Quantum D-branes and exotic smooth R^4

TL;DR

This paper explores the connection between exotic smooth R^4 structures and quantum D-branes in string theory, using noncommutative geometry and K-theory to describe stable quantum branes associated with these exotic structures.

Contribution

It introduces a novel framework linking small exotic R^4's with quantum D-branes via noncommutative C* algebras and extends the exotic R^4-brane correspondence using advanced topological tools.

Findings

Exotic R^4's correspond to generalized quantum branes in convolution algebras.

Stable quantum D-branes are described using K-theory and KK-theory in noncommutative settings.

The work extends previous exotic R^4-brane correspondences to a quantum and noncommutative context.

Abstract

In this paper, we present the idea that the formalism of string theory is connected with the dimension 4 in a new way, not covered by phenomenological or model-building approaches. The main connection is given by structures induced by small exotic smooth R^4's having intrinsic meaning for physics in dimension 4. We extend the notion of stable quantum D-branes in a separable noncommutative C* algebras over convolution algebras corresponding to the codimension-1 foliations of S^3 which are mainly connected to small exotic R^4. The tools of topological K-homology and K-theory as well KK-theory describe stable quantum branes in the C* algebras when naturally extended to algebras. In case of convolution algebras, small exotic smooth R^4's embedded in exotic R^4 correspond to a generalized quantum branes on the algebras. These results extend the correspondence between exotic R^4 and classical D and NS branes from our previous work.