The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method recently introduced which includes simultaneously all vertices although approximating their momentum dependence. The study is performed using the self-energy of the tridimensional scalar model at criticality. At least in this example, low order truncations miss quantities as the critical exponent $η$ by as much as 60%. However, if one goes to high order truncations the procedure seems to converge rapidly.
We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic fiel…
We investigate the non-perturbative renormalization group flow of the scalar Galileon model in flat space. We discuss different expansion schemes of the Galileon truncation, including a heat-kernel based derivative expansion, a vertex expansion in momentum space and a curvature expansion in terms of a covariant geometric formulation. We find that the Galileon symmetry prevents a quantum induced renormalization group running of the Galileon couplings. Consequently, the Galileon truncation only features a trivial Gaussian fixed point.
In this paper we explicitly carry out the perturbative renormalization of the $T\bar{T}$-deformed free massive Dirac fermion in two dimensions up to second order in the coupling constant. This is done by computing the two-to-two $S$-matrix using the LSZ reduction formula and canceling out the divergences by introducing counterterms. We demonstrate that the renormalized Lagrangian is unambiguously determined by demanding that it gives the correct $S$-matrix of a $T\bar{T}$-deformed integrable field theory. Remarkably, the renormalized Lagrangian is qualitatively very different from its classica…
We determine the non-perturbative corrections to the gauge coupling constant and the topological charge in the Yang Mills theory. The method makes no explicit use of instanton calculations but instead relies on boundary properties of the quantum partition function. The approach may offer important clues regarding the behavior of the coupling constant and the theta angle for other gauge theories like QCD and supersymmetric QCD.
The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the $π^{2}$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polar…
Weak solution method of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking and its application to beyond the ladder analysis in QCD
We report a rigorous quantization of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$ and $\mathbf{I}= [0, 1]$ in perturbative BV-BFV formalism. Costello's homotopic renormalization is extended, and incorporated in our construction. Moreover, BV quantization of the same model studied in our previous work is derived from the BV-BFV quantization, leading to a comparison between different interpretations of ''state'' in these two frameworks.
