Monads, Strings, and M Theory

The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant second quantized RNS superstrings as a topological field theory in two dimensions. Our construction is a natural non-Abelian extension of the RNS string. It also naturally leads to a model with manifest 11-dimensional covariance, which we conjecture to be a formulation of M theory. The non-commuting space-time coordinates of the strings are further generalized to non-commuting anti-symmetric tensors. The usual space-time picture and the free superstrings appear only in certain special phases of the model. We derive a simple set of algebraic equations, which determine the moduli space of our model. We test some aspects of our conjectual M theory for the case of compactification on $T^2$.Comment: 36 pages, TeX, harvmac, minor corrections with added referenc

U-Duality Invariance of the Four-dimensional Born-Infeld Theory

We calculate the Hamiltonian of a compactified D4-brane, with general fluxes and moduli, and find the BPS-mass. The results are invariant under the complete U-duality SO(5,5,Z).Comment: 9 pages, Late

Causal Structure of d=5 Vacua and Axisymmetric Spacetimes

We study the structure of closed timelike curves (CTCs) for the near horizon limit of the five dimensional BMPV black hole, in its overrotating regime. We argue that Bousso's holographic screens are inside the chronologically safe region, extending a similar observation of Boyda et al. hep-th/0212087 for Goedel type solutions. We then extend this result to quite generic axisymmetric spacetimes with CTCs, showing that causal geodesics can't escape the chronologically safe region. As a spin-off of our results, we fill a gap in the identification of all maximally supersymmetric solutions of minimal five dimensional supergravity, bringing this problem to a full conclusion.Comment: LaTeX, 36 pages, 3 figures; v2: added referenc

Deformations of Topological Open Strings

Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the complex of multilinear maps on the boundary Hilbert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc.Comment: LaTeX 30 pages, corrected typo

Gauge Bundles and Born-Infeld on the Noncommutative Torus

In this paper, we describe non-abelian gauge bundles with magnetic and electric fluxes on higher dimensional noncommutative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft fluxes. We discuss Morita equivalence between these bundles. The action of the duality is worked out in detail for the four-torus. As an application, we discuss Born-Infeld on this 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(4,4;Z). The U-duality invariant BPS mass-formula is discussed shortly. We comment on a discrepancy of this result with that of a recent calculation.Comment: 22 pages, LaTeX2e. Small errors correcte

Cohomological Yang-Mills Theories on Kahler 3-Folds

We study topological gauge theories with N=(2,0) supersymmetry based on stable bundles on general Kahler 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. Afterdimensional reduction to a Kahler 2-fold, the theory reduces to Vafa-Wittentheory. On a Calabi-Yau 3-fold, the supersymmetry is enhanced to N=(2,2). This model may be used to describe classical limits of certain compactifications of(matrix) string theory.Comment: 32 pages, LaTe

BV Quantization of Topological Open Membranes

We study bulk-boundary correlators in topological open membranes. The basic example is the open membrane with a WZ coupling to a 3-form. We view the bulk interaction as a deformation of the boundary string theory. This boundary string has the structure of a homotopy Lie algebra, which can be viewed as a closed string field theory. We calculate the leading order perturbative expansion of this structure. For the 3-form field we find that the C-field induces a trilinear bracket, deforming the Lie algebra structure. This paper is the first step towards a formal universal quantization of general quasi-Lie bialgebroids.Comment: 25 pages LaTeX; added some dicussions and clarifications, typos correcte

Super Yang-Mills With Flavors From Large N_f Matrix Models

We consider the exact effective superpotential of N=1 U(N_c) super Yang-Mills theory with N_f massive flavors an additional adjoint Higgs field. We use the proposal of Dijkgraaf and Vafa to calculate the superpotential in terms of a matrix model with a large number of flavors. We do this by gauging the flavor symmetry and forcing this sector in a classical vacuum. This gives rise to a 2-matrix model of ADE type A_2, and large flavors. This approach allows us to add an arbitrary polynomial tree level superpotential for the Higgs field, and use strict large N methods in the matrix model.Comment: 17 p. LaTeX, 17 p. v2: ref added, typos corrected. v3: typos corrected. v4: typos corrected, extended discussion on classical solution