1,172 research outputs found
Effective Gravitational Field of Black Holes
The problem of interpretation of the \hbar^0-order part of radiative
corrections to the effective gravitational field is considered. It is shown
that variations of the Feynman parameter in gauge conditions fixing the general
covariance are equivalent to spacetime diffeomorphisms. This result is proved
for arbitrary gauge conditions at the one-loop order. It implies that the
gravitational radiative corrections of the order \hbar^0 to the spacetime
metric can be physically interpreted in a purely classical manner. As an
example, the effective gravitational field of a black hole is calculated in the
first post-Newtonian approximation, and the secular precession of a test
particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos
correcte
Boundary changing operators in the O(n) matrix model
We continue the study of boundary operators in the dense O(n) model on the
random lattice. The conformal dimension of boundary operators inserted between
two JS boundaries of different weight is derived from the matrix model
description. Our results are in agreement with the regular lattice findings. A
connection is made between the loop equations in the continuum limit and the
shift relations of boundary Liouville 3-points functions obtained from Boundary
Ground Ring approach.Comment: 31 pages, 4 figures, Introduction and Conclusion improve
On the notion of potential in quantum gravity
The problem of consistent definition of the quantum corrected gravitational
field is considered in the framework of the -matrix method. Gauge dependence
of the one-particle-reducible part of the two-scalar-particle scattering
amplitude, with the help of which the potential is usually defined, is
investigated at the one-loop approximation. The -terms in the potential,
which are of zero order in the Planck constant are shown to be
independent of the gauge parameter weighting the gauge condition in the action.
However, the -terms, proportional to describing the first
proper quantum correction, are proved to be gauge-dependent. With the help of
the Slavnov identities, their dependence on the weighting parameter is
calculated explicitly. The reason the gauge dependence originates from is
briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure
Generalized Penner models to all genera
We give a complete description of the genus expansion of the one-cut solution
to the generalized Penner model. The solution is presented in a form which
allows us in a very straightforward manner to localize critical points and to
investigate the scaling behaviour of the model in the vicinity of these points.
We carry out an analysis of the critical behaviour to all genera addressing all
types of multi-critical points. In certain regions of the coupling constant
space the model must be defined via analytical continuation. We show in detail
how this works for the Penner model. Using analytical continuation it is
possible to reach the fermionic 1-matrix model. We show that the critical
points of the fermionic 1-matrix model can be indexed by an integer, , as it
was the case for the ordinary hermitian 1-matrix model. Furthermore the 'th
multi-critical fermionic model has to all genera the same value of
as the 'th multi-critical hermitian model. However, the
coefficients of the topological expansion need not be the same in the two
cases. We show explicitly how it is possible with a fermionic matrix model to
reach a multi-critical point for which the topological expansion has
alternating signs, but otherwise coincides with the usual Painlev\'{e}
expansion.Comment: 27 pages, PostScrip
Bethe Ansatz in Stringy Sigma Models
We compute the exact S-matrix and give the Bethe ansatz solution for three
sigma-models which arise as subsectors of string theory in AdS(5)xS(5):
Landau-Lifshitz model (non-relativistic sigma-model on S(2)),
Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and
Faddeev-Reshetikhin model (string sigma-model on S(3)xR).Comment: 37 pages, 11 figure
On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
We investigate the quantum Jaynes-Cummings model - a particular case of the
Gaudin model with one of the spins being infinite. Starting from the Bethe
equations we derive Baxter's equation and from it a closed set of equations for
the eigenvalues of the commuting Hamiltonians. A scalar product in the
separated variables representation is found for which the commuting
Hamiltonians are Hermitian. In the semi classical limit the Bethe roots
accumulate on very specific curves in the complex plane. We give the equation
of these curves. They build up a system of cuts modeling the spectral curve as
a two sheeted cover of the complex plane. Finally, we extend some of these
results to the XXX Heisenberg spin chain.Comment: 16 page
A Potts/Ising Correspondence on Thin Graphs
We note that it is possible to construct a bond vertex model that displays
q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary
topology, which we denote as ``thin'' random graphs in contrast to the fat
graphs of the planar diagram expansion.
Since the four vertex model in question also serves to describe the critical
behaviour of the Ising model in field, the formulation reveals an isomorphism
between the Potts and Ising models on thin random graphs. On planar graphs a
similar correspondence is present only for q=1, the value associated with
percolation.Comment: 6 pages, 5 figure
An Extension of Level-spacing Universality
Dyson's short-distance universality of the correlation functions implies the
universality of P(s), the level-spacing distribution. We first briefly review
how this property is understood for unitary invariant ensembles and consider
next a Hamiltonian H = H_0+ V , in which H_0 is a given, non-random, N by N
matrix, and V is an Hermitian random matrix with a Gaussian probability
distribution. n-point correlation function may still be expressed as a
determinant of an n by n matrix, whose elements are given by a kernel
as in the H_0=0 case. From this representation we can show
that Dyson's short-distance universality still holds. We then conclude that
P(s) is independent of H_0.Comment: 12 pages, Revte
Knizhnik-Zamolodchikov equations and the Calogero-Sutherland-Moser integrable models with exchange terms
It is shown that from some solutions of generalized Knizhnik-Zamolodchikov
equations one can construct eigenfunctions of the Calogero-Sutherland-Moser
Hamiltonians with exchange terms, which are characterized by any given
permutational symmetry under particle exchange. This generalizes some results
previously derived by Matsuo and Cherednik for the ordinary
Calogero-Sutherland-Moser Hamiltonians.Comment: 13 pages, LaTeX, no figures, to be published in J. Phys.
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