Unification with Low String Scale

I argue that in open-string theory with hierarchically small (or large) extra dimensions, gauge groups can unify naturally with logarithmically-running coupling constants at the high Kaluza-Klein (or string-winding) scale. This opens up the possibility of rescuing the standard logarithmic unification at $M_U\sim 10^{15-18}$ GeV even if the fundamental-string scale is much lower, at intermediate or possibly even electroweak scales. I also explain, however, why a low type-I string scale may not suffice to obliterate the ultraviolet problems usually associated with the gauge hierarchy.Comment: 6 pages, uses harvmac. Two minor changes. Final version to appear in JHE

(8,0) Quantum mechanics and symmetry enhancement in type I' superstrings

The low-energy supersymmetric quantum mechanics describing D-particles in the background of D8-branes and orientifold planes is analyzed in detail, including a careful discussion of Gauss' law and normal ordering of operators. This elucidates the mechanism that binds D-particles to an orientifold plane, in accordance with the predictions of heterotic/type I duality. The ocurrence of enhanced symmetries associated with massless bound states of a D-particle with one orientifold plane is illustrated by the enhancement of $SO(14) \times U(1)$ to $E_8$ and $SO(12)\times U(1)$ to $E_7$ at strong type I' coupling. Enhancement to higher-rank groups involves both orientifold planes. For example, the enhanced $E_8 \times E_8 \times SU(2)$ symmetry at the self-dual radius of the heterotic string is seen as the result of two D8-branes coinciding midway between the orientifold planes, while the enhanced $SU(18)$ symmetry results from the coincidence of all sixteen D8-branes and $SO(34)$ when they also coincide with an orientifold plane. As a separate by-product, the s-rule of brane-engineered gauge theories is derived by relating it through a chain of dualities to the Pauli exclusion principle.Comment: 30 pages LaTeX, Five figures. Two references added as well as some Comments in section4. v4: Missing backslashes added to four reference citations

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Loop Operators and the Kondo Problem

We analyse the renormalisation group flow for D-branes in WZW models from the point of view of the boundary states. To this end we consider loop operators that perturb the boundary states away from their ultraviolet fixed points, and show how to regularise and renormalise them consistently with the global symmetries of the problem. We pay particular attention to the chiral operators that only depend on left-moving currents, and which are attractors of the renormalisation group flow. We check (to lowest non-trivial order in the coupling constant) that at their stable infrared fixed points these operators measure quantum monodromies, in agreement with previous semiclassical studies. Our results help clarify the general relationship between boundary transfer matrices and defect lines, which parallels the relation between (non-commutative) fields on (a stack of) D-branes and their push-forwards to the target-space bulk.Comment: 22 pages, 2 figure

Permeable conformal walls and holography

We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.Comment: Latex file, 34 pages, 8 figures, uses JHEP3.cls. Typos corrected and references adde

World-sheet duality for D-branes with travelling waves

We study D-branes with plane waves of arbitrary profiles as examples of time-dependent backgrounds in string theory. We show how to reproduce the quantum mechanical (one-to-one) open-string S-matrix starting from the closed-string boundary state for the D-branes, thereby establishing the channel duality of this calculation. The required Wick rotation to a Lorentzian worldsheet singles out as 'prefered' time coordinate the open-string light-cone time.Comment: 17 pages, Latex file, uses JHEP3.cls, two figures. Added references and corrected two typo

Spin-2 spectrum of defect theories

We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincare or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltrami equation on a Riemann surface with disk topology, and in the simplest case of the supersymmetric Janus solution it further reduces to an ordinary differential equation known as Heun's equation. We solve this equation numerically, and exhibit the spectrum as a function of the dilaton-jump parameter $\Delta\phi$. In the limit of large $\Delta\phi$ a nearly-flat linear-dilaton dimension grows large, and the Janus geometry becomes effectively five-dimensional. We also discuss the difficulties of localizing four-dimensional gravity in the more general backgrounds with NS5-brane or D5-brane charge, which will be analyzed in detail in a companion paper.Comment: 41 pages, 6 figure