Maxim Zabzine

Boundary conditions, supersymmetry and A-field coupling for an open string in a B-field background

Abstract We discuss the non-linear sigma model representing a NSR open string in a curved background with non-zero Bμν-field. With this coupling the theory is not automatically supersymmetric, due to boundary contributions. When B=0 supersymmetry is ensured by the conditions that follow as the boundary contribution to the field equations. We show that inclusion of a particular boundary term restores this state of affairs also in the presence of a B-field. The boundary conditions derived from the field equations in this case agree with those that have been proposed for constant B-field. A coupling to a boundary Aμ-field will modify both the boundary conditions and affect the supersymmetry. It is shown that there is an A-coupling with non-standard fermionic part that respects both the supersymmetry and the shift symmetry (in the B and A fields), modulo the (modified) boundary conditions.

Hamiltonian systems with boundaries

Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should be applicable to a wide range of models defined on manifolds with boundaries. The goal of the present paper is to show how the boundary conditions can arise as constraints in a purely algebraic fashion within the hamiltonian approach without any reference to the lagrangian formulation of the theory. The construction of the boundary Dirac brackets is also given and some subtleties are pointed out. We consider four examples of field theories with boundaries: the topological sigma model, the open string theory with and without a constant B-field and electrodynamics with topological term. A curious result for electrodynamics on a manifold with boundaries is presented.

Strings at the tachyonic vacuum

We study the world-volume effective action of Dp-brane at the tachyonic vacuum which is equivalent to the zero tension limit. Using the Hamiltonian formalism we discuss the algebra of constraints and show that there is a non-trivial ideal of the algebra which corresponds to Virasoro like constraints. The Lagrangian treatment of the model is also considered. For the gauge fixed theory we construct the important subset of classical solutions which is equivalent to the string theory solutions in conformal gauge. We speculate on a possible quantization of the system. At the end a brief discussion of different background fields and fluctuations around the tachyonic vacuum is presented.

Note on bosonic open strings in a constant B field

We sketch the main steps of old covariant quantization of bosonic open strings in a constant B field background. We comment on its space-time symmetries and the induced effective metric. The low-energy spectrum is evaluated and the appearance of a new noncommutative gauge symmetry is addressed.

The Limits of D-Brane Action

This talk has been based on the preliminary results from [1]. We consider the D-brane action which is Born-Infeld action with Wess-Zumino terms. The main goal of present study is to review the different limits of the D-brane action. Even exotic limits are considered such as the strong coupling and high curvature limits.