Abstract
We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.
Highlights
The folded model is typically not rational with respect to the symmetry that is preserved by the defect
We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows
In order to find potential examples for our perturbation, we screen the spectrum of elementary topological defects in Virasoro Minimal Models [23] and in N = 1, 2 SuperVirasoro Minimal Models [24,25,26,27,28] for candidate perturbations of short flows
Summary
For a defect along the real axis in the complex plane, the local condition of preserving conformal symmetry transformations is lim T (1)(x + iy) − T(1)(x − iy) = lim T (2)(x + iy) − T(2)(x − iy) , y→0+. For time evolution orthogonal to the defect line, the defect acts as an operator I which maps states from the Hilbert space of one theory to the other. The above gluing condition turns into the statement that this operator satisfies the relation. With the generators of the conformal transformations. Besides this local condition, defects have to satisfy a Cardy condition, which ensures that quantization parallel and quantization orthogonal to the defect are equivalent. Quantization parallel to the defect gives rise to the spectrum of defect (changing) fields
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