Related papers: K-Theory, D-Branes and Ramond-Ramond Fields

In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a…

The spectrum of D2-branes wrapped on an ALE space of general ADE type is determined, by representing them as boundary states of N=2 superconformal minimal models. The stable quantum states have RR charges which precisely represent the gauge…

We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free. The mathematical setting being provided by the geometry of…

We consider compactifications of type II string theory in which a d-dimensional torus is fibered over a base X. In string theory, the transition functions of this fibration need not be simply diffeomorphisms of T^d but can involve elements…

In this note, we calculate all untwisted and twisted (Z/2)^n-equivariant K-groups with compact supports of real finite-dimensional linear representations of (Z/2)^n. The question was motivated by the question of D-brane charges for orbifold…

In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…

Engineering quantum field theories in String Theory in terms of branes is a powerful approach for understanding their dynamics. We review recent progress in the realization of $2d$ $\mathcal{N}=(0,2)$ gauge theories in terms of branes. We…

This paper provides an isomorphism $K_n (\mathscr{A}) \cong K_n (\mathscr{A}_1) \times_{K_n(\mathscr{A}_0)} K_n(\mathscr{A}_2)$ of $K$-groups, i.e., an exact sequence $0 \to K_n(\mathscr{A}) \to K_n(\mathscr{A}_1)\times K_n(\mathscr{A}_2)…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type corresponding to the…

We represent B fields and higher p-form potentials on a manifold M as connections on affine bundles over M. We realize D branes on M as special submanifolds of these affine bundles. We check the physical relevance of this representation by…

Dvali and Shifman have proposed a field-theoretic mechanism for localizing gauge fields to "branes" in higher dimensional spaces using confinement in a bulk gauge theory. The resulting objects have a number of qualitative features in common…

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This…

We construct Gepner models in terms of coset conformal field theories and compute their twisted equivariant K-theories. These classify the D-brane charges on the associated geometric backgrounds and therefore agree with the topological…

We consider D-branes in string theory and address the issue of how to describe them mathematically as a fundamental object (as opposed to a solitonic object) of string theory in the realm in differential and symplectic geometry. The notion…

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial…

We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge…

Generalising ideas of an earlier work \cite{Bo-Han}, we address the problem of constructing Brane Box Models of what we call the Z-D Type from a new point of view, so as to establish the complete correspondence between these brane setups…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory…