1,772 research outputs found
Consistent string backgrounds and completely integrable 2D field theories
After reviewing the -function equations for consistent string
backgrounds in the -model approach, including metric and antisymmetric
tensor, dilaton and tachyon potential, we apply this formalism to WZW models.
We particularly emphasize the case where the WZW model is perturbed by an
integrable marginal tachyon potential operator leading to the non-abelian Toda
theories. Already in the simplest such theory, there is a large non-linear and
non-local chiral algebra that extends the Virasoro algebra. This theory is
shown to have two formulations, one being a classical reduction of the other.
Only the non-reduced theory is shown to satisfy the -function equations.Comment: 12 pages, uses PHYZZ
Small-time expansion of the Fokker-Planck kernel for space and time dependent diffusion and drift coefficients
We study the general solution of the Fokker-Planck equation in d dimensions
with arbitrary space and time dependent diffusion matrix and drift term. We
show how to construct the solution, for arbitrary initial distributions, as an
asymptotic expansion for small time. This generalizes the well-known asymptotic
expansion of the heat-kernel for the Laplace operator on a general Riemannian
manifold. We explicitly work out the general solution to leading and
next-to-leading order in this small-time expansion, as well as to
next-to-next-to-leading order for vanishing drift. We illustrate our results on
a several examples.Comment: 30 page
Aspects of Exactly Solvable Quantum-Corrected 2D Dilaton Gravity Theories
After reviewing the basic aspects of the exactly solvable quantum-corrected
dilaton-gravity theories in two dimensions, we discuss a (subjective) selection
of other aspects: a) supersymmetric extensions, b) canonical formalism,
ADM-mass, and the functional integral measure, and c) a positive energy theorem
and its application to the ADM- and Bondi-masses.Comment: 30 pages. Based on Talks given at Strings 93, Berkeley, May 1993, and
at the Santa Barbara conference "Quantum Aspects of Black Holes". PUPT-141
Does Coupling To Gravity Preserve Integrability ?
These are notes based on a lecture given at the Cargese summer school 1995. I
describe evidence that the (two-dimensional) integrable chiral Gross-Neveu
model might remain integrable when coupled to gravity. The results presented
here were obtained in collaboration with Ian Kogan.Comment: 11 pages, uses PHYZZX, 7 figures (encapsulated postscript), (one
reference added
Anomaly Cancellations on Lower-Dimensional Hypersurfaces by Inflow from the Bulk
Lower-dimensional (hyper)surfaces that can carry gauge or gauge/gravitational
anomalies occur in many areas of physics: one-plus-one-dimensional boundaries
or two-dimensional defect surfaces in condensed matter systems,
four-dimensional brane-worlds in higher-dimensional cosmologies or various
branes and orbifold planes in string or M-theory. In all cases we may have
(quantum) anomalies localized on these hypersurfaces that are only cancelled by
``anomaly inflow'' from certain topological interactions in the bulk. Proper
cancellation between these anomaly contributions of different origin requires a
careful treatment of factors and signs. We review in some detail how these
contributions occur and discuss applications in condensed matter (Quantum Hall
Effect) and M-theory (five-branes and orbifold planes)Comment: 39 pages, to appear in: From Fields to Strings: Circumnavigating
Theoretical Physics, Ian Kogan Memorial Volum
NON-LOCAL EXTENSIONS OF THE CONFORMAL ALGEBRA : MATRIX -ALGEBRAS, MATRIX KdV-HIERARCHIES AND NON-ABELIAN TODA THEORIES,
In the present contribution, I report on certain {\it non-linear} and {\it
non-local} extensions of the conformal (Virasoro) algebra. These so-called
-algebras are matrix generalizations of -algebras. First, in the context
of two-dimensional field theory, I discuss the non-abelian Toda model which
possesses three conserved (chiral) ``currents". The Poisson brackets of these
``currents" give the simplest example of a -algebra. The classical solutions
of this model provide a free-field realization of the -algebra. Then I show
that this -algebra is identical to the second Gelfand-Dikii symplectic
structure on the manifold of -matrix Schr\"odinger operators
L=-\d^2+U (with \tr\sigma_3 U=0). This provides a relation with matrix
KdV-hierarchies and allows me to obtain an infinite family of conserved charges
(Hamiltonians in involution). Finally, I work out the general
-algebras as symplectic structures based on -matrix -order differential operators L=-\d^m +U_2\d^{m-2}+U_3 \d^{m-3}+\ldots
+U_m. It is the absence of , together with the non-commutativity of
matrices that leads to the non-local terms in the -algebras. I show
that the conformal properties are similar to those of -algebras, while the
complete -algebras are much more complicated, as is shown on the
explicit example of .Comment: 30 pages, uses phyzzx, lecture given at the "59. Rencontre de
Strasbourg
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