Pseudo-supersymmetry, Consistent Sphere Reduction and Killing Spinors for the Bosonic String

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S^5, and eleven-dimensional supergravity reduced on S^4 or S^7. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D-3)-sphere, retaining the gauge bosons of SO(4) or SO(D-2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to "pseudo-supersymmetry" in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.Comment: Latex, 15 page

Non-equilibrium dynamics of simple spherical spin models

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic dynamics has for large times and for large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation regime is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like the thermoremanent magnetization.Comment: 8 pages, 1 eps figur

AdS Wormholes

We obtain a large class of smooth Lorentzian p-brane wormholes in supergravities in various dimensions. They connect two asymptotically flat spacetimes. In cases where there is no dilaton involved in the solution, the wormhole can connect an AdS_n\times S^m in one asymptotic region to a flat spacetime in the other. We obtain explicit examples for (n,m)=(4,7), (7,4), (5,5), (3,3), (3,2). These geometries correspond to field theories with UV conformal fixed points, and they undergo decompactification in the IR region. In the case of AdS_3, we compute the central charge of the corresponding conformal field theory.Comment: 20 pages, references adde