https://doi.org/10.1140/epjc/s10052-018-5721-4
Regular Article - Theoretical Physics
Uncovering novel phase structures in
scalar theories with the renormalization group
1
Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126, Bologna, Italy
2
INFN - Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy
* e-mail: vacca@bo.infn.it
Received:
2
January
2018
Accepted:
7
March
2018
Published online:
22
March
2018
We present a detailed version of our recent work on the RG approach to multicritical scalar theories with higher derivative kinetic term and upper critical dimension
. Depending on whether the numbers k and n have a common divisor two classes of theories have been distinguished. For coprime k and
the theory admits a Wilson-Fisher type fixed point. We derive in this case the RG equations of the potential and compute the scaling dimensions and some OPE coefficients, mostly at leading order in
. While giving new results, the critical data we provide are compared, when possible, and accord with a recent alternative approach using the analytic structure of conformal blocks. Instead when k and
have a common divisor we unveil a novel interacting structure at criticality.
theories with odd n, which fall in this class, are analyzed in detail. Using the RG flows it is shown that a derivative interaction is unavoidable at the critical point. In particular there is an infrared fixed point with a pure derivative interaction at which we compute the scaling dimensions and, for the particular example of
theory in
, also some OPE coefficients.
© The Author(s), 2018