Influence of damping on the excitation of the double giant resonance

We study the effect of the spreading widths on the excitation probabilities of the double giant dipole resonance. We solve the coupled-channels equations for the excitation of the giant dipole resonance and the double giant dipole resonance. Taking Pb+Pb collisions as example, we study the resulting effect on the excitation amplitudes, and cross sections as a function of the width of the states and of the bombarding energy.Comment: 8 pages, 3 figures, corrected typo

Topological defects for the free boson CFT

Two different conformal field theories can be joined together along a defect line. We study such defects for the case where the conformal field theories on either side are single free bosons compactified on a circle. We concentrate on topological defects for which the left- and right-moving Virasoro algebras are separately preserved, but not necessarily any additional symmetries. For the case where both radii are rational multiples of the self-dual radius we classify these topological defects. We also show that the isomorphism between two T-dual free boson conformal field theories can be described by the action of a topological defect, and hence that T-duality can be understood as a special type of order-disorder duality.Comment: 43 pages, 4 figure

From boundary to bulk in logarithmic CFT

The analogue of the charge-conjugation modular invariant for rational logarithmic conformal field theories is constructed. This is done by reconstructing the bulk spectrum from a simple boundary condition (the analogue of the Cardy `identity brane'). We apply the general method to the c_1,p triplet models and reproduce the previously known bulk theory for p=2 at c=-2. For general p we verify that the resulting partition functions are modular invariant. We also construct the complete set of 2p boundary states, and confirm that the identity brane from which we started indeed exists. As a by-product we obtain a logarithmic version of the Verlinde formula for the c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in J.Phys.

Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model

We propose a formula for the eigenvalue integral of the hermitian one matrix model with infinite well potential in terms of dressed twist fields of the su(2) level one WZW model. The expression holds for arbitrary matrix size n, and provides a suggestive interpretation for the monodromy properties of the matrix model correlators at finite n, as well as in the 1/n-expansion.Comment: 27 pages, 4 figures; v2: typos corrected, reference added, version to be published in JHE

The fusion algebra of bimodule categories

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F. As a by-product we obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category in terms of endomorphisms of the tensor unit of the underlying modular tensor category.Comment: 16 page

W-Extended Fusion Algebra of Critical Percolation

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.Comment: 30 page

Conformal Field Theories, Graphs and Quantum Algebras

This article reviews some recent progress in our understanding of the structure of Rational Conformal Field Theories, based on ideas that originate for a large part in the work of A. Ocneanu. The consistency conditions that generalize modular invariance for a given RCFT in the presence of various types of boundary conditions --open, twisted-- are encoded in a system of integer multiplicities that form matrix representations of fusion-like algebras. These multiplicities are also the combinatorial data that enable one to construct an abstract ``quantum'' algebra, whose $6j$- and $3j$-symbols contain essential information on the Operator Product Algebra of the RCFT and are part of a cell system, subject to pentagonal identities. It looks quite plausible that the classification of a wide class of RCFT amounts to a classification of ``Weak $C^*$- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001 --Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in Math., Birkhauser. References and comments adde

Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page

Rolling Tachyons from Liouville theory

In this work we propose an exact solution of the c=1 Liouville model, i.e. of the world-sheet theory that describes the homogeneous decay of a closed string tachyon. Our expressions are obtained through careful extrapolation from the correlators of Liouville theory with c > 25. In the c=1 limit, we find two different theories which differ by the signature of Liouville field. The Euclidean limit coincides with the interacting c=1 theory that was constructed by Runkel and Watts as a limit of unitary minimal models. The couplings for the Lorentzian limit are new. In contrast to the behavior at c > 1, amplitudes in both c=1 models are non-analytic in the momenta and consequently they are not related by Wick rotation.Comment: 22 page