Related papers: $\phi^4$ Field theory on a Lie group

We find the leading RG logs in $\phi^4$ theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG…

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…

Irreversibility theorems -- such as the $A$-theorem -- establish a hierarchy among fixed points of the renormalization group flow. The strongest thesis of this type of theorems would be that there exists a scalar function $A$ (generally…

We introduce a new class of higgs type complex-valued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree…

In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present…

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their…

We prove that semisimple 4-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth 4-manifolds and homotopy equivalent simply connected…

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant…

When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…

We compute the phase and the modulus of an energy- and pressure-free, composite, adjoint, and inert field $\phi$ in an SU(2) Yang-Mills theory at large temperatures. This field is physically relevant in describing part of the ground-state…

We continue studies on quantum field theories on noncommutative geometric spaces, focusing on classes of noncommutative geometries which imply ultraviolet and infrared modifications in the form of nonzero minimal uncertainties in positions…

Three related analyses of $\phi^4$ theory with $O(N)$ symmetry are presented. In the first, we review the $O(N)$ model over the $p$-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking…

Let $M$ be a smooth finite-dimensional manifold, $G$ be a Lie group, and $\Phi:G \times M \to M$ be a smooth action. Consider the following mapping $\phi: C^{\infty}(M,G) \to C^{\infty}(M,M)$, defined by $\phi(\alpha)(x) = \alpha(x)\cdot…

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies…

The non-conserved $\phi^4$ model defined by a Langevin equation with external non-white noise is studied by means of the Dynamic Renormalization Group. The correlation time of the noise changes the critical point location but does not…

A generalization of non-Abelian gauge theories of compact Lie groups is developed by gauging the non-compact group of volume-preserving diffeomorphisms of a $D$-dimensional space R^D. This group is represented on the space of fields defined…

We classify, up to automorphism, left invariant Riemannian metrics on 4-dimensional simply connected nonunimodular Lie groups. This is equivalent to classifying, up to automorphism, inner products on 4-dimensional nonunimodular Lie…

We show that the simplest non commutative renormalizable field theory, the $\phi^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theory

It is shown that there exists a soluble four parameter model in (1+1) dimensions all of whose propagators can be determined in terms of the corresponding known propagators of the vector coupling theory. Unlike the latter case, however, the…

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…