Attractor Flows from Defect Lines

Deforming a two dimensional conformal field theory on one side of a trivial defect line gives rise to a defect separating the original theory from its deformation. The Casimir force between these defects and other defect lines or boundaries is used to construct flows on bulk moduli spaces of CFTs. It turns out, that these flows are constant reparametrizations of gradient flows of the g-functions of the chosen defect or boundary condition. The special flows associated to supersymmetric boundary conditions in N=(2,2) superconformal field theories agree with the attractor flows studied in the context of black holes in N=2 supergravity.Comment: 28 page

Idempotent ideals and non-finitely generated projective modules over integral group rings of polycyclic-by-finite groups

We prove that every non-finitely generated projective module over the integral group ring of a polycyclic-by-finite group G is free if and only if G is polycyclic.Comment: 15 pages, to appear in J. Algebr

Descent of Equivalences and Character Bijections

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source

The limit of N=(2,2) superconformal minimal models

The limit of families of two-dimensional conformal field theories has recently attracted attention in the context of AdS/CFT dualities. In our work we analyse the limit of N=(2,2) superconformal minimal models when the central charge approaches c=3. The limiting theory is a non-rational N=(2,2) superconformal theory, in which there is a continuum of chiral primary fields. We determine the spectrum of the theory, the three-point functions on the sphere, and the disc one-point functions.Comment: 37 pages, 3 figures; v2: minor corrections in section 5.3, version to be published in JHE

Efficacy of a skin care cream with TRPV1 inhibitor 4‐t‐butylcyclohexanol in the topical therapy of perioral dermatitis

Background Perioral dermatitis is a clinically distinctive reaction pattern of facial dermatitis, including redness, dryness, burning, pruritus and skin tightness. A gold standard treatment remains unclear. Objectives Our study evaluates the clinical value of a skin care cream with the transient receptor potential vanilloid type 1 inhibitor 4‐t‐butylcyclohexanol in POD patients over 8 weeks. Methods This open, unblinded 8‐week clinical trial included 48 patients. A skin care cream containing 4‐t‐butylcyclohexanol was applied over a period of 8 weeks. Standardized questionnaires were used at baseline, 4 and 8 weeks, for history documentation, objective and subjective severity scores, and quality of life assessments. Six different skin physiology parameters were assessed at all timepoints. Results The perioral dermatitis severity score decreased significantly during the treatment period. This was mirrored by significantly lower patients’ subjective numerical rating score and an improved quality of life score. Transepidermal water loss, stratum corneum hydration and skin erythema improved significantly during the treatment period. Conclusion This transient receptor potential vanilloid type 1 inhibitor‐based skin care cream improved subjective and objective parameters of perioral dermatitis. Decreased transepidermal water loss values and increased stratum corneum hydration demonstrate a restored skin barrier function. Consequently, the topical inhibition of these receptors is a promising management option for POD

Integrability of the N=2 boundary sine-Gordon model

We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements, refs added, to appear in J. Phys. A: Math. Ge

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

The geometry of the limit of N=2 minimal models

We consider the limit of two-dimensional N=(2,2) superconformal minimal models when the central charge approaches c=3. Starting from a geometric description as non-linear sigma models, we show that one can obtain two different limit theories. One is the free theory of two bosons and two fermions, the other one is a continuous orbifold thereof. We substantiate this claim by detailed conformal field theory computations.Comment: 35 pages, 3 figures; v2 minor corrections, version to be published in J. Phys.

B-type defects in Landau-Ginzburg models

We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the superpotentials. The composition of these defects and their action on B-type boundary conditions is described in this framework. The cases of Landau-Ginzburg models with superpotential W=X^d and W=X^d+Z^2 are analysed in detail, and the results are compared to the CFT treatment of defects in N=2 superconformal minimal models to which these Landau-Ginzburg models flow in the IR.Comment: 50 pages, 2 figure