Level-rank duality of untwisted and twisted D-branes of the so(N)_K WZW model

TL;DR

This paper investigates the level-rank duality in the so(N)_K WZW model, showing how D-branes characterized by certain representations map onto dual D-branes with isomorphic open string spectra, including both untwisted and twisted cases.

Contribution

It provides a detailed analysis and proof of the level-rank duality for untwisted and epsilon-twisted D-branes in the so(N)_K WZW model, including their spectra.

Findings

Level-rank duality maps D-branes between so(N)_K and so(K)_N.

Open string spectra on dual D-branes are isomorphic.

Duality extends to both untwisted and epsilon-twisted D-branes.

Abstract

We analyze the level-rank duality of untwisted and epsilon-twisted D-branes of the so(N)_K WZW model. Untwisted D-branes of so(N)_K are characterized by integrable tensor and spinor representations of so(N)_K. Level-rank duality maps untwisted so(N)_K D-branes corresponding to (equivalence classes of) tensor representations onto those of so(K)_N. The epsilon-twisted D-branes of so(2n)_2k are characterized by (a subset of) integrable tensor and spinor representations of so(2n-1)_2k+1. Level-rank duality maps spinor epsilon-twisted so(2n)_2k D-branes onto those of so(2k)_2n. For both untwisted and epsilon-twisted D-branes, we prove that the spectrum of an open string ending on these D-branes is isomorphic to the spectrum of an open string ending on the level-rank-dual D-branes.