Christiaan Hofman

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; ). The BPS mass even has a full SL(3;) × SL(2;) U-duality symmetry. The direct identification of the noncommutative parameter θ with the B-field modulus however seems to be problematic at finite volume.

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.

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,).

Sigma models for bundles on Calabi-Yau: a proposal for matrix string compactifications

Abstract We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite-dimensional space of bundles on a Calabi–Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped around the Calabi–Yau. We propose that this model can be used to define matrix string theory compactifications. In the infrared limit the model flows to a superconformal non-linear sigma-model whose target space is the moduli space of BPS configurations of branes on the compact space, containing the moduli space of semi-stable bundles. We argue that the bulk degrees of freedom decouple in the infrared limit if semi-stability implies stability. We study topological versions of the model on Calabi–Yau 3-folds. The resulting B -model is argued to be equivalent to the holomorphic Chern–Simons theory proposed by Witten. The A -model and half-twisted model define the quantum cohomology ring and the elliptic genus, respectively, of the moduli space of stable bundles on a Calabi–Yau 3-fold.