimensional methods for four-dimensional conformal field theories, Phys. Rev., D 82, 045031, (2010) |
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