Related papers: The Gauge Invariant ERG
The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the \beta functions of parameters with and without a mass dimension.
The gradient flow exact renormalization (GFERG) is a variant of the exact renormalization group of gauge theory that aims to preserve gauge symmetry as manifestly as possible. From an integral representation of the Wilson action in GFERG…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…
We establish that Polchinski's equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This provides a compelling information-theoretic formulation of the…
In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities.…
The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom. What all these methods have in common -- which is what explains their success -- is that…
We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky-De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to…
A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts.…
It has recently been determined that, within the framework of the Exact Renormalisation Group, continuum computations can be performed to any loop order in SU(N) Yang-Mills theory without fixing the gauge or specifying the details of the…
The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the…
It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function. We apply the method to a generic theory with a Gaussian fixed…
In this paper, inspired by the Costello's seminal work, we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and…
In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely…
We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG…
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
A gauge invariant regularisation which can be used for non-perturbative treatment of Yang-Mills theories within the exact renormalization group approach is constructed. It consists of a spontaneously broken SU(N|N) super-gauge extension of…
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG…