High Energy Theory Seminar

We review recent results of the renormalization group functions of scalar quantum field theories in various spacetime dimensions and their application to recent ideas in conformal field theories as a prelude to the extension to gauge theories. At the outset we concentrate on six dimensional phi^3 theory and briefly discuss and update its connection with condensed matter models. For instance, four loop estimates of critical exponents in various dimensions are given which are competitive with strong coupling methods. More generally the six dimensional theory is part of a tower of related field theories. Central to the connectivity of this d-dimensional tower of theories in the same universality class is the Wilson-Fisher fixed point. This is analysed via the large N expansion. A similar approach is then used for non-abelian gauge theories and the Lagrangian in that universal tower is also constructed from 4 to 6 dimensions building on the well-founded one from 2 to 4. Once the six dimensional gauge theory is established in the same universality class, the conformal window and critical exponents are determined at two loop order, for example. This analysis is extended to three loops for abelian theories and higher dimensions.