235 research outputs found
Generalized conformal structure, dilaton gravity and SYK
A theory admits generalized conformal structure if the only scale in the
quantum theory is set by a dimensionful coupling. SYK is an example of a theory
with generalized conformal structure and in this paper we investigate the
consequences of this structure for correlation functions and for the
holographic realization of SYK. The Ward identities associated with the
generalized conformal structure of SYK are implemented holographically in
gravity/multiple scalar theories, which always have a parent AdS origin.
For questions involving only the graviton/running scalar sector, one can always
describe the bulk running in terms of a single scalar but multiple running
scalars are in general needed once one includes the bulk fields corresponding
to all SYK operators. We then explore chaos in holographic theories with
generalized conformal structure. The four point function explored by Maldacena,
Shenker and Stanford exhibits exactly the same chaotic behaviour in any such
theory as in holographic realizations of conformal theories i.e. the
dimensionful coupling scale does not affect the chaotic exponential growth.Comment: 42 pages, 3 figure
Generalized entanglement entropy
We discuss two measures of entanglement in quantum field theory and their
holographic realizations. For field theories admitting a global symmetry, we
introduce a global symmetry entanglement entropy, associated with the
partitioning of the symmetry group. This quantity is proposed to be related to
the generalized holographic entanglement entropy defined via the partitioning
of the internal space of the bulk geometry. The second measure of quantum field
theory entanglement is the field space entanglement entropy, obtained by
integrating out a subset of the quantum fields. We argue that field space
entanglement entropy cannot be precisely realised geometrically in a
holographic dual. However, for holographic geometries with interior decoupling
regions, the differential entropy provides a close analogue to the field space
entanglement entropy. We derive generic descriptions of such inner throat
regions in terms of gravity coupled to massive scalars and show how the
differential entropy in the throat captures features of the field space
entanglement entropy.Comment: 40 pages, 3 figure
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