Related papers: The Bagger-Lambert model and Type IIA string theor…

$A_\infty$ categories are a mathematical structure that appears in topological field theory, string topology, and symplectic topology. This paper studies the cyclic homology of a Calabi-Yau $A_\infty$ category, and shows that it is…

We discuss the sigma model description of a D-string bound to k D-fivebranes in type I string theory. The effective theory is an (0,4) supersymmetric hyper-Kahler with torsion sigma model on the moduli space of Sp(k) instantons on R^4. Upon…

I discuss D0-brane quantum mechanics as a nonperturbative formulation of string theory, in particular the relation between the Banks-Fischler-Shenker-Susskind matrix model, the Maldacena conjecture for D0-branes, and type IIA/M-theory…

It is pointed out that affine Lie algebras appear to be the natural mathematical structure underlying the notion of integrability for two-dimensional systems. Their role in the construction and classification of 2D integrable systems is…

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology…

This article introduces and provides the mathematical foundation of the open string Floer theory of Landau-Ginzburg model viaWitten equation. We introduce the concept of regular tame exact Landau-Ginzburg system on a noncompact Kaehler…

The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie…

The 2-brane and 4-brane solutions of ten dimensional IIA supergravity have a dual interpretation as Dirichlet-branes, or `D-branes', of type IIA superstring theory and as `M-branes' of an $S^1$-compactified eleven dimensional supermembrane…

This paper, in a sense, completes a series of three papers. In the previous two hep-th/0404013, hep-th/0410293, we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic…

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the…

We introduce a common domain of definition for the loop product and the loop coproduct, reduced loop homology, on which they combine to a unital infinitesimal anti-symmetric bialgebra structure. In particular, a relation conjectured by…

We investigate Lie bialgebra structures on simple Lie algebras of non-split type $A$. It turns out that there are several classes of such Lie bialgebra structures, and it is possible to classify some of them. The classification is obtained…

We demonstrate that M-theory compactifications on 7-manifolds of G_2 holonomy, which yield 4d N=1 supersymmetric systems, often admit at special loci in their moduli space a description as type IIA orientifolds. In this way, we are able to…

The problem of quantizing a symplectic manifold (M,\omega) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space…

This thesis is based on two papers by the author and consists of two parts. We review the recent developments in the theory of multiple M2-branes and 3-algebras leading to multiple D2-brane theories. The inclusion of flux terms for the…

The superfield equations of massive IIA supergravity, in the form of constraints on the superspace geometry, are shown to be implied by $\kappa$-symmetry of the topologically massive D-2-brane.

In double field theory, the physical space has been understood as a subspace of the doubled space. Recently, the doubled space is defined as the para-Hermitian manifold and the physical space is realized as a leaf of a foliation of the…

We revisit open string mirror symmetry for the elliptic curve, using matrix factorizations for describing D-branes on the B-model side. We show how flat coordinates can be intrinsically defined in the Landau-Ginzburg model, and derive the…

This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to…

We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to…