Uncovering the Structure of the ε Expansion

Abstract: The ε expansion was invented almost 50 years ago and has been used extensively ever since to quantitatively describe critical phenomena. Its most famous applications are found in theories involving scalar fields in 4−ε dimensions. In this talk, we will be interested in the structure of the ε expansion of 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 very non trivial. (Based on arXiv:1707.06165, arXiv:1810.10541 and upcoming work with Hugh Osborn.

general relativity and quantum cosmologyHEP - phenomenologyHEP - theorymathematical physics

Audience: researchers in the topic

CCTP HEP Seminars

Series comments: Description: Seminars in high energy physics

Weekly HEP Seminars in the broad spectrum of High Energy Physics at University of Crete.

Recordings of past seminars can be found at conference.physics.uoc.gr/b/hep-kzk-2ad