An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term

Abstract

A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriously difficult systematic effects of the gauge theory in the toy model is to establish non-perturbatively that the theta parameter is actually a relevant coupling. This is done by showing that there exist quantities that are entirely given by the total topological charge and are well defined in the continuum limit and are non-zero, despite the fact that the topological susceptibility is divergent. More precisely it is established that the differences of connected correlation functions of the topological charge (the cumulants) are finite and non-zero and consequently there is only a single divergent parameter in Z(theta) but otherwise it is finite. This divergent constant can be removed by an appropriate counter term rendering the theory completely finite even at theta > 0.

9 pages, 2 figures, minor modification, references added

References in corpus (5)

• Nearly conformal gauge theories in finite volume
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Topological Lattice Actions
• Logarithmic corrections to O(a^2) lattice artifacts
• Non-trivial θ-Vacuum Effects in the 2-d O(3) Model

Cited by in corpus (19)

• Lattice tests of beyond Standard Model dynamics
• 125 GeV Higgs from a not so light Technicolor Scalar
• On the glueball spectrum of walking backgrounds from wrapped-D5 gravity duals
• Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case
• Light scalar from deformations of the Klebanov-Strassler background
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• S and T Parameters from a Light Nonstandard Higgs versus Near Conformal Dynamics
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• On the stability of multi-scale models of dynamical symmetry breaking from holography
• From asymptotic freedom to $\theta$ vacua: Qubit embeddings of the O(3) nonlinear $\sigma$ model
• Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations
• Hyperscaling violation and Electroweak Symmetry Breaking
• Topological Lattice Actions for the 2d XY Model
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models
• Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential
• Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results
• Walking in the 3-dimensional large $N$ scalar model
• Topology of the O(3) non-linear sigma model under the gradient flow