Abstract
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can be seen as nonperturbative extensions of the $\overline{\text{MS}}\,$ scheme. We support this claim by recovering all the multicritical models in two dimensions. We discuss a possible generalization to any dimension. Finally, we show that the method also preserves nonlinearly realized symmetries, which is a definite advantage with respect to other regulators.
Highlights
Dimensional regularization, together with modified minimal subtraction (MS),1 is the most widely used regularization and renormalization method in particle physics
The regulator depends on a scale parameter k with dimension of mass, and the derivative with respect to k gives the contribution to the effective action of an infinitesimal momentum shell
The main question that we shall address is the following: is there a choice of regulator that reproduces the beta functions of the MS scheme in the standard perturbative domain? We provide here a positive answer to this question: we show that by bending the standard rules and procedures of the functional renormalization group (FRG) it is possible to reproduce the results of dimreg=MS, at least up to two loops
Summary
Dimensional regularization (dimreg), together with modified minimal subtraction (MS), is the most widely used regularization and renormalization method in particle physics. It owes its popularity mainly to its simplicity and to the fact that it respects gauge invariance, one of the cornerstones of particle physics models. It is remarkably selective: in the language of momentum cutoffs, it extracts only the logarithmic divergences, which for most applications turn out to contain the important information (in particular, the beta functions of the marginal couplings). The functional renormalization group (FRG) equation (FRGE) is a convenient way of implementing Wilson’s idea of integrating out modes one momentum shell at the time. The regulator depends on a scale parameter k with dimension of mass, and the derivative with respect to k gives the contribution to the effective action of an infinitesimal momentum shell. We briefly recall their definition, and discuss the relation among them, and to standard perturbation theory
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