25 research outputs found
Higher spin JT gravity and a matrix model dual
We propose a generalization of the Saad-Shenker-Stanford duality relating
matrix models and JT gravity to the case in which the bulk includes higher spin
fields. Using a BF theory we compute the disk and
generalization of the trumpet partition function in this theory. We then study
higher genus corrections and show how this differs from the usual JT gravity
calculations. In particular, the usual quotient by the mapping class group is
not enough to ensure finite answers and so we propose to extend this group with
additional elements that make the gluing integrals finite. These elements can
be thought of as large higher spin diffeomorphisms. The cylinder contribution
to the spectral form factor then behaves as at late times ,
signaling a deviation from conventional random matrix theory. To account for
this deviation, we propose that the bulk theory is dual to a matrix model
consisting of commuting matrices associated to the conserved higher
spin charges. We find further evidence for the existence of the additional
mapping class group elements by interpreting the bulk gauge theory
geometrically and employing the formalism developed by Gomis et al. in the
nineties. This formalism introduces additional (auxiliary) boundary times so
that each conserved charge generates translations in those new directions. This
allows us to find an explicit description for the
Schwarzian theory for the disk and trumpet and view the additional mapping
class group elements as ordinary Dehn twists, but in higher dimensions.Comment: 44 pages, 7 figure
Comments on a state-operator correspondence for the torus
We investigate the existence of a state-operator correspondence on the torus.
This correspondence would relate states of the CFT Hilbert space living on a
spatial torus to the path integral over compact Euclidean manifolds with
operator insertions. Unlike the states on the sphere that are associated to
local operators, we argue that those on the torus would more naturally be
associated to line operators. We find evidence that such a correspondence
cannot exist and in particular, we argue that no compact Euclidean path
integral can produce the vacuum on the torus. Our arguments come solely from
field theory and formulate a CFT version of the Horowitz-Myers conjecture for
the AdS soliton.Comment: 29 pages, 8 figure
An integrable road to a perturbative plateau
As has been known since the 90s, there is an integrable structure underlying
two-dimensional gravity theories. Recently, two-dimensional gravity theories
have regained an enormous amount of attention, but now in relation with quantum
chaos - superficially nothing like integrability. In this paper, we return to
the roots and exploit the integrable structure underlying dilaton gravity
theories to study a late time, large double scaled limit of
the spectral form factor. In this limit, a novel cancellation due to the
integrable structure ensures that at each genus the spectral form factor
grows like , and that the sum over genera converges, realising a
perturbative approach to the late-time plateau. Along the way, we clarify
various aspects of this integrable structure. In particular, we explain the
central role played by ribbon graphs, we discuss intersection theory, and we
explain what the relations with dilaton gravity and matrix models are from a
more modern holographic perspective.Comment: 44 pages + appendice