We calculate the Rényi entropy S q (µ, λ), for spherical entangling surfaces in CFT's with Einstein-Gauss-Bonnet-Maxwell holographic duals. Rényi entropies must obey some interesting inequalities by definition. However, for Gauss-Bonnet couplings λ, larger than a specific value, but still allowed by causality, we observe a violation of the inequality ∂ ∂q q−1 q S q (µ, λ) ≥ 0, which is related to the existence of negative entropy black holes, providing interesting restrictions in the bulk theory. Moreover, we find an interesting distinction of the behaviour of the analytic continuation of S q (µ, λ) for imaginary chemical potential, between negative and non-negative λ.

Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category C_F which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed from V (the Cardy case). Then C = Rep(V) and an object in C_F corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in C_F an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through the Grothendieck ring of C_F. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.Comment: 38 pages; v2: corrected typos and expanded section 3.2, version to appear in CM

Two-dimensional σ-models corresponding to coset CFTs of the type (ĝ k ⊕ĥ )/ĥ k+ admit a zoom-in limit involving sending one of the levels, say , to infinity. The result is the non-Abelian T-dual of the WZW model for the algebraĝ k with respect to the vector action of the subalgebra h of g. We examine modular invariant partition functions in this context. Focusing on the case with g = h = su(2) we apply the above limit to the branching functions and modular invariant partition function of the coset CFT, which as a whole is a delicate procedure. Our main concrete result is that such a limit is well defined and the resulting partition function is modular invariant.