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arXiv:hep-th/0309102 · Progress of Theoretical Physics

Conformal Boundary States in

Atsushi Yamaguchi

Published Jul 1, 2004• 2 citations
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Abstract

We construct boundary states in a particular c = 1 conformal field theory, the orbifold with G a binary finite subgroup of SU(2). These states preserve the conformal symmetry, at least, but break rational symmetries of the orbifold in general.
DOI
10.1143/ptp.112.119

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We construct a large class of conformal interfaces between two-dimensional c = 1 conformal field theories describing compact free bosons and their Z2 {\mathrm{\mathbb{Z}}}_2 Z2​ orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c = 2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent theory.
We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e.g. in the AdS/CFT correspondence when branes extend to the boundary of the AdS-space.
A bstract A state in a quantum system with a given global symmetry, G , can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G -symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.