15154154
Chern-Simons theory as the large-mass limit of topologically massive Yang-Mills theory
We study quantum Chern-Simons theory as the large-mass limit of the limit D --> 3 of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift k --> k + c(v), k being the bare Chern-Simons parameter. In passing, we also prove by explicit computation that topologically massive Yang Mills theory is UV finite.
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.
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.
118725047
BRS techniques applied to the temporal-planar gauge with the vienna prescription: The dependence on the axial vectors
116367467
The Shift of the Chern-Simons parameter beyond one loop
121471524
UV-divergent part of the vacuum polarization tensor in the temporal gauge with the LM prescription. BRS identities
Abstract The one-loop UV-divergent contribution to the vacuum polarization tensor (Πμνab) is computed in a temporal-planar gauge using the LM prescription that gives the correct exponential behaviour for the Wilson loop. Its dependence on the gauge parameter and on the magnitude of the unphysical vectors n and n′ - introduced by the LM prescription - is derived from the BRS invariance of the theory and shown to be consistent with our result for Πabμν.
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.
18639875
Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections☆
Abstract We have investigated the standard one-loop quantum corrections for a particularly simple non-commutative geometry model containing fermions interacting with a unique abelian gauge field and a unique scalar through Yukawa couplings. In this model there are certain relations among the different coupling constants quite similar to the ones appearing in the Connes-Lott version of the standard model. We find that it is not possible to implement those relations in a renormalization-group invariant way.
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.
15588873
Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
We show at one loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories - chiral or otherwise - defined by means of Seiberg-Witten maps that are the same - barring the gauge group representation - for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the standard model.
119412558
THE POLE PART OF THE 1PI FOUR-POINT FUNCTION IN LIGHT-CONE GAUGE YANG-MILLS THEORY
Abstract The complete UV-divergent contribution to the one-loop 1PI four-point function of Yang-Mills theory in the light-cone gauge is computed in this paper. The formidable UV-divergent contributions arising from each four-point Feynman diagram yield a succinct final result which contains non-local terms as expected. These non-local contributions are consistent with gauge symmetry, and correspond to a non-local renormalization of the wave function. Renormalization of Yang-Mills theory in the light-cone gauge is thus shown explicitly at the one-loop level.