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We discuss D-branes from a conformal field theory point of view. In this approach, branes are described by boundary states providing sources for closed string modes, independently of classical notions. The boundary states must satisfy constraints which fall into two classes: The first consists of gluing conditions between left-and right-moving Virasoro or(More)
In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume algebras from the operator product expansions of open string vertex operators. For branes in a flat background with constant(More)
The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary(More)
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically(More)
In 2], 3] we suggested a new quantum algebra, the moduli algebra, which is conjectured to be a quantum algebra of observables of the Hamiltonian Chern-Simons theory. This algebra provides the quantization of the algebra of functions on the moduli space of at connections on a 2-dimensional surface. In this paper we classify unitary representations of this(More)
Branes in non-trivial backgrounds are expected to exhibit interesting dynamical properties. We use the boundary conformal field theory approach to study branes in a curved background with non-vanishing Neveu-Schwarz 3-form field strength. For branes on an S 3 , the low-energy effective action is computed to leading order in the string tension. It turns out(More)
In this work we propose an exact microscopic description of maximally symmetric branes in a Euclidean AdS 3 background. As shown by Bachas and Petropoulos, the most important such branes are localized along a Euclidean AdS 2 ⊂ AdS 3. We provide explicit formulas for the coupling of closed strings to such branes (boundary states) and for the spectral density(More)
Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which reproduces the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we(More)