Emergent spacetime and holographic CFTs

By S. El-Showk, K. Papadodimas. 2011

321 citations recorded by the source corpus.

A bstractWe discuss universal properties of conformal field theories with holographic duals. A central feature of these theories is the existence of a low-lying sector of operators whose correlators factorize. We demonstrate that factorization can only hold in the large central charge limit. Using conformal invariance and factorization we argue that these operators are naturally represented as fields in AdS as this makes the underlying linearity of the system manifest. In this class of CFTs the solution of the conformal bootstrap conditions can be naturally organized in structures which coincide with Witten diagrams in the bulk. The large value of the central charge suggests that the theory must include a large number of new operators not captured by the factorized sector. Consequently we may think of the AdS hologram as an effective representation of a small sector of the CFT, which is embedded inside a much larger Hilbert space corresponding to the black hole microstates.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7defee399cf07c484b3cfa9cff5957c8e020cce9

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Citations in the corpus

Virasoro conformal blocks in closed form (2015, unknown): “[41–43]).”
The analytic bootstrap and AdS superhorizon locality (2012, background): “In a parallel series of developments, there has been significant progress understanding effective field theory in AdS and its interpretation in CFT [10, 13, 16–19].”
Causality constraints in conformal field theory (2015, background): “The story for scalars, initiated in [23] and developed for example in [16, 24–33], is that effective field theories in the bulk are in one-to-one correspondence with solutions of crossing symmetry in CFT, order by order in 1/N .”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “One can quickly check this against the d = 4 example in Appendix B of [45].”
Bootstrapping the O(N) archipelago (2015, unknown): “The one-point functions B and Hxx are in principle determined by the spectrum and OPE coefficients of the theory [63].”
Worldline approach to semi-classical conformal blocks (2015, background): “, both due to their central role in the revival of the conformal bootstrap program [4], and also as a useful way to think about how local physics can emerge in the bulk in examples of AdS/CFT duality [5,6,7,8,9,10].2 It is the latter perspective which is closest to our considerations here. Recent wo”
Loops in AdS from conformal field theory (2016, background): “Knowing loop amplitudes in a given bulk theory would open the door to nonplanar extensions of dynamical aspects of holography and the conformal bootstrap [34–50].”
Universality of long-distance AdS physics from the CFT bootstrap (2014, result): “This is in contrast to analyses that demonstrate sub-AdS scale locality after making various additional assumptions about the CFT [9–14].”
Inconsistency of islands in theories with long-range gravity (2021, background): “Even if one attempts to “discard” the asymptotic metric from the algebra of operators in I at leading order, it will reappear in the algebra at subleading order [82].”
Holographic duality from random tensor networks (2016, background): “In the particular case when the bulk geometry is a hyperbolic space, the suppression of two-point correlations discussed here translates into the scaling dimension gap of boundary operators, which is known to be a required property for CFTs with gravity duals [23–25].”
Lessons from the information paradox (2020, background): “(For a discussion of “generalized free fields”, we refer the reader to [189] and to section 2 of [59].”
Bootstrapping inflationary correlators in Mellin space (2019, background): “Holography has by now inspired a great number of tools to understand boundary observables for theories on asymptotic anti-de Sitter (AdS) space in terms of simple consistency requirements on correlators in Conformal Field Theory (CFT) [1–4].”
Holographic Quantum Matter (2016, background): “Beyond the holographic approach discussed here, the development of purely quantum field theoretic methods exploiting the existence of an operator gap has recently been initiated [237; 262; 264; 331].”