Deformations of Closed Strings and Topological Open Membranes

We study deformations of topological closed strings. A well-known example is the perturbation of a topological closed string by itself, where the associative OPE product is deformed, and which is governed by the WDVV equations. Our main interest will be closed strings that arise as the boundary theory for topological open membranes, where the boundary string is deformed by the bulk membrane operators. The main example is the topological open membrane theory with a nonzero 3-form field in the bulk. In this case the Lie bracket of the current algebra is deformed, leading in general to a correction of the Jacobi identity. We identify these deformations in terms of deformation theory. To this end we describe the deformation of the algebraic structure of the closed string, given by the BRST operator, the associative product and the Lie bracket. Quite remarkably, we find that there are three classes of deformations for the closed string, two of which are exemplified by the WDVV theory and the topological open membrane. The third class remains largely mysterious, as we have no explicit example.Comment: 50 pages, LaTeX; V2: minor changes, 2 references added, V3: typos corrected, signs added, modified discussion on higher correlator

Freund-Rubin Revisited

We utilise the duality between M theory and Type IIA string theory to show the existence of Freund-Rubin compactifications of M theory on 7-manifolds with singularities supporting chiral fermions. This leads to a concrete way to study phenomenologically interesting quantum gravity vacua using a holographically dual three dimensional field theory.Comment: reference adde

The viscosity bound in string theory

The ratio of shear viscosity to entropy density $\eta/s$ of any material in nature has been conjectured to have a lower bound of $1/4\pi$, the famous KSS bound. We examine string theory models for evidence in favour of and against this conjecture. We show that in a broad class of models quantum corrections yield values of $\eta/s$ just above the KSS bound. However, incorporating matter fields in the fundamental representation typically leads to violations of this bound. We also outline a program to extend AdS/CFT methods to RHIC phenomenology.Comment: 4 pages, To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

A Record of the Taxes Which A. C. V. R. Paid to the City of Holland for the Year 1868 in the Amount of $659.59

A record of the taxes which A.C.V.R. paid to the City of Holland, C. Hofman, City Treasurer, for the year 1868 in the amount of $659.59. A.C.V.R. still owned a considerable amount of property in the City of Holland. The listing of the properties takes 13 pages.https://digitalcommons.hope.edu/vrp_1860s/1493/thumbnail.jp

U-Duality of Born-Infeld on the Noncommutative Two-Torus

We discuss Born-Infeld on the noncommutative two-torus as a description of compactified string theory. We show that the resulting theory, including the fluctuations, is manifestly invariant under the T-duality group SO(2,2;Z). The BPS mass even has a full SL(3,Z)xSL(2,Z) U-duality symmetry. The direct identification of the noncommutative parameter \theta with the B-field modulus however seems to be problematic at finite volume

Cohomological Yang-Mills theories on Kähler 3-folds

We study topological gauge theories with Nc = (2; 0) supersymmetry based on stable bundles on general Kähler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual holomorphic bundle by including a holomorphic 3-form. The correlation functions of the model describe complex 3-dimensional generalizations of Donaldson-Witten type invariants. We show that the path integral can be written as a sum of contributions from stable bundles and a complex 3-dimensional version of Seiberg-Witten monopoles. We study certain deformations of the theory, which allow us to consider the situation of reducible connections. We shortly discuss situations of reduced holonomy. After dimensional reduction to a Kähler 2-fold, the theory reduces to Vafa-Witten theory. On a Calabi-Yau 3-fold, the supersymmetry is enhanced to Nc = (2; 2). This model may be used to describe classical limits of certain compactifications of (matrix) string theory