285 research outputs found
Another derivation of the geometrical KPZ relations
We give a physicist's derivation of the geometrical (in the spirit of
Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a
covariant way to define neighborhoods of fractals in 2d quantum gravity, and
shows that these relations are in the realm of conformal field theory
On the fundamental representation of Borcherds algebras with one imaginary simple root
Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.Comment: 8 page
Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
We study open strings in the noncritical bosonic string theory
compactified on a circle at self-dual radius. These strings live on D-branes
that are extended along the Liouville direction ({\it FZZT} branes). We present
explicit expressions for the disc two- and three-point functions of boundary
operators in this theory, as well as the bulk-boundary two-point function. The
expressions obtained are divergent because of resonant behaviour at self-dual
radius. However, these can be regularised and renormalized in a precise way to
get finite results. The boundary correlators are found to depend only on the
differences of boundary cosmological constants, suggesting a fermionic
behaviour. We initiate a study of the open-string field theory localised to the
physical states, which leads to an interesting matrix model.Comment: 29 pages, harvma
Thermal Correlators in Little String Theory
We calculate, using holographic duality, the thermal two-point function in
finite temperature little string theory. The analysis of those correlators
reveals possible instabilities of the thermal ensemble, as in previous
discussions of the thermodynamics of little string theory. We comment on the
dependence of the instability on the spatial volume of the system.Comment: 13 page
Quantum geometry of 3-dimensional lattices
We study geometric consistency relations between angles on 3-dimensional (3D)
circular quadrilateral lattices -- lattices whose faces are planar
quadrilaterals inscribable into a circle. We show that these relations generate
canonical transformations of a remarkable ``ultra-local'' Poisson bracket
algebra defined on discrete 2D surfaces consisting of circular quadrilaterals.
Quantization of this structure leads to new solutions of the tetrahedron
equation (the 3D analog of the Yang-Baxter equation). These solutions generate
an infinite number of non-trivial solutions of the Yang-Baxter equation and
also define integrable 3D models of statistical mechanics and quantum field
theory. The latter can be thought of as describing quantum fluctuations of
lattice geometry. The classical geometry of the 3D circular lattices arises as
a stationary configuration giving the leading contribution to the partition
function in the quasi-classical limit.Comment: 27 pages, 10 figures. Minor corrections, references adde
On Holomorphic Factorization in Asymptotically AdS 3D Gravity
This paper studies aspects of ``holography'' for Euclidean signature pure
gravity on asymptotically AdS 3-manifolds. This theory can be described as
SL(2,C) CS theory. However, not all configurations of CS theory correspond to
asymptotically AdS 3-manifolds. We show that configurations that do have the
metric interpretation are parameterized by the so-called projective structures
on the boundary. The corresponding asymptotic phase space is shown to be the
cotangent bundle over the Schottky space of the boundary. This singles out a
``gravitational'' sector of the SL(2,C) CS theory. It is over this sector that
the path integral has to be taken to obtain the gravity partition function. We
sketch an argument for holomorphic factorization of this partition function.Comment: 32+1 pages, no figures; (v2) one reference added, a statement
regarding priorities modified; (v3) presentational changes, an important sign
mistake correcte
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
Combined application of XPS, XANES and mass spectrometry to in situ study of methanol oxidation over vanadium based catalysts
Ethylene epoxidation over copper-silver bimetallic catalyst: surface characterisation under reaction conditions
A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
We argue that topological matrix models (matrix models of the Kontsevich
type) are examples of exact open/closed duality. The duality works at finite N
and for generic `t Hooft couplings. We consider in detail the paradigm of the
Kontsevich model for two-dimensional topological gravity. We demonstrate that
the Kontsevich model arises by topological localization of cubic open string
field theory on N stable branes. Our analysis is based on standard worldsheet
methods in the context of non-critical bosonic string theory. The stable branes
have Neumann (FZZT) boundary conditions in the Liouville direction. Several
generalizations are possible.Comment: v2: References added; a new section with generalization to non-zero
bulk cosmological constant; expanded discussion on topological localization;
added some comment
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