120066907
Critical exponents from stochastic continuum regularization
A new method for computing critical exponents based on renormalised Quantum Field Theory is presented. It arises from a new regularization procedure based on Stochastic Quantization. A version of this procedure, containing a dimensionless parameter ρ, allows an expansion analogous to the ε-expansion. Results to leading order are presented, showing at least the same accuracy as other methods to this order.
118419260
SO(10) GUTs with large tensor representations on Noncommutative Space-time
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
117863195
Chiral gauge anomalies on noncommutative space-time
The consistent form and the covariant form of the gauge anomaly for fundamental U(N) chiral fermions on even-dimensional noncommutative space-time are computed and discussed.
17379629
The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability
We discuss the renormalizability of the noncommutative U(1) Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in θμν, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.
122147161
The light-cone gauge, Chern-Simons theory and topologically massive Yang-Mills theory
Abstract In this paper, we complete our study of one-loop perturbative Chern-Simons theory in the light-cone gauge n · A a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, which defines Chern-Simons theory as the large-mass limit of a topologically massive field theory, we evaluate the three-point function Λ μνω abc ( p 1 , p 2 , p 3 ) to one loop. The spurious poles of ( q · n ) −1 in the gauge propagator are treated with the n μ ∗ - prescription . It is shown that the vertex function, which contains both local and nonlocal terms, is UV finite, respects the Ward identity and agrees with the one-loop effective action proposed in the preceding paper.
121374470
Fermionic langevin equations without kernel and Zwanzinger's gauge fixing procedure☆
Abstract We study the compatibility of Zwanzinger's gauge fixing procedure and the Langevin equations without kernel for massive fermions from the renormalization theory point of view. The UV divergent part of the QED fermionic propagator is computed at the one-loop level. The problems encountered in its subtraction are analyzed.
120724746
DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES
We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.
12423687
Regularization and Renormalization of Chern-Simons Theory
The topological field theory most familiar both to physicists and to mathematicians is surely Chern-Simons theory.
119536533
Axial gauge Chern-Simons theory in the Leibbrandt-Mandelstam prescription for a certain class of UV regulators
Abstract We show that the complete perturbative effective action of an SU ( N ) Chern-Simons theory in an homogenous axial-type gauge ( nA a =0, n 2 >0, n 2 n 2 =0) with the generalized Leibbrandt-Mandelstam prescription is the tree-level action for a certain class of regulators. The Gauss linking number is expressed in terms of the axial propagators for the gauge fields.
15512478
Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)
U(1) gauge theory on non-commutative Minkowski spacetime in the Feynman–'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism — producing UV charge anti-screening — prevailing over diamagnetism — giving rise to UV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.
16683941
Ground state properties and glueball spectrum in SU(2) Yang-Mills theory using gauge invariant variables
We describe a nonperturbative calculation of the spectrum of SU(2) Yang-Mills theory based on a Hamiltonian formulation. Our approach exploits gauge invariant variables similar to those used in nuclear physics to describe collective motion in nuclei.