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In this highly speculative note we conjecture that it may be possible to understand features of coincident D-branes, such as the appearance of enhanced non-abelian gauge symmetry, in a purely geometric fashion, using a form of geometry known as scheme theory. We give a very brief introduction to some relevant ideas from scheme theory, and point out how these ideas work in special cases.
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In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C^*-algebra. In the case of B-fields whose curvature is pure torsion our description is shown to coincide with that of Witten.
We review the boundary state description of D-branes in type I string theory and show that the only stable non-BPS configurations are the D-particle and the D-instanton. We also compute the gauge and gravitational interactions of the non-BPS D-particles and compare them with the interactions of the dual non-BPS states of the heterotic string, finding complete agreement.
A classification of D-branes in Type IIB Op^- orientifolds and orbifolds in terms of Real and equivariant KK-groups is given. We classify D-branes intersecting orientifold planes from which are recovered some special limits as the spectrum for D-branes on top of Type I Op^- orientifold and the bivariant classification of Type I D-branes. The gauge group and transformation properties of the low energy effective field theory living in the corresponding unstable D-brane system are computed by extensive use of Clifford algebras. Some speculations about the existence of oth
We study correlation functions of D-branes and a supergravity mode in AdS, which are dual to structure constants of two sub-determinant operators with large charge and a BPS single-trace operator. Our approach is inspired by the large charge expansion of CFT and resolves puzzles and confusions in the literature on the holographic computation of correlation functions of heavy operators. In particular, we point out two important effects which are often missed in the literature; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. To demonstrate the power of the method, we first analyze the three-point functions in $mathcal{N}=4$ super Yang-Mills and reproduce the results in field theory from holography, including the cases for which the previous holographic computation gives incorrect answers. We then apply it to ABJM theory and make solid predictions at strong coupling. Finally we comment on possible applications to states dual to black holes and fuzzballs.
We use the boundary state formalism to study, from the closed string point of view, superpositions of branes and anti-branes which are relevant in some non-perturbative string dualities. Treating the tachyon instability of these systems as proposed by A. Sen, we show how to incorporate the effects of the tachyon condensation directly in the boundary state. In this way we manage to show explicitly that the D1 -- anti-D1 pair of Type I is a stable non-BPS D-particle, and compute its mass. We also generalize this construction to describe other non-BPS D-branes of Type I. By requiring the absence of tachyons in the open string spectrum, we find which configurations are stable and compute their tensions. Our classification is in complete agreement with the results recently obtained using the K-theory of space-time.
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