Starts 16 Mar 2021 17:00
Ends 16 Mar 2021 18:00
Central European Time
ABSTRACT: The ε expansion was invented almost 50 years ago and has been used extensively ever since to study aspects of renormalization group flows and critical phenomena. Its most famous applications are found in theories involving scalar fields in 4−ε dimensions. In this talk, we will discuss the structure of the ε expansion in scalar field theories and the fixed points that can be obtained within it. Our motivation is based on the goal of classifying conformal field theories in d=3 dimensions. We will describe recently discovered universal constraints obtained within the framework of the ε expansion, focusing mostly on the 4−ε case although 3−ε will also be discussed. It will be shown that a “heavy handed" way to search for fixed points yields a plethora of new fixed points that reveal aspects of the structure of the ε expansion and suggest that a classification of conformal field theories in d=3 is likely to be highly non-trivial. (Based on arXiv:1707.06165, arXiv:1810.10541 and arXiv:2010.15915.)