A mathematical formalism for the Kondo effect in Wess-Zumino-Witten branes

Abstract

In the paper, we adapt our previous formalism for a mathematical treatment of branes to include processes, specifically the Kondo flow for Wess-Zumino-Witten (WZW) branes. In this framework, we give the precise mathematical definitions and formulate a mathematical conjecture relating WZW branes to nonequivariant twisted K theory in the case of the group SU(n). We also discuss regularization of the Kondo flow, thereby giving a first step toward proving our conjecture.

Perturbative Deformations of Conformal Field Theories Revisited

“…In the models considered, notably the Baxter model [11], the Ashkin-Teller model [8] and the Gaussian model [48], vanishing of the primary obstruction did correspond to a continuous line of deformations, and it was therefore believed that the primary obstruction tells the whole story. (A similar story also occurs in the case of deformations of boundary sectors, see [1,2,12,22,51,52,58,38]. )…”

“…We shall work in the framework of [59] (see also [36][37][38]). In the bosonic case (without considering supersymmetry), a conformal field theory in this framework is characterized by a Hilbert space of states H, and for a worldsheet, by which one means a Riemann surface Σ (a 1-dimensional complex manifold) with analytically parametrized boundary components, a trace class element…”

“…where λ * denotes the contragredient label (cf. [35]). (In the case of the Gepner model, we will need a slightly more general scenario, but our methods still apply to that case analogously.)…”

On Effective F-Theory Action in Type Iia Compactifications

“…For the purposes of the present paper, we choose a somewhat artificial (although, again, suggestive) solution. Recalling (10), we see that in the finite-dimensional case, the Rarita-Schwinger index serves to simply cancel the 12-dimensional term of the gravitational anomaly. In the loop case, we encounter a similar term.…”

“…Indeed, it is not obvious what kind of analogue of the Rarita-Schwinger operator one should consider on loop space. Observing ( 9) and (10), however, suggests that we could solve this problem here simply by dropping the 12-dimensional term (not counting the dimension of G). Perhaps this points, however, to the deeper point that boundary phenomena become more complicated on loop space, since the "boundary" of the space of loops on a manifold cannot be identified simply with the loop space on the boundary.…”