84 research outputs found
Warped Entanglement Entropy
We study the applicability of the covariant holographic entanglement entropy
proposal to asymptotically warped AdS spacetimes with an SL(2,R) x U(1)
isometry. We begin by applying the proposal to locally AdS backgrounds
which are written as a real-line fibration over AdS. We then perturb away
from this geometry by considering a warping parameter to get an
asymptotically warped AdS spacetime and compute the dual entanglement
entropy perturbatively in . We find that for large separation in the
fiber coordinate, the entanglement entropy can be computed to all orders in
and takes the universal form appropriate for two-dimensional CFTs. The
warping-dependent central charge thus identified exactly agrees with previous
calculations in the literature. Performing the same perturbative calculations
for the warped BTZ black hole again gives universal two-dimensional CFT
answers, with the left-moving and right-moving temperatures appearing
appropriately in the result.Comment: 25 pages plus appendices; v2 references added, discussions clarified
and equations sharpene
Grassmann Matrix Quantum Mechanics
We explore quantum mechanical theories whose fundamental degrees of freedom
are rectangular matrices with Grassmann valued matrix elements. We study
particular models where the low energy sector can be described in terms of a
bosonic Hermitian matrix quantum mechanics. We describe the classical curved
phase space that emerges in the low energy sector. The phase space lives on a
compact Kahler manifold parameterized by a complex matrix, of the type
discovered some time ago by Berezin. The emergence of a semiclassical bosonic
matrix quantum mechanics at low energies requires that the original Grassmann
matrices be in the long rectangular limit. We discuss possible holographic
interpretations of such matrix models which, by construction, are endowed with
a finite dimensional Hilbert space.Comment: 25 pages + appendice
Matrix integrals finite holography
We explore the conjectured duality between a class of large matrix
integrals, known as multicritical matrix integrals (MMI), and the series
of non-unitary minimal models on a fluctuating background. We match
the critical exponents of the leading order planar expansion of MMI, to those
of the continuum theory on an topology. From the MMI perspective this is
done both through a multi-vertex diagrammatic expansion, thereby revealing
novel combinatorial expressions, as well as through a systematic saddle point
evaluation of the matrix integral as a function of its parameters. From the
continuum point of view the corresponding critical exponents are obtained upon
computing the partition function in the presence of a given conformal primary.
Further to this, we elaborate on a Hilbert space of the continuum theory, and
the putative finiteness thereof, on both an and a topology using
BRST cohomology considerations. Matrix integrals support this finiteness.Comment: 42 pages + appendices, comments welcom
Marginal Deformations and Rotating Horizons
Motivated by the near-horizon geometry of four-dimensional extremal black
holes, we study a disordered quantum mechanical system invariant under a global
symmetry. As in the Sachdev-Ye-Kitaev model, this system exhibits an
approximate symmetry at low energies, but also allows for a
continuous family of breaking marginal deformations. Beyond a certain
critical value for the marginal coupling, the model exhibits a quantum phase
transition from the gapless phase to a gapped one and we calculate the critical
exponents of this transition. We also show that charged, rotating extremal
black holes exhibit a transition when the angular velocity of the horizon is
tuned to a certain critical value. Where possible we draw parallels between the
disordered quantum mechanics and charged, rotating black holes.Comment: 29 pages, 5 figure
Higher Spin de Sitter Holography from Functional Determinants
We discuss further aspects of the higher spin dS/CFT correspondence. Using a
recent result of Dunne and Kirsten, it is shown how to numerically compute the
partition function of the free Sp(N) model for a large class of SO(3)
preserving deformations of the flat/round metric on R^3/S^3 and the source of
the spin-zero single-trace operator dual to the bulk scalar. We interpret this
partition function as a Hartle-Hawking wavefunctional. It has a local maximum
about the pure de Sitter vacuum. Restricting to SO(3) preserving deformations,
other local maxima (which exceed the one near the de Sitter vacuum) can peak at
inhomogeneous and anisotropic values of the late time metric and scalar
profile. Numerical experiments suggest the remarkable observation that, upon
fixing a certain average of the bulk scalar profile at I^+, the wavefunction
becomes normalizable in all the other (infinite) directions of the deformation.
We elucidate the meaning of double trace deformations in the context of dS/CFT
as a change of basis and as a convolution. Finally, we discuss possible
extensions of higher spin de Sitter holography by coupling the free theory to a
Chern-Simons term.Comment: 30 pages plus appendices; v2 references adde
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