1302.0884 (Yu Nakayama)

A lecture note on scale invariance vs conformal invariance    [PDF]

Yu Nakayama

In this lecture note, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. As of January 2013, our consensus is that there is no known example of scale invariant but non-conformal field theories in d=4 under the assumptions of (1) unitarity, (2) Poincar\'e invariance (causality), (3) discrete spectrum in scaling dimension, (4) existence of scale current and (5) unbroken scale invariance. We have a perturbative proof based on the higher dimensional analogue of Zamolodchikov's c-theorem, but the non-perturbative proof is yet to come. We give a complementary holographic argument to support the claim. We also try to make this lecture note a good reference for examples of scale invariance without conformal invariance. We have tried to collect as many interesting examples as possible.

View original: http://arxiv.org/abs/1302.0884