Nested T-duality

We identify the obstructions for T-dualizing the boundary WZW model and make explicit how they depend on the geometry of branes. In particular, the obstructions disappear for certain brane configurations associated to non-regular elements of the Cartan torus. It is shown in this case that the boundary WZW model is "nested" in the twisted boundary WZW model as the dynamical subsystem of the latter.Comment: 13 page

Symplectic structure of the moduli space of flat connections on a Riemann surface

We consider canonical symplectic structure on the moduli space of flat {\g}-connections on a Riemann surface of genus $g$ with $n$ marked points. For {\g} being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum of $n$ copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie group $G^{*}$ and $g$ copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group $G$ (the pair ($G,G^{*}$) corresponds to the Lie algebra {\g}).Comment: 20 page

Abelian Current Algebra and the Virasoro Algebra on the Lattice

We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.Comment: 11 pages, LATEX, HU-TFT-93-2

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

Numerical Simulation of Tsunami Wave Propagation to the Balaklava Bay

Purpose. To investigate the process of tsunami wave propagation from the hypothetical earthquake foci to the Balaklava Bay, and to zone the tsunami impact upon the bay coastline based on the results of numerical modeling, are the purposes of the paper. Methods and Results. The results of numerical simulation of the tsunami wave propagation to the Balaklava Bay with subsequent flooding of the coast are presented. The problem of the tsunami wave propagation from three hypothetical earthquake foci and their evolution in the Black Sea was solved using the nonlinear model of long waves. Time dependences of the sea level fluctuations at the entrance to the Balaklava Bay were obtained. They were applied as boundary conditions at the liquid boundary of the computational domain, where the SWASH model had been used to simulate numerically the tsunami wave propagation in the bay with their subsequent run-up to the coast. Conclusions. Propagation of tsunami waves in the Balaklava Bay is accompanied by formation of the sea level seiche oscillations with a period ~ 8 min which correspond to the Helmholtz mode. Inside the bay, the tsunami heights increase by 5–6 times as compared to those at the entrance to the computational domain. The sea level fluctuations are maximal at the bay top, where its rise achieves 1.4–1.5 m. The eastern coast of the Balaklava Bay and the one adjacent to its top are subject to the strongest flooding. The values of water level on land measured from the ground level, reach 1.0–1.5 m, and at the bay top – 1.8 m. At the eastern coast of the bay, the flooding maximum length constitutes 60 m, at its top – 90 m

Derivation of Index Theorems by Localization of Path Integrals

We review the derivation of the Atiyah-Singer and Callias index theorems using the recently developed localization method to calculate exactly the relevant supersymmetric path integrals. (Talk given at the III International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 13-24, 1993)Comment: 11 pages in LaTeX, HU-TFT-93-3

Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

The zero modes' Fock space for the extended chiral $su(2)$ WZNW model gives room to a realization of the Grothendieck fusion ring of representations of the restricted $U_q sl(2)$ quantum universal enveloping algebra (QUEA) at an even ($2h$-th) root of unity, and of its extension by the Lusztig operators. It is shown that expressing the Drinfeld images of canonical characters in terms of Chebyshev polynomials of the Casimir invariant $C$ allows a streamlined derivation of the characteristic equation of $C$ from the defining relations of the restricted QUEA. The properties of the fusion ring of the Lusztig's extension of the QUEA in the zero modes' Fock space are related to the braiding properties of correlation functions of primary fields of the extended $su(2)_{h-2}$ current algebra model.Comment: 36 pages, 1 figure; version 3 - improvements in Sec. 2 and 3: definitions of the double, as well as R- (and M-)matrix changed to fit the zero modes' one

D-branes in the Euclidean AdS3AdS_3 and T-duality

We show that D-branes in the Euclidean $AdS_3$ can be naturally associated to the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This picture makes very transparent the residual loop group symmetry of the D-brane configurations and gives also immediately the D-branes shapes and the $\sigma$-model boundary conditions in the de Sitter T-dual of the $SL(2,C)/SU(2)$ WZW model.Comment: 29 pages, LaTeX, references adde

Fermion Propagators in Type II Fivebrane Backgrounds

The fermion propagators in the fivebrane background of type II superstring theories are calculated. The propagator can be obtained by explicitly evaluating the transition amplitude between two specific NS-R boundary states by the propagator operator in the non-trivial world-sheet conformal field theory for the fivebrane background. The propagator in the field theory limit can be obtained by using point boundary states. We can explicitly investigate the lowest lying fermion states propagating in the non-trivial ten-dimensional space-time of the fivebrane background: M^6 x W_k^(4), where W_k^(4) is the group manifold of SU(2)_k x U(1). The half of the original supersymmetry is spontaneously broken, and the space-time Lorentz symmetry SO(9,1) reduces to SO(5,1) in SO(5,1) x SO(4) \subset SO(9,1) by the fivebrane background. We find that there are no propagations of SO(4) (local Lorentz) spinor fields, which is consistent with the arguments on the fermion zero-modes in the fivebrane background of low-energy type II supergravity theories.Comment: 15 page