We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r 4 when compactified on two dimensions having Kaluza-Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of nonsupersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in submillimeter tests of gravity and at the Large Hadron Collider. We do find self tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam-Sezgin gauged 6D supergravity compactified on a 2sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.

We present warped compactification solutions of six-dimensional supergravity, which are generalizations of the Randall-Sundrum (RS) warped brane world to codimension two and to a supersymmetric context. In these solutions the dilaton varies over the extra dimensions, and this makes the electroweak hierarchy only power-law sensitive to the proper radius of the extra dimensions (as opposed to being exponentially sensitive as in the RS model). Warping changes the phenomenology of these models because the Kaluza-Klein gap can be much larger than the internal space's inverse proper radius. We provide examples both for Romans' nonchiral supergravity and Salam-Sezgin chiral supergravity, and in both cases the solutions break all of the supersymmetries of the models. We interpret the solution as describing the fields sourced by a 3-brane and a boundary 4-brane (Romans' supergravity) or by one or two 3-branes (Salam-Sezgin supergravity), and we identify the topological constraints which are required by this interpretation. For both types of solutions the 3-branes are flat for all topologically-allowed values of the brane tensions. We identify the general mechanism for and limitations of the self-tuning of the effective 4D cosmological constant in higher-dimensional supergravity which these models illustrate.Keywords: brane-world, supergravity, warped geometries. 42 7. Appendix: Explicit Solution with λ 4 = −ζ 4 = 1 2 44 -1 - 4 We are outlining the calculation for the case where the vacuum expectation value of the gauge field lies in the U (1) subgroup, but the result is the same in the case that it lies in SU (2). 5 If b 2 = 0, such as when A = 0, then instead one finds r 2 3 = B/b 1 .

We construct the 4D N = 1 supergravity which describes the low-energy limit of 6D supergravity compactified on a sphere with a monopole backgroundà la Salam and Sezgin. This provides a simple setting sharing the main properties of realistic string compactifications such as flat 4D spacetime, chiral fermions and N = 1 supersymmetry as well as Fayet-Iliopoulos terms induced by the GreenSchwarz mechanism. The matter content of the resulting theory is a supersymmetric SO(3) × U(1) gauge model with two chiral multiplets, S and T . The expectation value of T is fixed by the classical potential, and S describes a flat direction to all orders in perturbation theory. We consider possible perturbative corrections to the Kähler potential in inverse powers of Re S and Re T , and find that under certain circumstances, and when taken together with low-energy gaugino condensation, these can lift the degeneracy of the flat direction for Re S. The resulting vacuum breaks supersymmetry at moderately low energies in comparison with the compactification scale, with positive cosmological constant. It is argued that the 6D model might itself be obtained from string compactifications, giving rise to realistic string compactifications on non Ricci flat manifolds. Possible phenomenological and cosmological applications are briefly discussed.

We study a general configuration of parallel branes having co-dimension ≥ 2 situated inside a compact d-dimensional bulk space within the framework of a scalar and flux field coupled to gravity in D dimensions, such as arises in the bosonic part of some D-dimensional supergravities. A general relation is derived which relates the induced curvature of the observable noncompact n dimensions to the asymptotic behaviour of the bulk fields near the brane positions. For compactifications down to n = D − d dimensions we explicitly solve the bulk field equations to obtain the near-brane asymptotics, and by so doing relate the n-dimensional induced curvature to physical near-brane properties. In the special case where the bulk geometry remains nonsingular (or only conically singular) at the brane positions our analysis shows that the resulting n dimensions must be flat. As an application of these results we specialize to n = 4 and D = 6 and derive a new class of solutions to chiral 6D supergravity for which the noncompact 4 dimensions have de Sitter or anti-de Sitter

We study the effects of interactions in ratchet models for one-dimensional Brownian motors. In these models, directed motion of a single particle ͑the motor͒ is produced by subjecting it to the action of a one-dimensional time-dependent asymmetric potential and thermal noise. We consider here the collective behavior of a finite density of such motors that move on a line and interact with each other through excluded volume interactions. We show that the density-density correlation function, calculated in the steady state, exhibits dynamical scaling at long wavelengths and times. Our Monte Carlo simulations support the conjecture that the hydrodynamic properties of interacting Brownian motors are governed by the Kardar-Parisi-Zhang universality class ͓Phys. Rev. Lett. 56, 889 ͑1986͔͒. We demonstrate numerically that the effective noise governing the stochastic dynamics in a coarse-grained version of our model has short-range spatial correlations. Our results should be applicable to a wide variety of models for Brownian motors with short-range interactions.