Dirichlet Boundary State in Linear Dilaton Background

Dirichlet-branes have emerged as important objects in studying nonperturbative string theory. It is important to generalize these objects to more general backgrounds other than the usual flat background. The simplest case is the linear dilaton condensate. The usual Dirichlet boundary condition violates conformal invariance in such a background. We show that by switching on a certain boundary interaction, conformal invariance is restored. An immediate application of this result is to two dimensional string theory.Comment: 6 pages, harvmac, some remarks are modified and one reference is added, formulas remain the sam

The Virtual Black Hole in 2d Quantum Gravity and its Relevance for the S-matrix

As shown recently 2d quantum gravity theories -- including spherically reduced Einstein-gravity -- after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a "virtual black hole". We discuss the lowest order tree vertex for minimally and non-minimally coupled scalars and find a non-trivial finite S-matrix for gravitational s-wave scattering in the latter case.Comment: 4 pages, Talk given at the Fifth Workshop on "Quantum Field Theory under the Influence of External Conditions" in Leipzig, Sept. 200

Loop Variables and Gauge Invariance in (Open) Bosonic String Theory

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite world-sheet cutoff and that in the infrared limit, equivalence with the Callan-Symanzik $\beta$-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon-photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite world sheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into standard form.Comment: 20 pages, Late

CT-duality as a local property of the world-sheet

In the present article, we study the local features of the world-sheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in space-time to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the world-sheet described by this relation we will refer as CT-dual surface.Comment: Latex, 15 pages, 2 Figure

Quantum Black Holes

Static solutions of large-$N$ quantum dilaton gravity in $1+1$ dimensions are analyzed and found to exhibit some unusual behavior. As expected from previous work, infinite-mass solutions are found describing a black hole in equilibrium with a bath of Hawking radiation. Surprisingly, the finite mass solutions are found to approach zero coupling both at the horizon and spatial infinity, with a ``bounce'' off of strong coupling in between. Several new zero mass solutions -- candidate quantum vacua -- are also described.Comment: 14 pages + 6 figure

Exact C=1 Boundary Conformal Field Theories

We present a solution of the problem of a free massless scalar field on the half line interacting through a periodic potential on the boundary. For a critical value of the period, this system is a conformal field theory with a non-trivial and explicitly calculable S-matrix for scattering from the boundary. Unlike all other exactly solvable conformal field theories, it is non-rational ({\it i.e.} has infinitely many primary fields). It describes the critical behavior of a number of condensed matter systems, including dissipative quantum mechanics and of barriers in ``quantum wires''.Comment: harvmac, 10 pages, PUPT-1432/IASSNS-HEP-93/7

Gauge Fields and Space-Time

In this article I attempt to collect some ideas,opinions and formulae which may be useful in solving the problem of gauge/ string / space-time correspondence This includes the validity of D-brane representation, counting of gauge-invariant words, relations between the null states and the Yang-Mills equations and the discussion of the strong coupling limit of the string sigma model. The article is based on the talk given at the "Odyssey 2001" conference.Comment: 20 page

Active Gel Model of Amoeboid Cell Motility

We develop a model of amoeboid cell motility based on active gel theory. Modeling the motile apparatus of a eukaryotic cell as a confined layer of finite length of poroelastic active gel permeated by a solvent, we first show that, due to active stress and gel turnover, an initially static and homogeneous layer can undergo a contractile-type instability to a polarized moving state in which the rear is enriched in gel polymer. This agrees qualitatively with motile cells containing an actomyosin-rich uropod at their rear. We find that the gel layer settles into a steadily moving, inhomogeneous state at long times, sustained by a balance between contractility and filament turnover. In addition, our model predicts an optimal value of the gel-susbstrate adhesion leading to maximum layer speed, in agreement with cell motility assays. The model may be relevant to motility of cells translocating in complex, confining environments that can be mimicked experimentally by cell migration through microchannels.Comment: To appear in New Journal of Physic

Junctions of three quantum wires and the dissipative Hofstadter model

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find non-trivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.Comment: 4 pages, 1 figur