677 research outputs found
Multi-Instantons and Multi-Cuts
We discuss various aspects of multi-instanton configurations in generic
multi-cut matrix models. Explicit formulae are presented in the two-cut case
and, in particular, we obtain general formulae for multi-instanton amplitudes
in the one-cut matrix model case as a degeneration of the two-cut case. These
formulae show that the instanton gas is ultra-dilute, due to the repulsion
among the matrix model eigenvalues. We exemplify and test our general results
in the cubic matrix model, where multi-instanton amplitudes can be also
computed with orthogonal polynomials. As an application, we derive general
expressions for multi-instanton contributions in two-dimensional quantum
gravity, verifying them by computing the instanton corrections to the string
equation. The resulting amplitudes can be interpreted as regularized partition
functions for multiple ZZ-branes, which take into full account their
back-reaction on the target geometry. Finally, we also derive structural
properties of the trans-series solution to the Painleve I equation.Comment: 34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes;
v3: added 1 reference, more minor changes, final version for JMP; v4: more
typos correcte
Future Foam
We study pocket universes which have zero cosmological constant and
non-trivial boundary topology. These arise from bubble collisions in eternal
inflation. Using a simplified dust model of collisions we find that boundaries
of any genus can occur. Using a radiation shell model we perform analytic
studies in the thin wall limit to show the existence of geometries with a
single toroidal boundary. We give plausibility arguments that higher genus
boundaries can also occur. In geometries with one boundary of any genus a
timelike observer can see the entire boundary. Geometries with multiple
disconnected boundaries can also occur. In the spherical case with two
boundaries the boundaries are separated by a horizon. Our results suggest that
the holographic dual description for eternal inflation, proposed by Freivogel,
Sekino, Susskind and Yeh, should include summation over the genus of the base
space of the dual conformal field theory. We point out peculiarities of this
genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure
Comment on ``Inflation and flat directions in modular invariant superstring effective theories''
The inflation model of Gaillard, Lyth and Murayama is revisited, with a
systematic scan of the parameter space for dilaton stabilization during
inflation.Comment: 7 pages, 2 figure
Black Holes and Large Order Quantum Geometry
We study five-dimensional black holes obtained by compactifying M theory on
Calabi-Yau threefolds. Recent progress in solving topological string theory on
compact, one-parameter models allows us to test numerically various conjectures
about these black holes. We give convincing evidence that a microscopic
description based on Gopakumar-Vafa invariants accounts correctly for their
macroscopic entropy, and we check that highly nontrivial cancellations -which
seem necessary to resolve the so-called entropy enigma in the OSV conjecture-
do in fact occur. We also study analytically small 5d black holes obtained by
wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II
duality we obtain exact formulae for the microscopic degeneracies in various
geometries, and we compute their asymptotic expansion for large charges.Comment: 42 pages, 20 eps figures, small correction
Black Holes and Random Matrices
We argue that the late time behavior of horizon fluctuations in large anti-de
Sitter (AdS) black holes is governed by the random matrix dynamics
characteristic of quantum chaotic systems. Our main tool is the
Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole.
We use an analytically continued partition function as well
as correlation functions as diagnostics. Using numerical techniques we
establish random matrix behavior at late times. We determine the early time
behavior exactly in a double scaling limit, giving us a plausible estimate for
the crossover time to random matrix behavior. We use these ideas to formulate a
conjecture about general large AdS black holes, like those dual to 4D
super-Yang-Mills theory, giving a provisional estimate of the crossover time.
We make some preliminary comments about challenges to understanding the late
time dynamics from a bulk point of view.Comment: 73 pages, 15 figures, minor errors correcte
The Cost of Stability in Coalitional Games
A key question in cooperative game theory is that of coalitional stability,
usually captured by the notion of the \emph{core}--the set of outcomes such
that no subgroup of players has an incentive to deviate. However, some
coalitional games have empty cores, and any outcome in such a game is unstable.
In this paper, we investigate the possibility of stabilizing a coalitional
game by using external payments. We consider a scenario where an external
party, which is interested in having the players work together, offers a
supplemental payment to the grand coalition (or, more generally, a particular
coalition structure). This payment is conditional on players not deviating from
their coalition(s). The sum of this payment plus the actual gains of the
coalition(s) may then be divided among the agents so as to promote stability.
We define the \emph{cost of stability (CoS)} as the minimal external payment
that stabilizes the game.
We provide general bounds on the cost of stability in several classes of
games, and explore its algorithmic properties. To develop a better intuition
for the concepts we introduce, we provide a detailed algorithmic study of the
cost of stability in weighted voting games, a simple but expressive class of
games which can model decision-making in political bodies, and cooperation in
multiagent settings. Finally, we extend our model and results to games with
coalition structures.Comment: 20 pages; will be presented at SAGT'0
A Renormalization Group for Hamiltonians: Numerical Results
We describe a renormalization group transformation that is related to the
breakup of golden invariant tori in Hamiltonian systems with two degrees of
freedom. This transformation applies to a large class of Hamiltonians, is
conceptually simple, and allows for accurate numerical computations. In a
numerical implementation, we find a nontrivial fixed point and determine the
corresponding critical index and scaling. Our computed values for various
universal constants are in good agreement with existing data for
area-preserving maps. We also discuss the flow associated with the nontrivial
fixed point.Comment: 11 Pages, 2 Figures. For future updates, check
ftp://ftp.ma.utexas.edu/pub/papers/koch
Analytic Study for the String Theory Landscapes via Matrix Models
We demonstrate a first-principle analysis of the string theory landscapes in
the framework of non-critical string/matrix models. In particular, we discuss
non-perturbative instability, decay rate and the true vacuum of perturbative
string theories. As a simple example, we argue that the perturbative string
vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is
inescapably a false vacuum. Surprisingly, most of perturbative minimal string
vacua are unstable, and their true vacuum mostly does not suffer from
non-perturbative ambiguity. Importantly, we observe that the instability of
these tachyon-less closed string theories is caused by ghost D-instantons (or
ghost ZZ-branes), the existence of which is determined only by non-perturbative
completion of string theory.Comment: v1: 5 pages, 2 figures; v2: references and footnote added; v3: 7
pages, 4 figures, organization changed, explanations expanded, references
added, reconstruction program from arbitrary spectral curves shown explicitl
Phases of Josephson Junction Ladders
We study a Josephson junction ladder in a magnetic field in the absence of
charging effects via a transfer matrix formalism. The eigenvalues of the
transfer matrix are found numerically, giving a determination of the different
phases of the ladder. The spatial periodicity of the ground state exhibits a
devil's staircase as a function of the magnetic flux filling factor . If the
transverse Josephson coupling is varied a continuous superconducting-normal
transition in the transverse direction is observed, analogous to the breakdown
of the KAM trajectories in dynamical systems.Comment: 12 pages with 3 figures, REVTE
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