Bulk flows in Virasoro minimal models with boundaries

Abstract

The behaviour of boundary conditions under relevant bulk perturbations is studied for the Virasoro minimal models. In particular, we consider the bulk deformation by the least relevant bulk field which interpolates between the mth and (m − 1)th unitary minimal model. In the presence of a boundary, this bulk flow induces an RG flow on the boundary, which ensures that the resulting boundary condition is conformal in the (m − 1)th model. By combining perturbative RG techniques with insights from defects and results about nonperturbative boundary flows, we determine the endpoint of the flow, i.e. the boundary condition to which an arbitrary boundary condition of the mth theory flows to.

Form factor relocalisation and interpolating renormalisation group flows from the staircase model

“…Further motivation comes from the fact that the S-matrices associated with the roaming trajectories are often far simpler than those of the interpolating flows that they ultimately come to approximate: for example, Zamolodchikov's original staircase S-matrix is diagonal, while the massless S-matrices associated with the M p → M p−1 interpolating flows [14] are non-diagonal and significantly more complicated. This has recently been used to conjecture exact equations describing combined bulk and boundary flows between minimal models [15], confirming and extending previous perturbative results [16].…”

Holographic renormalization group flows and boundary conformal field theories

“…For recent examples concerning flows of minimal model CFTs see e.g. [48,49,50]. Note that in these examples the relevant perturbations do not have the x ⊥ dependence as the ones discussed in the present paper.…”

Entanglement in Nonunitary Quantum Critical Spin Chains

“…It also agrees with computations in the Potts spin representation for Q = n 2 integer (see below). For larger M it is hard to compute this final partial trace directly, since the form of log ρ A will be substantially more complicated than (25). A much more convenient option is to recall that gluing corresponding sites on top and bottom of any word in the TL algebra means technically to take the so-called Markov trace MTr.…”

“…Recall now the expression (see e.g. [25]) of the Affleck-Ludwig entropy [26]-we restrict here to the unitary case p = 1 for simplicity: We see that the h bdy dependence of the O(1) contribution to the Rényi entropy matches the (logarithm of) the degeneracy factor g 1h bdy . Meanwhile, it is well known that fixing the RSOS height to h bdy corresponds to the boundary condition (1h bdy ) in the above notation, while it is also known that the conformal boundary condition contributes to the entanglement by a factor O(1) which is precisely the logarithm of the degeneracy factor-the Affleck-Ludwig entropy [26].…”

“…In this Letter we explore this vast subject by concen-arXiv:1611.08506v1 [cond-mat.stat-mech] 25 Nov 2016 trating on non-Hermitian models with SUSY or quantum group (QG) symmetry. We extend the general framework of Coulomb gas and loop model representations to EE calculations.…”