8,212 research outputs found
Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known
to display rapid oscillations whose frequency is the Regge action. In this
note, we reformulate this result through a difference equation, asymptotically
satisfied by these models, and whose semi-classical solutions are precisely the
sine and the cosine of the Regge action. This equation is then interpreted as
coming from the canonical quantization of a simple constraint in Regge
calculus. This suggests to lift and generalize this constraint to the phase
space of loop quantum gravity parametrized by twisted geometries. The result is
a reformulation of the flat model for topological BF theory from the
Hamiltonian perspective. The Wheeler-de-Witt equation in the spin network basis
gives difference equations which are exactly recursion relations on the
15j-symbol. Moreover, the semi-classical limit is investigated using coherent
states, and produces the expected results. It mimics the classical constraint
with quantized areas, and for Regge geometries it reduces to the semi-classical
equation which has been introduced in the beginning.Comment: 16 pages, the new title is that of the published version (initial
title: A taste of Hamiltonian constraint in spin foam models
String Theory in Polar Coordinates and the Vanishing of the One-Loop Rindler Entropy
We analyze the string spectrum of flat space in polar coordinates, following
the small curvature limit of the cigar CFT. We first
analyze the partition function of the cigar itself, making some clarifications
of the structure of the spectrum that have escaped attention up to this point.
The superstring spectrum (type 0 and type II) is shown to exhibit an involution
symmetry, that survives the small curvature limit. We classify all marginal
states in polar coordinates for type II superstrings, with emphasis on their
links and their superconformal structure. This classification is confirmed by
an explicit large analysis of the partition function. Next we compare
three approaches towards the type II genus one entropy in Rindler space: using
a sum-over-fields strategy, using a Melvin model approach and finally using a
saddle point method on the cigar partition function. In each case we highlight
possible obstructions and motivate that the correct procedures yield a
vanishing result: . We finally discuss how the QFT UV divergences of the
fields in the spectrum disappear when computing the free energy and entropy
using Euclidean techniques.Comment: 58 pages + appendices, v2: typos corrected, matches published versio
Revisiting noninteracting string partition functions in Rindler space
We revisit non-interacting string partition functions in Rindler space by
summing over fields in the spectrum. In field theory, the total partition
function splits in a natural way in a piece that does not contain surface terms
and a piece consisting of solely the so-called edge states. For open strings,
we illustrate that surface contributions to the higher spin fields correspond
to open strings piercing the Rindler origin, unifying the higher spin surface
contributions in string language. For closed strings, we demonstrate that the
string partition function is not quite the same as the sum over the partition
functions of the fields in the spectrum: an infinite overcounting is present
for the latter. Next we study the partition functions obtained by excluding the
surface terms. Using recent results of JHEP 1505 (2015) 106, this construction,
first done by Emparan, can be put on much firmer ground. We generalize to type
II and heterotic superstrings and demonstrate modular invariance. All of these
exhibit an IR divergence that can be interpreted as a maximal acceleration
close to the black hole horizon. Ultimately, since these partition functions
are only part of the full story, divergences here should not be viewed as a
failure of string theory: maximal acceleration is a feature of a faulty
treatment of the higher spin fields in the string spectrum. We comment on the
relevance of this to Solodukhin's recent proposal. A possible link with the
firewall paradox is apparent.Comment: 33 pages, v2: added several clarifications including a section on the
difference between closed strings and the sum-of-fields approach, matches
published versio
Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples
In this paper, we discuss several explicit examples of the results obtained
in JHEP 1402 (2014) 127. We elaborate on the random walk picture in these
spacetimes and how it is modified. Firstly we discuss the linear dilaton
background. Then we analyze a previously studied toroidally compactified
background where we determine the Hagedorn temperature and study the random
walk picture. We continue with flat space orbifold models where we discuss
boundary conditions for the thermal scalar. Finally, we study the general link
between the quantum numbers in the fundamental domain and the strip and their
role in thermodynamics.Comment: 34 pages, v2: matches published versio
On the Relevance of the Thermal Scalar
We discuss near-Hagedorn string thermodynamics in general spacetimes using
the formalism of the thermal scalar. Building upon earlier work by Horowitz and
Polchinski, we relate several properties of the thermal scalar field theory
(i.e. the stress tensor and U(1) charge) to properties of the highly excited or
near-Hagedorn string gas. We apply the formulas on several examples. We find
the pressureless near-Hagedorn string gas in flat space and a non-vanishing
(angular) string charge in . We also find the thermal stress tensor for
the highly excited string gas in Rindler space.Comment: 36 pages, v2: section on correlators rewritten and clarifications
added, matches published versio
The Thermal Scalar and Random Walks in AdS3 and BTZ
We analyze near-Hagedorn thermodynamics of strings in the WZW model.
We compute the thermal spectrum of all primaries and find the thermal scalar
explicitly in the string spectrum using CFT twist techniques. Then we use the
link to the Euclidean WZW BTZ black hole and write down the Euclidean BTZ
spectrum. We give a Hamiltonian interpretation of the thermal partition
function of angular orbifolds where we find a reappearance of discrete states
that dominate the partition function. Using these results, we discuss the
nature of the thermal scalar in the WZW BTZ model. As a slight generalization
of the angular orbifolds, we discuss the string gas with a non-zero
chemical potential corresponding to angular momentum around the spatial cigar.
For this model as well, we determine the thermal spectrum and the Hagedorn
temperature as a function of chemical potential. Finally the nature of
corrections to the thermal scalar action is analyzed and we
find the random walk behavior of highly excited strings in this particular
background.Comment: 74 pages, v2: version accepted for publication in JHE
Hagedorn temperature and physics of black holes
A mini-review devoted to some implications of the Hagedorn temperature for
black hole physics. The existence of a limiting temperature is a generic
feature of string models. The Hagedorn temperature was introduced first in the
context of hadronic physics. Nowadays, the emphasis is shifted to fundamental
strings which might be a necessary ingredient to obtain a consistent theory of
black holes. The point is that, in field theory, the local temperature close to
the horizon could be arbitrarily high, and this observation is difficult to
reconcile with the finiteness of the entropy of black holes. After preliminary
remarks, we review our recent attempt to evaluate the entropy of large black
holes in terms of fundamental strings. We also speculate on implications for
dynamics of large-N gauge theories arising within holographic models.Comment: 6 pages, ICNFP2015 Conference Proceeding
Perturbative String Thermodynamics near Black Hole Horizons
We provide further computations and ideas to the problem of near-Hagedorn
string thermodynamics near (uncharged) black hole horizons, building upon our
earlier work JHEP 1403 (2014) 086. The relevance of long strings to one-loop
black hole thermodynamics is emphasized. We then provide an argument in favor
of the absence of -corrections for the (quadratic) heterotic thermal
scalar action in Rindler space. We also compute the large limit of the
cigar orbifold partition functions (for both bosonic and type II superstrings)
which allows a better comparison between the flat cones and the cigar cones. A
discussion is made on the general McClain-Roth-O'Brien-Tan theorem and on the
fact that different torus embeddings lead to different aspects of string
thermodynamics. The black hole/string correspondence principle for the 2d black
hole is discussed in terms of the thermal scalar. Finally, we present an
argument to deal with arbitrary higher genus partition functions, suggesting
the breakdown of string perturbation theory (in ) to compute
thermodynamical quantities in black hole spacetimes.Comment: 51 pages, v2: matches published versio
The long string at the stretched horizon and the entropy of large non-extremal black holes
We discuss how long strings can arise at the stretched horizon and how they
can account for the Bekenstein-Hawking entropy. We use the thermal scalar field
theory to derive the asymptotic density of states and corresponding stress
tensor of a microcanonical long string gas in Rindler space. We show that the
equality of the Hagedorn and Hawking temperatures gives rise to the tree-level
entropy of large black holes in accordance with the Bekenstein-Hawking-Wald
formula.Comment: 19 pages, v2: added discussion on rotating black holes, matches
published versio
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