arXiv subjects

Antony J. Speranza

Publications and source records attributed to Antony J. Speranza.

24 records · Page 2Linked to original sources

arXiv2017

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, $SL(2,\mathbb{R})$ 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.

hep-th↗

arXiv2016

Entanglement equilibrium for higher order gravity

We show that the linearized higher derivative gravitational field equations are equivalent to an equilibrium condition on the entanglement entropy of small spherical regions in vacuum. This extends Jacobson's recent derivation of the Einstein equation using entanglement to include general higher derivative corrections. The corrections are naturally associated with the subleading divergences in the entanglement entropy, which take the form of a Wald entropy evaluated on the entangling surface. Variations of this Wald entropy are related to the field equations through an identity for causal diamonds in maximally symmetric spacetimes, which we derive for arbitrary higher derivative theories. If the variations are taken holding fixed a geometric functional that we call the generalized volume, the identity becomes an equivalence between the linearized constraints and the entanglement equilibrium condition. We note that the fully nonlinear higher curvature equations cannot be derived from the linearized equations applied to small balls, in contrast to the situation encountered in Einstein gravity. The generalized volume is a novel result of this work, and we speculate on its thermodynamic role in the first law of causal diamond mechanics, as well as its possible application to holographic complexity.

hep-th↗

arXiv2016

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 $R^d$, the entanglement entropy calculation gives rise to terms scaling as $R^{2Δ}$, where $Δ$ is the dimension of the deforming operator. When $Δ\leq\frac{d}{2}$, the latter terms dominate the former, and suggest that a modification to the conjecture is needed.

hep-th↗

arXiv2015

Variations on an aethereal theme

We consider a class of Lorentz-violating theories of gravity involving a timelike unit vector field (the aether) coupled to a metric, two examples being Einstein-aether theory and Hořava gravity. The action always includes the Ricci scalar of the metric and the invariants quadratic in covariant derivatives of the aether, but the theories differ in how the aether is constructed from other fields, and whether those fields are varied in the action. Fields that are not varied define background structures breaking diffeomorphsim invariance, including threadings, folations, and clocks, which generally produce novel degrees of freedom arising from the violation of what would otherwise be initial value constraints. The principal aims of this paper are to survey the nature of the theories that arise, and to understand the consequences of breaking diffeomorphism invariance in this setting. In a companion paper [arXiv:1504.03305], we address some of the phenomenology of the "ponderable aether" case in which the presence of a background clock endows the aether with a variable internal energy density that behaves in some respects like dark matter.

gr-qc↗

arXiv2015

Ponderable aether

We consider a Lorentz-violating theory of gravity where the aether vector is taken to be nondynamical. This "ponderable aether theory" is almost the same as Einstein-aether theory (where the aether vector is dynamical), but involves additional integration constants arising due to the loss of initial value constraints. One of these produces an effective energy density for the aether fluid, similar to the appearance of dark matter in projectable Hořava gravity and the mimetic dark matter theory. Here we investigate the extent to which this energy density can reproduce the phenomenology of dark matter. Although it is indistinguishable from cold dark matter in homogeneous, isotropic cosmology, it encounters phenomenological problems in both spherically symmetric configurations and cosmological perturbations. Furthermore, inflationary considerations lead us to expect a tiny value for the ponderable aether energy density today unless a sourcing effect is added to the theory. The theory then effectively reduces to dynamical Einstein-aether theory, rendering moot the question of whether an aether must be dynamical in order to be consistent.

gr-qc↗

arXiv2014

Comment on "Scalar Einstein-Aether theory"

A recent paper studies a modification of Einstein-aether theory in which the aether vector is restricted, at the level of the action, to be the gradient of a scalar. In this comment we note that this scalar version of Einstein-aether theory is equivalent to the projectable version of the IR limit of Hořava gravity when the potential for the scalar is constant. This provides a generally covariant formulation for projectable Hořava gravity.

gr-qc↗