Limit theories and continuous orbifolds

Abstract

Relativistic QFTs are in general defined by a collection of effective actions, describing the dynamics of quantum fields at different energy scales. The consequent natural idea of a space of theories is still a rather imprecise notion, since a detailed knowledge or a classification of QFTs is out of reach. In two dimensions the situation is in a better shape: in this context CFTs are under control in many instances, and we know sequences of rational theories emerging as end-points of RG flows. The present thesis explores the behaviour of sequences of rational two-dimensional CFTs when the central charge approaches its supremum. After a review of various notions useful to study limit theories, like the concept of averaged fields and the construction of continuous orbifolds, we analyse in detail the limit of sequences of N=2 supersymmetric CFTs that are connected by RG flows. The limit is not unique, since with extended Virasoro symmetry one can choose different scalings for the labels of the spectrum in the limit. We construct explicitly two c=3 CFTs emerging as the large level limit of minimal models, and we identify both of them: one is the N=2 CFT of two uncompactified free real bosons and two free real fermions, the other is its continuous orbifold by U(1). We compare spectrum, torus partition function, correlators and boundary conditions. The neatest interpretation of this result is given by studying the realisation of N=2 minimal models as gauged WZW models: taking the two different limits amounts to zooming into two different regions of the target-space geometry. At the end we speculate about possible extensions and generalisations.