Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: General properties of multiscalar RG Flows in $$d=4-\varepsilon$$

Journal Article · · SciPost Physics
 [1]; ORCiD logo [2]
  1. Institut des Hautes Études Scientifiques, Bures-sur-Yvette (France); Sorbonne Univ., Paris (France)
  2. European Organization for Nuclear Research (CERN), Geneva (Switzerland); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

Fixed points of scalar field theories with quartic interactions in $$d=4-\varepsilon$$ dimensions are considered in full generality. For such theories it is known that there exists a scalar function $$A$$ of the couplings through which the leading-order beta-function can be expressed as a gradient. It is here proved that the fixed-point value of $$A$$ is bounded from below by a simple expression linear in the dimension of the vector order parameter, $$N$$. Saturation of the bound requires a marginal deformation, and is shown to arise when fixed points with the same global symmetry coincide in coupling space. Several general results about scalar CFTs are discussed,and a review of known fixed points is given.

Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1544746
Report Number(s):
LA-UR-19--25904
Journal Information:
SciPost Physics, Journal Name: SciPost Physics Journal Issue: 1 Vol. 6; ISSN 2542-4653
Publisher:
SciPost FoundationCopyright Statement
Country of Publication:
United States
Language:
English

References (48)

Limit cycles and conformal invariance journal January 2013
Bootstrapping hypercubic and hypertetrahedral theories in three dimensions journal May 2018
Seeking fixed points in multiple coupling scalar theories in the ε expansion journal May 2018
Scale without conformal invariance at three loops journal August 2012
Scalar CFTs and their large N limits journal September 2018
Walking, weak first-order transitions, and complex CFTs journal October 2018
Generalized F-theorem and the ϵ expansion journal December 2015
On Cones of Nonnegative Quartic Forms journal November 2015
Gradient properties of the renormalisation group equations in multicomponent systems journal July 1975
Gradient flow and the renormalisation group journal July 1974
Critical behavior of the mn-component field model in three dimensions journal November 1988
Critical behavior of the mn-component field model in three dimensions II. Three-loop results journal December 1989
Analogs of the c-theorem for four-dimensional renormalisable field theories journal October 1990
Critical phenomena and renormalization-group theory journal October 2002
Large-n critical behavior of O(n)×O(m) spin models journal July 2001
Critical behaviour of anisotropic cubic systems journal April 1973
Critical behaviour of anisotropic cubic systems journal December 1974
epsilon -expansion analysis of some physically realizable n⩾4 vector models journal November 1975
Stable fixed points in models with many coupling constants journal January 1982
Critical thermodynamics of three-dimensional MN -component field model with cubic anisotropy from higher-loop ε expansion journal May 2001
On the uniqueness of ϕ 4 interactions in two- and three-component spin systems journal July 1975
Critical behaviour of the continuous n-component Potts model journal September 1975
Fixed point stability and decay of correlations journal December 2006
Discussion of critical phenomena for general n -vector models journal August 1974
Bicritical and tetracritical points in anisotropic antiferromagnetic systems journal January 1976
Physical realizations of n ≥ 4 -component vector models. II. ε -expansion analysis of the critical behavior journal June 1976
Renormalization-group fixed points of general n -vector models journal March 1984
Renormalization-group study of the fixed points and of their stability for phase transitions with four-component order parameters journal June 1985
Selection of stable fixed points by the Toledano-Michel symmetry criterion: Six-component example journal December 1985
Classification of continuous phase transitions and stable phases. I. Six-dimensional order parameters journal February 1986
Renormalization-group classification of continuous structural phase transitions induced by six-component order parameters journal May 1986
Stability of the three-dimensional fixed point in a model with three coupling constants from the ε expansion: Three-loop results journal March 1998
Multicritical phenomena in O ( n 1 ) ⊕ O ( n 2 ) -symmetric theories journal February 2003
Critical Behavior of Magnets with Dipolar Interactions. I. Renormalization Group near Four Dimensions journal October 1973
Critical Behavior of Anisotropic Cubic Systems journal November 1973
Unitarity violation at the Wilson-Fisher fixed point in 4 − ε dimensions journal June 2016
Critical Exponents in 3.99 Dimensions journal January 1972
Renormalization-Group Analysis of Bicritical and Tetracritical Points journal September 1974
Symmetry Criterion for the Lack of a Stable Fixed Point in the Renormalization-Group Recursion Relations journal April 1985
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
On New Classes of Nonnegative Symmetric Tensors journal January 2017
Generalized Chiral Universality journal July 1990
Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ journal January 2018
On Subvariants, i.e. Semi-Invariants to Binary Quantics of an Unlimited Order journal January 1882
Scalar CFTs and Their Large N Limits text January 2017
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018
Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ text January 2018
Large-n Critical Behavior of O(n)xO(m) Spin Models text January 2001

Cited By (1)

Bootstrapping MN and tetragonal CFTs in three dimensions journal January 2019

Similar Records

Counting RG flows
Journal Article · 2016 · Journal of High Energy Physics (Online) · OSTI ID:1327329
Bootstrapping 3D fermions
Journal Article · 2016 · Journal of High Energy Physics (Online) · OSTI ID:1326984
+3 more
A conformal truncation framework for infinite-volume dynamics
Journal Article · 2016 · Journal of High Energy Physics (Online) · OSTI ID:1358561

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
atomic physics
nuclear physics
particle physics