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The continuous multi-scale entanglement renormalization ansatz (cMERA) is a variational class of states for quantum fields. As originally formulated, the cMERA applies to infinite systems only. In this paper we generalize the cMERA…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric…
In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
Several recent works suggested the possibility of describing inflation by means of a renormalization group equation. In this paper we discuss the application of these methods to models of quintessence. In this framework a period of…
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…
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the Lyapunov-Schmidt reduction for…
The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a field theoretic renormalization group. The environment motion is modelled by the stochastic Navier--Stokes equation, which includes…
Vector fields in the expanding Universe are considered within the multidimensional theory of General Relativity. Vector fields in general relativity form a three-parametric variety. Our consideration includes the fields with a nonzero…
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
The paper studies the complex 1-dimensional polynomial vector fields with real coefficients under topological orbital equivalence preserving the separatrices of the pole at infinity. The number of generic strata is determined, and a…
We describe a functional renormalization group-based method to search for `$C$-like' functions with properties similar to that in 2D conformal field theory. It exploits the mode counting properties of the effective average action and is…
We prove a discrete time analogue of 1967 Moser's normal form of real analytic perturbations of vector fields possessing an invariant, reducible, Diophantine torus; in the case of diffeomorphisms too, the persistence of such an invariant…
We holographically investigate the renormalization group flow in a two-dimensional conformal field theory deformed by a relevant operator. If the relevant operator allows another fixed point, the UV conformal field theory smoothly flows to…