Non-commutativity and Open Strings Dynamics in Melvin Universes

We compute the Moyal phase factor for open strings ending on D3-branes wrapping a NSNS Melvin universe in a decoupling limit explicitly using world sheet formalism in cylindrical coordinates.Comment: 12 pages, 1 figure, references adde

Solvable model of strings in a time-dependent plane-wave background

We investigate a string model defined by a special plane-wave metric ds^2 = 2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a ``null cosmology'' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) This spacetime is a Lorentzian homogeneous space. In particular, like Minkowski space, it admits a boost isometry in u,v. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that its exponent (i.e. effective string coupling) goes to zero at u=infinity and at the singularity u=0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions; thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using certain analytic continuation prescription we argue that string propagation through the singularity can be smooth.Comment: 58 pages, latex. v2: several references to related previous work adde

Probing partially localized supergravity background of fundamental string ending on Dp-brane

We study the dynamics of the probe fundamental string in the field background of the partially localized supergravity solution for the fundamental string ending on Dp-brane. We separately analyze the probe dynamics for its motion along the worldvolume direction and the transverse direction of the source Dp-brane. We compare the dynamics of the probe along the Dp-brane worldvolume direction to the BIon dynamics.Comment: 20 pages, LaTeX, revised version to appear in Phys. Rev.

Power-law singularities in string theory and M-theory

We extend the definition of the Szekeres-Iyer power-law singularities to supergravity, string and M-theory backgrounds, and find that are characterized by Kasner type exponents. The near singularity geometries of brane and some intersecting brane backgrounds are investigated and the exponents are computed. The Penrose limits of some of these power-law singularities have profiles $A\sim {\rm u}^{-\gamma}$ for $\gamma\geq 2$. We find the range of the exponents for which $\gamma=2$ and the frequency squares are bounded by 1/4. We propose some qualitative tests for deciding whether a null or timelike spacetime singularity can be resolved within string theory and M-theory based on the near singularity geometry and its Penrose limits.Comment: 32 page

On duality symmetry in perturbative quantum theory

Non-compact symmetries of extended 4d supergravities involve duality rotations of vectors and thus are not manifest off-shell invariances in standard "second-order" formulation. To study how such symmetries are realised in the quantum theory we consider examples in 2 dimensions where vector-vector duality is replaced by scalar-scalar one. Using a "doubled" formulation, where fields and their momenta are treated on an equal footing and the duality becomes a manifest symmetry of the action (at the expense of Lorentz symmetry), we argue that the corresponding on-shell quantum effective action or S-matrix are duality symmetric as well as Lorentz invariant. The simplest case of discrete Z_2 duality corresponds to a symmetry of the S-matrix under flipping the sign of the negative-chirality scalars in 2 dimensions or phase rotations of chiral (definite-helicity) parts of vectors in 4 dimensions. We also briefly discuss some 4d models and comment on implications of our analysis for extended supergravities.Comment: 21 pages, Latex v2: comments and references added v3: references and minor comments adde

Strings in a Time-Dependent Orbifold

We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both in light-cone gauge and covariantly. We also compute some tree and one loop amplitudes which exhibit interesting behavior near the singularity. Our results are compatible with the possibility that strings can pass through the singularity from the contracting to the expanding universe, but they also indicate the need for further study of certain divergent scattering amplitudes.Comment: 27 pages, minor changes and note adde

Bubbling Orientifolds

We investigate a class of 1/2-BPS bubbling geometries associated to orientifolds of type IIB string theory and thereby to excited states of the SO(N)/Sp(N) N=4 supersymmetric Yang-Mills theory. The geometries are in correspondence with free fermions moving in a harmonic oscillator potential on the half-line. Branes wrapped on torsion cycles of these geometries are identified in the fermi fluid description. Besides being of intrinsic interest, these solutions may also occur as local geometries in flux compactifications where orientifold planes are present to ensure global charge cancellation. We comment on the extension of this procedure to M-theory orientifolds.Comment: 25 pages, 11 figures. v2: few references adde

On Smooth Time-Dependent Orbifolds and Null Singularities

We study string theory on a non-singular time-dependent orbifold of flat space, known as the `null-brane'. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.Comment: 24 pages, one figur

Some comments about Schwarzschield black holes in Matrix theory

In the present paper we calculate the statistical partition function for any number of extended objects in Matrix theory in the one loop approximation. As an application, we calculate the statistical properties of K clusters of D0 branes and then the statistical properties of K membranes which are wound on a torus.Comment: 15 page