28 research outputs found
Local phase space and edge modes for diffeomorphism-invariant theories
We discuss an approach to characterizing local degrees of freedom of a
subregion in diffeomorphism-invariant theories using the extended phase space
of Donnelly and Freidel, [JHEP 2016 (2016) 102]. Such a characterization is
important for defining local observables and entanglement entropy in
gravitational theories. Traditional phase space constructions for subregions
are not invariant with respect to diffeomorphisms that act at the boundary. The
extended phase space remedies this problem by introducing edge mode fields at
the boundary whose transformations under diffeomorphisms render the extended
symplectic structure fully gauge invariant. In this work, we present a general
construction for the edge mode symplectic structure. We show that the new
fields satisfy a surface symmetry algebra generated by the Noether charges
associated with the edge mode fields. For surface-preserving symmetries, the
algebra is universal for all diffeomorphism-invariant theories, comprised of
diffeomorphisms of the boundary, transformations of the
normal plane, and, in some cases, normal shearing transformations. We also show
that if boundary conditions are chosen such that surface translations are
symmetries, the algebra acquires a central extension.Comment: 29+12 pages, references added and minor typos fixe
Ambiguity resolution for integrable gravitational charges
Recently, Ciambelli, Leigh, and Pai (CLP) [arXiv:2111.13181] have shown that
nonzero charges integrating Hamilton's equation can be defined for all
diffeomorphisms acting near the boundary of a subregion in a gravitational
theory. This is done by extending the phase space to include a set of embedding
fields that parameterize the location of the boundary. Because their
construction differs from previous works on extended phase spaces by a
covariant phase space ambiguity, the question arises as to whether the
resulting charges are unambiguously defined. Here, we demonstrate that
ambiguity-free charges can be obtained by appealing to the variational
principle for the subregion, following recent developments on dealing with
boundaries in the covariant phase space. Resolving the ambiguity produces
corrections to the diffeomorphism charges, and also generates additional
obstructions to integrability of Hamilton's equation. We emphasize the fact
that the CLP extended phase space produces nonzero diffeomorphism charges
distinguishes it from previous constructions in which diffeomorphisms are pure
gauge, since the embedding fields can always be eliminated from the latter by a
choice of unitary gauge. Finally, we show that Wald-Zoupas charges, with their
characteristic obstruction to integrability, are associated with a modified
transformation in the extended phase space, clarifying the reason behind
integrability of Hamilton's equation for standard diffeomorphisms.Comment: 22 pages; v2, updated discussion, references adde
Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
For a conformal field theory (CFT) deformed by a relevant operator, the
entanglement entropy of a ball-shaped region may be computed as a perturbative
expansion in the coupling. A similar perturbative expansion exists for excited
states near the vacuum. Using these expansions, this work investigates the
behavior of excited state entanglement entropies of small, ball-shaped regions.
The motivation for these calculations is Jacobson's recent work on the
equivalence of the Einstein equation and the hypothesis of maximal vacuum
entropy [arXiv:1505.04753], which relies on a conjecture stating that the
behavior of these entropies is sufficiently similar to a CFT. In addition to
the expected type of terms which scale with the ball radius as , the
entanglement entropy calculation gives rise to terms scaling as ,
where is the dimension of the deforming operator. When
, the latter terms dominate the former, and suggest that
a modification to the conjecture is needed.Comment: 31 pages + appendices and references, 2 figure
Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
We consider CFT states defined by adding nonlocal multi-trace sources to the
Euclidean path integral defining the vacuum state. For holographic theories, we
argue that these states correspond to states in the gravitational theory with a
good semiclassical description but with a more general structure of bulk
entanglement than states defined from single-trace sources. We show that at
leading order in large N, the entanglement entropies for any such state are
precisely the same as those of another state defined by appropriate
single-trace effective sources; thus, if the leading order entanglement
entropies are geometrical for the single-trace states of a CFT, they are
geometrical for all the multi-trace states as well. Next, we consider the
perturbative calculation of 1/N corrections to the CFT entanglement entropies,
demonstrating that these show qualitatively different features, including
non-analyticity in the sources and/or divergences in the naive perturbative
expansion. These features are consistent with the expectation that the 1/N
corrections include contributions from bulk entanglement on the gravity side.
Finally, we investigate the dynamical constraints on the bulk geometry and the
quantum state of the bulk fields which must be satisfied so that the entropies
can be reproduced via the quantum-corrected Ryu-Takayanagi formula.Comment: 60 pages + appendices, 7 figures; v2: minor additions, published
versio