Abstract
Following on from a previous article [1], we consider open strings in the non-Abelian T-dual of the SU(2)k WZW model, with respect to the vector SU(2) isometry. Since in this case the dual theory has an exact CFT description, we look at the chiral algebra-preserving D-branes. The general conclusion is that a large set of branes, while consistent boundary conditions on the worldsheet, are sent to infinity in the target space. This suggests inconsistency of the strict non-Abelian duality with open strings, in this case.
Highlights
The goal of the present paper is to consider open strings in the truncation, in the process fleshing out certain aspects of the picture
The SU(2) WZW model has target space SU(2) ≃ S3, which we parametrize by embedding in R4 as α02 + |α|2 = 1, and we define a polar angle α0 ≡ cos ψ
Representations of the chiral algebra su(2)k are labelled by an integer 0 ≤ λ ≤ k, and the classical su(2)k-preserving Cardy brane worldvolumes are given by conjugacy classes Cλ = Cψ=(λ/k)π [8,9,10], which are the spaces of constant α0, each one isomorphic to S2 except two points at each pole α0 = ±1, as shown in fig 1a
Summary
We are interested in boundary states which preserve a given chiral algebra A. An orthogonal basis of solutions to (2.1) is given by the Ishibashi states |i , one for each representation i of A appearing in the spectrum (we consider here the diagonal modular invariant). Consistency with modular transformations picks specific linear combinations of the |i to be good boundary states for the CFT. The embedding of the D-brane in the target space may be deduced from identifying the zero-mode distributions of the Ishibashi states with the solutions of the scalar Laplacian - this yields functions which reduce at large level to delta functions supported on the D-brane worldvolume
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