34 research outputs found
Non-renormalization for the Liouville wave function
Using an exact functional method, within the framework of the gradient
expansion for the Liouville effective action, we show that the kinetic term for
the Liouville field is not renormalized.Comment: 13 pages Latex, no figure
On the Yang-Lee and Langer singularities in the O(n) loop model
We use the method of `coupling to 2d QG' to study the analytic properties of
the universal specific free energy of the O(n) loop model in complex magnetic
field. We compute the specific free energy on a dynamical lattice using the
correspondence with a matrix model. The free energy has a pair of Yang-Lee
edges on the high-temperature sheet and a Langer type branch cut on the
low-temperature sheet. Our result confirms a conjecture by A. and Al.
Zamolodchikov about the decay rate of the metastable vacuum in presence of
Liouville gravity and gives strong evidence about the existence of a weakly
metastable state and a Langer branch cut in the O(n) loop model on a flat
lattice. Our results are compatible with the Fonseca-Zamolodchikov conjecture
that the Yang-Lee edge appears as the nearest singularity under the Langer cut.Comment: 38 pages, 16 figure
Can a Lattice String Have a Vanishing Cosmological Constant?
We prove that a class of one-loop partition functions found by Dienes, giving
rise to a vanishing cosmological constant to one-loop, cannot be realized by a
consistent lattice string. The construction of non-supersymmetric string with a
vanishing cosmological constant therefore remains as elusive as ever. We also
discuss a new test that any one-loop partition function for a lattice string
must satisfy.Comment: 14 page
Classical Solutions in Two-Dimensional String Theory and Gravitational Collapse
A general solution to the 1-loop beta functions equations including
tachyonic back reaction on the metric is presented. Dynamical black hole
(classical) solutions representing gravitational collapse of tachyons are
constructed. A discussion on the correspondence with the matrix-model approach
is given.Comment: 7 pages, UTTG-31-9
Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
Euclidean dilaton gravity in two dimensions is studied exploiting its
representation as a complexified first order gravity model. All local classical
solutions are obtained. A global discussion reveals that for a given model only
a restricted class of topologies is consistent with the metric and the dilaton.
A particular case of string motivated Liouville gravity is studied in detail.
Path integral quantisation in generic Euclidean dilaton gravity is performed
non-perturbatively by analogy to the Minkowskian case.Comment: 27 p., LaTeX, v2: included new refs. and a footnot
Simulating hot Abelian gauge dynamics
The time evolution of soft modes in a quantum gauge field theory is to first
approximation classical, but the equations of motion are non-local. We show how
they can be written in a local and Hamiltonian way in an Abelian theory, and
that this formulation is particularly suitable for numerical simulations. This
makes it possible to simulate numerically non-equilibrium processes such as the
phase transition in the Abelian Higgs model and and to study, for instance,
bubble nucleation and defect formation. Such simulations would also help to
understand phase transitions in more complicated gauge theories. Moreover, we
show that the existing analytical results for the time-evolution in a
pure-gauge theory correspond to a special class of initial conditions and that
different initial conditions can lead to qualitatively different behavior. We
compare the results of the simulations to analytical calculations and find an
excellent agreement.Comment: 18 pages, 5 figures, REVTe
A simple way to generate high order vacuum graphs
We describe an efficient practical procedure for enumerating and regrouping
vacuum Feynman graphs of a given order in perturbation theory. The method is
based on a combination of Schwinger-Dyson equations and the
two-particle-irreducible ("skeleton") expansion. The regrouping leads to
skeletons containing only free propagators, together with "ring diagrams"
containing all the self-energy insertions. As a consequence, relatively few
diagrams need to be drawn and integrations carried out at any single stage of
the computation and, in low dimensions, overlapping ultraviolet/infrared
subdivergences can be cleanly isolated. As an illustration we enumerate the
graphs contributing to the 4-loop free energy in QCD, explicitly in a continuum
and more compactly in a lattice regularization.Comment: 19 pages. Reference added. To appear in Phys.Rev.
Measuring the Broken Phase Sphaleron Rate Nonperturbatively
We present details for a method to compute the broken phase sphaleron rate
(rate of hot baryon number violation below the electroweak phase transition)
nonperturbatively, using a combination of multicanonical and real time lattice
techniques. The calculation includes the ``dynamical prefactor,'' which
accounts for prompt recrossings of the sphaleron barrier. The prefactor depends
on the hard thermal loops, getting smaller with increasing Debye mass; but for
realistic Debye masses the effect is not large. The baryon number erasure rate
in the broken phase is slower than a perturbative estimate by about exp(-3.6).
Assuming the electroweak phase transition has enough latent heat to reheat the
universe to the equilibrium temperature, baryon number is preserved after the
phase transition if the ratio of (``dimensionally reduced'' thermal) scalar to
gauge couplings (lambda / g^2) is less than .037.Comment: 41 pages, 13 figures included with psfig. Some wordings clarified,
nothing substantial change
String Theory and Water Waves
We uncover a remarkable role that an infinite hierarchy of non-linear
differential equations plays in organizing and connecting certain {hat c}<1
string theories non-perturbatively. We are able to embed the type 0A and 0B
(A,A) minimal string theories into this single framework. The string theories
arise as special limits of a rich system of equations underpinned by an
integrable system known as the dispersive water wave hierarchy. We observe that
there are several other string-like limits of the system, and conjecture that
some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain
how these and several string-like special points arise and are connected. In
some cases, the framework endows the theories with a non-perturbative
definition for the first time. Notably, we discover that the Painleve IV
equation plays a key role in organizing the string theory physics, joining its
siblings, Painleve I and II, whose roles have previously been identified in
this minimal string context.Comment: 49 pages, 4 figure
A Note on Background (In)dependence
In general quantum systems there are two kinds of spacetime modes, those that
fluctuate and those that do not. Fluctuating modes have normalizable
wavefunctions. In the context of 2D gravity and ``non-critical'' string theory
these are called macroscopic states. The theory is independent of the initial
Euclidean background values of these modes. Non-fluctuating modes have
non-normalizable wavefunctions and correspond to microscopic states. The theory
depends on the background value of these non-fluctuating modes, at least to all
orders in perturbation theory. They are superselection parameters and should
not be minimized over. Such superselection parameters are well known in field
theory. Examples in string theory include the couplings (including the
cosmological constant) in the matrix models and the mass of the two-dimensional
Euclidean black hole. We use our analysis to argue for the finiteness of the
string perturbation expansion around these backgrounds.Comment: 16 page