A 2-form higher Berry connection on boundary conformal manifolds is defined from boundary-condition-changing operator OPE phases; it reproduces the B-field and WZ term in string theory examples.
Symmetry-breaking boundary states for WZW models
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Starting with the SU(2)_k WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k, quotients of SU(2) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU(2) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.
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Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory
A 2-form higher Berry connection on boundary conformal manifolds is defined from boundary-condition-changing operator OPE phases; it reproduces the B-field and WZ term in string theory examples.