Spherical Casimir energies and Dedekind sums

Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in Discussion altered. v3:typos corrected, 1 reference and comments added. v4:typos corrected. Ancillary results added in an appendi

M-branes and N=2 Strings

The string field theory of N=(2,1) heterotic strings describes a set of self-dual Yang-Mills fields coupled to self-dual gravity in 2+2 dimensions. We show that the exact classical action for this field theory is a certain complexification of the Green-Schwarz/Dirac-Born-Infeld string action, closely related to the four dimensional Wess-Zumino action describing self-dual gauge fields. This action describes the world-volume of a 2+2d ``M-brane'', which gives rise upon different null reductions to critical strings and membranes. We discuss a number of further properties of N=2 heterotic strings, such as the geometry of null reduction, general features of a covariant formulation, and possible relations to BPS and GKM algebras.Comment: 49 pages, harvmac; 1 figure (uses epsf.tex). References adde

Closed String Tachyon Condensation: An Overview

These notes are an expanded version of a review lecture on closed string tachyon condensation at the RTN workshop in Copenhagen in September 2003. We begin with a lightning review of open string tachyon condensation, and then proceed to review recent results on localized closed string tachyon condensation, focusing on two simple systems, C/Z_n orbifolds and twisted circle compactifications.Comment: harvmac, 59 pages; references adde

Closed string tachyons, flips and conifolds

Following the analysis of tachyons and orbifold flips described in hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric conifold singularity and show using their toric geometry description that they are nonsupersymmetric orbifolds of the latter. Using linear sigma models, we see that these are unstable to localized closed string tachyon condensation and exhibit flip transitions between their two small resolutions (involving 2-cycles), in the process mediating mild dynamical topology change. Our analysis shows that the structure of these nonsupersymmetric conifolds as quotients of the supersymmetric conifold obstructs the 3-cycle deformation of such singularities, suggesting that these nonsupersymmetric conifolds decay by evolving towards their stable small resolutions.Comment: Latex, 22 pgs, 2 figs. v4: matches JHEP version, 29 pgs, 3 figures, more elaborate Introduction, various clarifications adde