Local products of fields deformed by the so-called Yang-Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy-momentum tensor in the lattice formulation of the pure Yang-Mills theory. In the present paper, this construction is further generalized for vector-like gauge theories containing fermions.
We give an alternative perturbative proof of the renormalizability of the
system defined by the gradient flow and the fermion flow in vector-like gauge
theories.Comment: 29 pages, the final version to appear in Nuclear Physics
We study four-dimensional conformal field theories with an SU (N ) global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin 0 operator φk i which belongs to the adjoint representation of SU (N ). For N = 12 for example, we found that the theory contains a spin 0 SU (12)-breaking relevant operator when the scaling dimension of φk i , ∆ φk i , is smaller than 1.71. Considering the lattice simulation of many-flavor quantum chromodynamics with 12 flavors on the basis of the staggered fermion, the above SU (12)breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above SU (12)breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point γ * m ≤ 1.29 from the relation γ * m = 3 − ∆ φk i . Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another SU (12)-breaking operator.
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter t, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then illustrate the Wilsonian RG flow on the basis of the gradient flow in two examples that possess an infrared fixed point, the 4D many-flavor gauge theory and the 3D O(N ) linear sigma model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.