Cornelius Schmidt-Colinet

Conformal perturbation theory beyond the leading order

Higher-order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients at next-to-leading order in terms of integrated correlation functions. As an example, we analyse the radius dependence of the conformal dimension of some boundary operators for the case of a single Neumann brane on a circle, and for an intersecting brane configuration on a torus, reproducing in both cases the expected geometrical answer.

Bounds for state degeneracies in 2D conformal field theory

In this note we explore the application of modular invariance in 2-dimensional CFT to derive universal bounds for quantities describing certain state degeneracies, such as the thermodynamic entropy, or the number of marginal operators. We show that the entropy at inverse temperature 2π satisfies a universal lower bound, and we enumerate the principal obstacles to deriving upper bounds on entropies or quantum mechanical degeneracies for completely general CFT. We then restrict our attention to infrared-stable CFT with moderately low central charge, in addition to the usual assumptions of modular invariance, unitarity and discrete operator spectrum. For CFT in the range cLu2009+u2009cRu2009<u200948 with no relevant operators, we are able to prove an upper bound on the thermodynamic entropy at inverse temperature 2π. Under the same conditions we also prove that a CFT can have no more than

Bulk flows in Virasoro minimal models with boundaries

left( {frac{{{c_{text{L}}} + {c_{text{R}}}}}{{48 - {c_{text{L}}} - {c_{text{R}}}}}} right) cdot exp left{ { + 4pi } right} - 2

Reflection and transmission of conformal perturbation defects

marginal deformations.

Entropy of conformal perturbation defects

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 m th and (m − 1) st 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) st model. By combining perturbative RG techniques with insights from defects and results about non-perturbative boundary flows, we determine the endpoint of the flow, i.e. the boundary condition to which an arbitrary boundary condition of the m th theory flows to.

Lower bound on the entropy of boundaries and junctions in (1+1)-dimensional quantum critical systems

We consider reflection and transmission of interfaces which implement renormalisation group flows between conformal fixed points in two-dimensions. Such an RG interface is constructed from the identity defect in the ultraviolet CFT by perturbing the theory on one side of the defect line. We compute reflection and transmission coefficients in perturbation theory to third order in the coupling constant and check our calculations against exact constructions of RG interfaces between coset models.

Tensor product and permutation branes on the torus

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 with the boundary entropy of the defect constructed by Gaiotto (2012 J. High Energy Phys. JHEP12(2012)103) and find a match at the first two orders in the expansion.

Precise lower bound on Monster brane boundary entropy

A lower bound is derived for the boundary entropy s=lng of a (1+1)-dimensional quantum critical system with boundary under the conditions c≥1 on the bulk conformal central charge and Δ1>(c-1)/12 on the most relevant bulk scaling dimension. This is the first general restriction on the possible values of g for bulk critical systems with c≥1.

The One-Loop Effective K\'ahler Potential. I: Chiral Multiplets

We consider B-type D-branes in the Gepner model consisting of two minimal models at k = 2. This Gepner model is mirror to a torus theory. We establish the dictionary identifying the B-type D-branes of the Gepner model with A-type Neumann and Dirichlet branes on the torus.

The One-Loop Effective Kähler Potential. I: Chiral Multiplets

A bstractIn this paper we develop further the linear functional method of deriving lower bounds on the boundary entropy of conformal boundary conditions in 1+1 dimensional conformal field theories (CFTs). We show here how to use detailed knowledge of the bulk CFT spectrum. Applying the method to the Monster CFT with c =