74 research outputs found
2D Black Hole and Holographic Renormalization Group
In hep-th/0311177, the Large renormalization group (RG) flows of a
modified matrix quantum mechanics on a circle, capable of capturing effects of
nonsingets, were shown to have fixed points with negative specific heat. The
corresponding rescaling equation of the compactified matter field with respect
to the RG scale, identified with the Liouville direction, is used to extract
the two dimensional Euclidean black hole metric at the new type of fixed
points. Interpreting the large RG flows as flow velocities in holographic
RG in two dimensions, the flow equation of the matter field around the black
hole fixed point is shown to be of the same form as the radial evolution
equation of the appropriate bulk scalar coupled to 2D black hole.Comment: 21 page
No Page curves for the de Sitter horizon
We investigate the fine-grained entropy of the de Sitter cosmological
horizon. Starting from three-dimensional pure de Sitter space, we consider a
partial reduction approach, which supplies an auxiliary system acting as a heat
bath both at future infinity and inside the static patch. This allows us to
study the time-dependent entropy of radiation collected for both observers in
the out-of-equilibrium Unruh-de Sitter state, analogous to black hole
evaporation for a cosmological horizon. Central to our analysis in the static
patch is the identification of a weakly gravitating region close to the past
cosmological horizon; this is suggestive of a relation between observables at
future infinity and inside the static patch. We find that in principle, while
the meta-observer at future infinity naturally observes a pure state, the
static patch observer requires the use of the island formula to reproduce a
unitary Page curve. However, in practice, catastrophic backreaction occurs at
the Page time, and neither observer will see unitary evaporation.Comment: 33 pages, 8 figures. v2: references added, minor edits. v3: as
published in JHEP. Minor edits. Comments and clarifications added, regarding
e.g. the static patch backreacted dilaton, and the weakly-coupled radiation
regio
Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
We study the semi-classical thermodynamics of two-dimensional de Sitter space
() in Jackiw-Teitelboim (JT) gravity coupled to conformal
matter. We extend the quasi-local formalism of Brown and York to
, where a timelike boundary is introduced in the static patch to
uniquely define conserved charges, including quasi-local energy. The boundary
divides the static patch into two systems, a cosmological system and a black
hole system, the former being unstable under thermal fluctuations while the
latter is stable. A semi-classical quasi-local first law is derived, where the
Gibbons--Hawking entropy is replaced by the generalized entropy. In the
microcanonical ensemble the generalized entropy is stationary. Further, we show
the on-shell Euclidean microcanonical action of a causal diamond in
semi-classical JT gravity equals minus the generalized entropy of the diamond,
hence extremization of the entropy follows from minimizing the action. Thus, we
provide a first principles derivation of the island rule for symmetric
backgrounds, without invoking the replica trick. We discuss the
implications of our findings for static patch de Sitter holography.Comment: 48 pages + 4 appendices, 13 figure
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality invariants of the dyonic charges, the symmetry group of the root system as the extended S-duality group PGL(2,Z) of the theory, and the walls of Weyl chambers as the walls of marginal stability for the relevant two-centered solutions. This leads to an interpretation for the Weyl group as the group of wall-crossing, or the group of discrete attractor flows. Furthermore we propose an equivalence between a ''second-quantized multiplicity'' of a charge- and moduli-dependent highest weight vector and the dyon degeneracy, and show that the wall-crossing formula following from our proposal agrees with the wall-crossing formula obtained from the supergravity analysis. This can be thought of as providing a microscopic derivation of the wall-crossing formula of this theory
Kahler Quantization of H3(CY3,R) and the Holomorphic Anomaly
Studying the quadratic field theory on seven dimensional spacetime
constructed by a direct product of Calabi-Yau three-fold by a real time axis,
with phase space being the third cohomology of the Calabi-Yau three-fold, the
generators of translation along moduli directions of
Calabi-Yau three-fold are constructed. The algebra of these generators is
derived which take a simple form in canonical coordinates. Applying the Dirac
method of quantization of second class constraint systems, we show that the
Schr\"{o}dinger equations corresponding to these generators are equivalent to
the holomorphic anomaly equations if one defines the action functional of the
quadratic field theory with a proper factor one-half.Comment: 10 pages, few typos corrected, to appear in JHE
Quantization and holomorphic anomaly
We study wave functions of B-model on a Calabi-Yau threefold in various
polarizations.Comment: 15 page
Counting Dyons in N=8 String Theory
A recently discovered relation between 4D and 5D black holes is used to
derive exact (weighted) BPS black hole degeneracies for 4D N=8 string theory
from the exactly known 5D degeneracies. A direct 4D microscopic derivation in
terms of weighted 4D D-brane bound state degeneracies is sketched and found to
agree.Comment: 10 page
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