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arXiv:hep-th/0205011 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Boundary renormalization group flows in coset conformal field theories

Stefan Fredenhagen, Volker Schomerus

Published Apr 8, 2003• 29 citations
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Abstract

We propose a new rule for boundary renormalization group flows in fixed-point free coset models. Our proposal generalizes the ``absorption of boundary spin'' principle formulated by Affleck and Ludwig to a large class of perturbations in boundary conformal field theories. We illustrate the rule in the case of unitary minimal models.

DOI
10.1103/physrevd.67.085001

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We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for ddd-dimensional BCFTs between two nearby fixed points. We also use the AdSd+1/BCFTd{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}AdSd+1​/BCFTd​ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient renormalization group flow both in conformal perturbation theory and the AdSd+1/BCFTd{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}AdSd+1​/BCFTd​ model. In a special case, the change of the boundary entropy in the AdSd+1/BCFTd{\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_{d}AdSd+1​/BCFTd​ model reduces to that of the conformal perturbation theory.
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We consider perturbation defects obtained by perturbing a 2D conformal field theory (CFT) by a relevant operator on a half-plane. If the perturbed bulk theory flows to an infrared fixed point described by another CFT, the defect flows to a conformal defect between the ultraviolet and infrared fixed point CFTs. For short bulk renormalization group flows connecting two fixed points which are close in theory space we find a universal perturbative formula for the boundary entropy of the corresponding conformal perturbation defect. We compare the value of the boundary entropy that our formula gives for the flows between nearby Virasoro minimal models Mm with the boundary entropy of the defect constructed by Gaiotto in [1] and find a match at the first two orders in the 1/m expansion.
We propose using smeared boundary states e^{-\tau H}|\cal B\rangle as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT.