K-Theory from a physical perspective

TL;DR

This paper offers a physical perspective on K-theory, explaining how renormalization group flows, anomaly cancellation, and instanton effects relate to the classification of D-branes, exemplified through SU(N).

Contribution

It introduces a novel physical interpretation of K-theory in the context of D-branes, integrating RG flows and spacetime phenomena.

Findings

Relates RG flows to K-theoretic classification of D-branes

Connects anomaly cancellation with K-theory

Describes twisted K-theory of SU(N) groups

Abstract

This is an expository paper which aims at explaining a physical point of view on the K-theoretic classification of D-branes. We combine ideas of renormalization group flows between boundary conformal field theories, together with spacetime notions such as anomaly cancellation and D-brane instanton effects. We illustrate this point of view by describing the twisted K-theory of the special unitary groups SU(N).