120228894
Perturbative Chern-Simons theory in the light cone gauge: The One loop vacuum polarization tensor in a gauge invariant formalism
Abstract Perturbative Chern-Simons (CS) theory, with gauge group SU( N ), is studied in the physical light-cone gauge n σ A σ a = 0, n 2 = 0. Using a gauge-invariant regularization procedure, we compute the vacuum polarization tensor to one-loop order. The regularized theory is consistent with BRS invariance. It is shown that the vacuum polarization tensor is UV finite and transverse, but contains one non-local term which is strictly gauge-dependent. A finite, non-multiplicative (gauge-dependent) wave function renormalization enables us to express the one-loop effective action as Γ one-loop ( A μ (ren) , k ) = (( k + sign( k ) c v )/4 π ) S CS ( A μ (ren) , where S CS is the classical action and k is the bare Chern-Simons parameter.
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.
122604338
Nonlocalities in field theory
It has been known since the early 1980's that the computation of light-cone gauge Feynman integrals in the nμ∗ prescription yields both local and nonlocal ultraviolet divergences. Nevertheless, it was recently claimed that the nonlocal contributions to the Yang-Mills vacuum polarization tensor arise from application of the decomposition formula [q·n(q+p)·n]−1=(p·n)−1{−[(q+p)·n]−1+(q·n)−1}, p·n≠0. The purpose of this paper is to show that nonlocal ultraviolet divergences automatically appear in light-cone gauge Feynman integrals defined by the nμ∗ prescription, regardless whether the above decomposition formula is employed or not.
116367467
The Shift of the Chern-Simons parameter beyond one loop
118725047
BRS techniques applied to the temporal-planar gauge with the vienna prescription: The dependence on the axial vectors
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.
11076298
The BRS invariance of noncommutative U(N) Yang–Mills theory at the one-loop level
Abstract We show that U(N) Yang–Mills theory on noncommutative Minkowski spacetime can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov–Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order ℏ , for the MS renormalized noncommutative U(N) Yang–Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.
18871973
Noncommutative SU(N) theories, the axial anomaly, Fujikawa's method and the Atiyah-Singer index
Abstract Fujikawa's method is employed to compute at first order in the noncommutative parameter the U ( 1 ) A anomaly for noncommutative SU ( N ) . We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ μ ν , which is of “magnetic” type. Our results for SU ( N ) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.
15556638
The Standard Model as a noncommutative geometry: the low-energy regime
Abstract We render a thorough, physicist's account of the formulation of the Standard Model (SM) of particle physics within the framework of noncommutative differential geometry (NCG). We work in Minkowski spacetime rather than in Euclidean space. We lay the stress on the physical ideas both underlying and coming out of the noncommutative derivation of the SM, while we provide the necessary mathematical tools. Postdiction of most of the main characteristics of the SM is shown within the NCG framework. This framework, plus standard renormalization technique at the one-loop level, suggest that the Higgs and top masses should verify 1.3 m top ≲ m H ≲ 1.73 m top .
118345116
Computing the $\theta$-exact Seiberg-Witten map for arbitrary gauge groups
We discuss how to obtain \theta-exact Seiberg-Witten maps by expanding in the gauge coupling constant or, equivalently, in the number of ordinary gauge fields. We do so for arbitrary compact gauge groups in arbitrary unitary representations. For gauge and matter fields, we fully work out \theta-exact non-hybrid Seiberg-Witten maps up to order three in the number of ordinary gauge fields.
13961384
The one loop UV divergent structure of U(1) Yang-Mills theory on noncommutative R**4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized at the one-loop level by multiplicative dimensional renormalization of the coupling constant and fields of the theory. We compute the beta function of the theory and conclude that the theory is asymptotically free. We also show that the Weyl-Moyal matrix defining the deformed product over the space of functions on R^4 is not renormalized at the one-loop level.