D-branes In Group Manifolds Research Articles

Open strings in Lie groups and associative products

Firstly, we generalize a semi-classical limit of open strings on D-branes in group manifolds. The limit gives rise to rigid open strings, whose dynamics can efficiently be described in terms of a matrix algebra. Alternatively, the dynamics is coded in group theory coefficients whose properties are translated in a diagrammatical language. In the case of compact groups, it is a simplified version of rational boundary conformal field theories, while for non-compact groups, the construction gives rise to new associative products. Secondly, we argue that the intuitive formalism that we provide for the semi-classical limit, extends to the case of quantum groups. The associative product we construct in this way is directly related to the boundary vertex operator algebra of open strings on symmetry preserving branes in WZW models, and generalizations thereof, e.g. to non-compact groups. We treat the groups SU ( 2 ) and SL ( 2 , R ) explicitly. We also discuss the precise relation of the semi-classical open string dynamics to Berezin quantization and to star product theory.

Coset models and D-branes in group manifolds

Abstract We conjecture the existence of a duality between heterotic closed strings on homogeneous spaces and symmetry-preserving D-branes on group manifolds, based on the observation about the coincidence of the low-energy field description for the two theories. For the closed string side we also give an explicit proof of a no-renormalization theorem as a consequence of a hidden symmetry and infer that the same property should hold true for the higher order terms of the dbi action.

A note on singular D-branes in group manifolds

We develop the classification and systematic construction of all possible untwisted D-branes in Lie groups of A-D-E series. D-branes are classified according to their positions in the maximal torus. We construct all untwisted singular D-branes by the method of iterative deletion in the Dynkin diagram and count their dimensions, which turn out to be always even numbers.

On the hierarchy of symmetry breaking D-branes in group manifolds

We construct the boundary WZNW functional for symmetry breaking \mbox{D-branes} on a group manifold which are localized along a product of a number of twisted conjugacy classes and which preserve an action of an arbitrary continuous subgroup. These branes provide a geometric interpretation for the algebraic formulation of constructing D-branes developed recently in [20]. We apply our results to obtain new symmetry breaking and non-factorizing D-branes in the background SL(2,) × SU(2).

Classification and quantum moduli space of D-branes in group manifolds

We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the maximal torus. We describe rank 2 cases, namely B2, C2, G2, explicitly and construct all the D-branes in Br, Cr, F4 by the method of iterative deletion in the Dynkin diagram. The discussion of moduli space involves global issues that can be treated in terms of the exact homotopy sequence and various lattices. We also show that singular D-branes can exist at quantum mechanical level.

A geometric approach to D-branes in group manifolds

This is a brief review of some recent results on the geometric approach to symmetric D-branes in group manifolds, both twisted and untwisted. We describe the geometry of the gluing conditions and the quantisation condition in the boundaryWZWmodel, and we illustrate this by determining the consistent twisted and untwisted D-branes in the Lie group SU3.

A note on D-branes in group manifolds: flux quantisation and D0-charge

We show that a D-brane in a group manifold given by a (twisted) conjugacy class is characterised by a gauge invariant two-form field determined in terms of the matrix of gluing conditions. Using a quantisation argument based on the path integral one obtains the known quantisation condition for the corresponding D-branes. We find no evidence for the existence of a quantised U(1) gauge field flux. We propose an expression for the D0 charge of such D-branes.

D-branes in group manifolds

In this paper we re-examine the geometric interpretation of gluing conditions in WZW models and the possible D-brane configurations that they give rise to. We show how the boundary conditions are encoded in the gluing conditions imposed on the chiral currents. We analyse two special classes of gluing conditions: the first, which preserves the affine symmetry of the bulk theory, describes D-branes whose worldvolumes are given by `twisted' conjugacy classes; the second class describes configurations which include subgroups and cosets.