Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.     

Dimensional regularisation in the presence of large background fields

The method of dimensional regularisation is introduced and discussed in detail for the case of quantum field theories with large (i.e., not infinitesimal) classical background fields. Examples considered are the φ⁴-theory on four-dimensional compact curved spaces as well as Yang-Mills gauge theories on S⁴ with an arbitrary multi-instanton background field.     

On tachyon condensation of intersecting noncommutative branes in M(atrix) theory

The interaction between the intersecting noncommutative D-branes (or membranes) is investigated within the M(atrix) theory. We first evaluate the spectrum of the off-diagonal fluctuation and see that there is a tachyon mode, which signals the instability of the intersecting branes. We next explain in detail how the tachyon modes (which are the off-diagonal fluctuations) can be combined with the original branes (which are the diagonal elements) to become a new diagonal matrix, which then represents the new recombined configurations after the tachyon condensation. The tachyon condensation configurations of the noncommutative branes we find are different from those of the commutative cases studied in the previous literatures.     

Intersectingp — p′ branes inpp-wave background

Several supergravity solutions corresponding to bothDp, as well asDp—Dp′ systems, inNS-NS andR-R pp-wave background originating fromAdS ₃ xS ³ xR ⁴ are presented. The supersymmetry properties of these solutions are analysed along with a brief outline of the world sheet construction for thep — p′ branes.     

Unitary constraints for string propagation in the presence of background fields

We discuss the constraints imposed by the unitary of the S-matrix on the theory of a closed basonic string propagating in a background consisting of a condensate of the string modes. The equations of motion for some of the low mass modes are thus obtained to all orders in α′ but to second order in a weak field expansion about a flat background.     

Gravitational and electromagnetic fields of a charged tachyon

An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the uncharged tachyon which was earlier obtained by Vaidya. The null surfaces for the charged tachyon are discussed.     

Superstring propagation in curved superspace in the presence of background super Yang-Mills fields

A gauge invariant action is presented which describes the propagation of the superstring in curved superspace in the presence of background super Yang-Mills fields. It is shown that this action posseses the local fermionic world-sheet symmetry needed for a consistent coupling of the string to background fields. Some other aspects of the superspace non-linear σ-model described by this action are also discussed.     

Rotating black branes in the presence of nonlinear electromagnetic field

In this paper, we consider a class of gravity whose action represents itself as a sum of the usual Einstein–Hilbert action with cosmological constant and an U(1) gauge field for which the action is given by a power of the Maxwell invariant. We present a class of rotating black branes with Ricci flat horizon and show that the presented solutions may be interpreted as black brane solutions with two event horizons, extreme black hole and naked singularity provided the parameters of the solutions are chosen suitably. We investigate the properties of the solutions and find that for the special values of the nonlinear parameter, the solutions are not asymptotically anti-de Sitter. Finally, we obtain the conserved quantities of the rotating black branes and find that the nonlinear source has effects on the electric field, the behavior of spacetime, the type of singularity and other quantities.     

Localization of scalar fields on self-gravitating thick branes

The model of a domain wall (“thick” brane) in noncompact five-dimensional spacetime is considered with geometries of AdS ₅ type generated by self-interacting scalar matter. The scalar matter is composed of two fields with O(2) symmetric self interaction. One of them is mixed with gravity scalar modes and plays role of the brane formation mode (due to a kink background) and another one is of a Higgs-field type. The interplay between soft breaking of O(2) symmetry and gravity influence is thoroughly investigated around the critical point of spontaneous t symmetry breaking when the v.e.v. of the Higgs-type scalar field occurs. The possibility of (quasi)localization of scalar modes on such thick branes is examined.     

The heterotic sigma model in the presence of background gauge fields. Three-loop results

The covariant part of the β-functions for the heterotic σ-model in the presence of background gauge fields is calculated up to three-loop order. The equations β=0 are shown to coincide with the equations of motion derived from an effective space-time action. This effective action has been obtained previously via the string S-matrix approach.     

Fractal reconstruction in the presence of background events

An analysis of a data set containing fractals and background events is carried out using the method of the equation system of P-adic coverings (SePaC) and by the box-counting (BC) method. The peculiarities of these methods applied to the search for fractals in sets containing only fractals and background events are studied. Procedures allowing one to establish the presence of fractals, estimate their number in the initial set, separate fractals, and evaluate the portion of background events in the extracted set are suggested. A comparison of the result of an analysis of mixed events by these methods is carried out.     

Two-loop background field calculations for arbitrary background fields

The ultraviolet divergences of two-loop vacuum graphs in the presence of an arbitrary background field are determined for four-dimensional φ⁴ and gauge theories on flat space. Dimensional regularisation is employed and the heat kernel is used to analyse the short-distance singularities in the products of propagators, in the presence of the background field, that occur for two-loop graphs. The single and double poles in ? = 4 ? d are determined in a concise fashion, giving known results for the β function. A procedure for determining the remaining finite parts in terms of explicit convergent integrals in four dimensions is described.     

Heterotic string in background gauge fields

The higher order corrections to the two-dimensional nonlinear σ-model for the heterotic string are considered. The divergent parts of the effective action are calculated explicitly to two-loop order in the presence of arbitrary background gauge fields. It is shown that the full gauge Chern-Simons term appears in the divergent terms. We also discuss its relevance to the equations of motion for the massless modes of the heterotic string with emphasis on the local gauge invariance of the heterotic string theory.