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The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…
We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local…
In this paper we investigate renormalisation group flows of supersymmetric minimal models generated by the boundary perturbing field (\hat G_{-1/2}\phi_{1,3}). Performing the Truncated Conformal Space Approach analysis the emerging pattern…
We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full…
We study the $q\bar{q}$ potential in strongly coupled non-conformal field theories with a non-trivial renormalization group flow via holography. We focus on the properties of this potential at an inter-quark separation $L$ large compared to…
Applying functional renormalization group methods, we describe two inequivalent ways of defining the renormalization group of matter-coupled four dimensional gravity, in the approximation where only the conformal factor is dynamical and…
This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities…
By reviewing the application of the renormalization group to different theoretical problems, we emphasize the role played by the general symmetry properties in identifying the relevant running variables describing the behavior of a given…
Evaluating quantum loop corrections to curvature perturbations in non-attractor inflation presents theoretical ambiguities. A crucial aspect of this challenge lies in the unconstrained finite contributions in renormalization counterterms…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and SU(2)) on (hyper) cubic lattices. We explain that contrarily to some common belief,…
Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at…
The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often…
We propose a general procedure for extracting the running coupling constants of the underlying field theory of a given classical statistical model on a two-dimensional lattice, combining tensor network renormalization (TNR) and the…
Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation…
We explain the recent numerical successes obtained by Tao Xiang's group, who developed and applied Tensor Renormalization Group methods for the Ising model on square and cubic lattices, by the fact that their new truncation method sharply…