357 research outputs found
Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models
The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset
space Diff/, where Diff, or Virasoro group, is the
group of diffeomorphisms of the time coordinate valued on the real line or a
circle. It is known that the coadjoint orbit action of Diff naturally turns out
to be the two-dimensional quantum gravity action of Polyakov without
cosmological constant, in a certain gauge, in an asymptotically flat spacetime.
Motivated by this observation, we explore Polyakov action with cosmological
constant and boundary terms, and study the possibility of such a
two-dimensional quantum gravity model being the AdS dual to the low energy (NG)
sector of the SYK model. We find strong evidences for this duality: (a) the
bulk action admits an exact family of asymptotically AdS spacetimes,
parameterized by Diff/, in addition to a fixed
conformal factor of a simple functional form; (b) the bulk path integral
reduces to a path integral over Diff/ with a
Schwarzian action; (c) the low temperature free energy qualitatively agrees
with that of the SYK model. We show, up to quadratic order, how to couple an
infinite series of bulk scalars to the Polyakov model and show that it
reproduces the coupling of the higher modes of the SYK model with the NG
bosons.Comment: 2+33 pages (including Appendices), 3 figures; v2 has revised
discussion of orbits in Section 2, typos corrected; v3 has a new appendix
analysing the off-shell equations of motion; v4 is published version with
some more typos corrected; v5 corrects some typesetting error
All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be
used to compute all tree level scattering amplitudes in terms of
scattering amplitude in Chern-Simons
(CS) theory coupled to matter in fundamental representation. As a byproduct, we
also obtain a recursion relation for the CS theory coupled to regular fermions,
even though in this case standard BCFW deformations do not have a good
asymptotic behaviour. Moreover at large , scattering can be
computed exactly to all orders in 't Hooft coupling as was done in earlier
works by some of the authors. In particular, for theory, it
was shown that scattering is tree level exact to all orders
except in the anyonic channel arXiv:1505.06571, where it gets renormalized by a
simple function of 't Hooft coupling. This suggests that it may be possible to
compute the all loop exact result for arbitrary higher point scattering
amplitudes at large .Comment: RevTEX 4.1, 5 pages+6 Appendices, 7 figures; V2 Published versio
Dual Superconformal Symmetry of Chern-Simons theory with Fundamental Matter at Large
Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes
that have aided the study of scattering amplitudes in highly supersymmetric
theories like SYM and ABJM. However, in general such symmetries
are absent from the theories with lesser or no supersymmetry. In this paper, we
show that the tree level scattering amplitude in the 3d
Chern-Simons theory coupled to a fundamental chiral multiplet is dual
superconformal invariant. In the 't Hooft large limit, the
scattering amplitude in this theory has been shown to be tree-level exact in
non-anyonic channels, while having only an overall multiplicative coupling
dependent renormalisation in the anyonic channel. Therefore, the dual
superconformal symmetry that we demonstrate in this paper is all loop exact.
This is unlike the previously studied highly supersymmetric theories where dual
superconformal symmetry is anomalous at loop levels.
Furthermore, we reverse the argument to study the extent to which dual
superconformal invariance fixes the scattering amplitude in an
supersymmetric theory. We demonstrate that requiring the dual superconformal
invariance completely fixes the momentum dependence of the amplitude,
while the coupling constant dependence remain unfixed. Further, we use a
combination of parity invariance, unitarity and self-duality of the amplitude
to constrain the coupling dependence of scattering amplitude.Comment: V2 Published versio
Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity
We generalize the eigenstate thermalization hypothesis to systems with global
symmetries. We present two versions, one with microscopic charge conservation
and one with exponentially suppressed violations. They agree for correlation
functions of simple operators, but differ in the variance of charged one-point
functions at finite temperature. We then apply these ideas to holography and to
gravitational low-energy effective theories with a global symmetry. We show
that Euclidean wormholes predict a non-zero variance for charged one-point
functions, which is incompatible with microscopic charge conservation. This
implies that global symmetries in quantum gravity must either be gauged or
explicitly broken by non-perturbative effects.Comment: 6 pages, 1 figure; v2 references and comments added, correction of
the Wilson line argument. Version as published in Scipos
From operator statistics to wormholes
For a generic quantum many-body system, the quantum ergodic regime is defined
as the limit in which the spectrum of the system resembles that of a random
matrix theory (RMT) in the corresponding symmetry class. In this paper we
analyse the time dependence of correlation functions of operators. We study
them in the ergodic limit as well as their approach to the ergodic limit which
is controlled by non-universal massive modes. An effective field theory (EFT)
corresponding to the causal symmetry and its breaking describes the ergodic
phase. We demonstrate that the resulting Goldstone-mode theory has a
topological expansion, analogous to the one described in arXiv:2008.02271 with
added operator sources, whose leading non-trivial topologies give rise to the
universal ramp seen in correlation functions. The ergodic behaviour of
operators in our EFT is seen to result from a combination of RMT-like spectral
statistics and Haar averaging over wave-functions. Furthermore we analytically
capture the plateau behaviour by taking into account the contribution of a
second saddle point. Our main interest are quantum many-body systems with
holographic duals and we explicitly establish the validity of the EFT
description in the SYK-class of models, starting from their microscopic
description. By studying the tower of massive modes above the Goldstone sector
we get a detailed understanding of how the ergodic EFT phase is approached and
derive the relevant Thouless time scales. We point out that the topological
expansion can be reinterpreted in terms of contributions of bulk wormholes and
baby-universes.Comment: 31 pages, 7 figures, 3 appendices; v2: added some reference
On the Dynamics of Near-Extremal Black Holes
We analyse the dynamics of near-extremal Reissner-Nordstr\"om black holes in
asymptotically four-dimensional Anti-de Sitter space (AdS). We work in the
spherically symmetric approximation and study the thermodynamics and the
response to a probe scalar field. We find that the behaviour of the system, at
low energies and to leading order in our approximations, is well described by
the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be
understood from symmetry considerations and arises due to the breaking of time
reparametrisation invariance. The JT model has been analysed in considerable
detail recently and related to the behaviour of the SYK model. Our results
indicate that features in these models which arise from symmetry considerations
alone are more general and present quite universally in near-extremal black
holes.Comment: 44 (=26+18) pages, 1 figure, 6 appendices; v2: references added; v3:
minor changes made; v4: additional references added, version accepted in JHE
Approximate CFTs and Random Tensor Models
A key issue in both the field of quantum chaos and quantum gravity is an
effective description of chaotic conformal field theories (CFTs), that is CFTs
that have a quantum ergodic limit. We develop a framework incorporating the
constraints of conformal symmetry and locality, allowing the definition of
ensembles of `CFT data'. These ensembles take on the same role as the ensembles
of random Hamiltonians in more conventional quantum ergodic phases of many-body
quantum systems. To describe individual members of the ensembles, we introduce
the notion of approximate CFT, defined as a collection of `CFT data' satisfying
the usual CFT constraints approximately, i.e. up to small deviations. We show
that they generically exist by providing concrete examples. Ensembles of
approximate CFTs are very natural in holography, as every member of the
ensemble is indistinguishable from a true CFT for low-energy probes that only
have access to information from semi-classical gravity. To specify these
ensembles, we impose successively higher moments of the CFT constraints.
Lastly, we propose a theory of pure gravity in AdS as a random
matrix/tensor model implementing approximate CFT constraints. This tensor model
is the maximum ignorance ensemble compatible with conformal symmetry, crossing
invariance, and a primary gap to the black-hole threshold. The resulting theory
is a random matrix/tensor model governed by the Virasoro 6j-symbol.Comment: 45 pages + appendices, 6 figure
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