Structure constants in the N=1 superoperator algebra

Using the Coulomb Gas formulation of N=1 Superconformal Field Theories, we extend the arguments of Dotsenko and Fateev for the bosonic case to evaluate the structure constants of N=1 minimal Superconformal Algebras in the Neveu-Schwarz sector.Comment: 68 page

Curvature formula for the space of 2-d conformal field theories

We derive a formula for the curvature tensor of the natural Riemannian metric on the space of two-dimensional conformal field theories and also a formula for the curvature tensor of the space of boundary conformal field theories.Comment: 36 pages, 1 figure; v2 references adde

Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation

It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa models with unbroken flavour and chiral symmetries and no doubling of the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is avoided, because the chiral symmetry is realized in a different way than has been assumed when proving the theorem.Comment: plain tex source, 8 pages, no figure

Infrared properties of boundaries in 1-d quantum systems

We present some partial results on the general infrared behavior of bulk-critical 1-d quantum systems with boundary. We investigate whether the boundary entropy, s(T), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the IR limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviors far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta-function is the gradient of the boundary entropy, which implies that s(T) decreases with T. The metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.Comment: 26 pages, Late

Gradient formula for the beta-function of 2d quantum field theory

We give a non-perturbative proof of a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form \partial_{i}c = - (g_{ij}+\Delta g_{ij} +b_{ij})\beta^{j} where \beta^{j} are the beta functions, c and g_{ij} are the Zamolodchikov c-function and metric, b_{ij} is an antisymmetric tensor introduced by H. Osborn and \Delta g_{ij} is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.Comment: LaTex file, 31 pages, no figures; v.2 referencing corrected in the introductio