242 research outputs found
Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model
We study the IIB matrix model, which is conjectured to be a nonperturbative
definition of superstring theory, by introducing an integer deformation
parameter `nu' which couples to the imaginary part of the effective action
induced by fermions. The deformed IIB matrix model continues to be well-defined
for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and
the cluster property. We study the model at `nu' = infinity using a
saddle-point analysis, and show that ten-dimensional Lorentz invariance is
spontaneously broken at least down to an eight-dimensional one. We argue that
it is likely that the remaining eight-dimensional Lorentz invariance is further
broken, which can be checked by integrating over the saddle-point
configurations using standard Monte Carlo simulation.Comment: 12 pages, latex, no figures, references added, version to appear in
JHE
Prediction of RNA pseudoknots by Monte Carlo simulations
In this paper we consider the problem of RNA folding with pseudoknots. We use
a graphical representation in which the secondary structures are described by
planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze
the non-planar topologies of RNA structures and propose a classification of RNA
pseudoknots according to the minimal genus of the surface on which the RNA
structure can be embedded. This classification provides a simple and natural
way to tackle the problem of RNA folding prediction in presence of pseudoknots.
Based on that approach, we describe a Monte Carlo algorithm for the prediction
of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure
3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model
The asymmetric ABAB-matrix model describes the transfer matrix of
three-dimensional Lorentzian quantum gravity. We study perturbatively the
scaling of the ABAB-matrix model in the neighbourhood of its symmetric solution
and deduce the associated renormalization of three-dimensional Lorentzian
quantum gravity.Comment: 21 pages, typo in references correcte
Macroscopic and microscopic (non-)universality of compact support random matrix theory
A random matrix model with a σ-model like constraint, the restricted trace ensemble (RTE), is solved in the large-n limit. In the macroscopic limit the smooth connected two-point resolvent G(z,w) is found to be non-universal, extending previous results from monomial to arbitrary polynomial potentials. Using loop equation techniques we give a closed though non-universal expression for G(z,w), which extends recursively to all higher k-point resolvents. These findings are in contrast to the usual unconstrained one-matrix model. However, in the microscopic large-n limit, which probes only correlations at distance of the mean level spacing, we are able to show that the constraint does not modify the universal sine-law. In the case of monomial potentials V(M)=M2p, we provide a relation valid for finite-n between the k-point correlation function of the RTE and the unconstrained model. In the microscopic large-n limit they coincide which proves the microscopic universality of RTEs
Dark-energy instabilities induced by gravitational waves
We point out that dark-energy perturbations may become unstable in the presence of a gravitational wave of sufficiently large amplitude. We study this effect for the cubic Horndeski operator (braiding), proportional to \u3b1B. The scalar that describes dark-energy fluctuations features ghost and/or gradient instabilities for gravitational-wave amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for |\u3b1B | 73 10-2, i.e. when the modification of gravity is sizeable. The instability is triggered by massive black-hole binaries down to frequencies corresponding to 1010 km: the instability is thus robust, unless new physics enters on even longer wavelengths. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. The same kind of instability is present in beyond-Horndeski theories for |\u3b1H| 73 10-20. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are k-essence models, with a possible conformal coupling with matter
Lorentzian 3d Gravity with Wormholes via Matrix Models
We uncover a surprising correspondence between a non-perturbative formulation
of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix
model with ABAB-interaction. The gravitational transfer matrix can be expressed
as the logarithm of a two-matrix integral, and we deduce from the known
structure of the latter that the model has two phases. In the phase of weak
gravity, well-defined two-dimensional universes propagate in proper time,
whereas in the strong-coupling phase the spatial hypersurfaces disintegrate
into many components connected by wormholes.Comment: 35 pages, 9 figure
Topological phase transition in a RNA model in the de Gennes regime
We study a simplified model of the RNA molecule proposed by G. Vernizzi, H.
Orland and A. Zee in the regime of strong concentration of positive ions in
solution. The model considers a flexible chain of equal bases that can pairwise
interact with any other one along the chain, while preserving the property of
saturation of the interactions. In the regime considered, we observe the
emergence of a critical temperature T_c separating two phases that can be
characterized by the topology of the predominant configurations: in the large
temperature regime, the dominant configurations of the molecule have very large
genera (of the order of the size of the molecule), corresponding to a complex
topology, whereas in the opposite regime of low temperatures, the dominant
configurations are simple and have the topology of a sphere. We determine that
this topological phase transition is of first order and provide an analytic
expression for T_c. The regime studied for this model exhibits analogies with
that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure
Covariant generalization of cosmological perturbation theory
We present an approach to cosmological perturbations based on a covariant
perturbative expansion between two worldlines in the real inhomogeneous
universe. As an application, at an arbitrary order we define an exact scalar
quantity which describes the inhomogeneities in the number of e-folds on
uniform density hypersurfaces and which is conserved on all scales for a
barotropic ideal fluid. We derive a compact form for its conservation equation
at all orders and assign it a simple physical interpretation. To make a
comparison with the standard perturbation theory, we develop a method to
construct gauge-invariant quantities in a coordinate system at arbitrary order,
which we apply to derive the form of the n-th order perturbation in the number
of e-folds on uniform density hypersurfaces and its exact evolution equation.
On large scales, this provides the gauge-invariant expression for the curvature
perturbation on uniform density hypersurfaces and its evolution equation at any
order.Comment: Minor changes to match the version published in PRD. RevTex, 22
pages, 1 figur
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