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.
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.
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.
10342426
Physically meaningful and not so meaningful symmetries in Chern-Simons theory.
We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action that is both Becchi-Rouet-Stora (BRS) invariant and Landau supersymmetric and an effective action that is only BRS invariant is a finite field redefinition. Having established this, we use a BRS-invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift [ital k][r arrow][ital k]+[ital c][sub [ital V]] of the bare Chern-Simons parameter [ital k] in connection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS-invariant regulators used as yet yield the same value for the shift.
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.
120311682
The three-gluon vertex in the temporal-planar gauge with the Leibbrandt-Vienna prescription: The one-loop effective action
Abstract The UV-divergent part of the one-loop contribution to the three-gluon vertex, Γμνϱabc, is computed in the temporal-planar gauge. The generalized Leibbrandt-Mandelstam (or Leibbrandt-Vienna) prescription - which is free from the inconsistencies that are known to affect the principal value prescription - is used to define the unphysical poles 1/(k·n)j. We compute the (one-loop) UV-divergent part of the gauge-field effective action up to order g3. We show that all the awkward non-local divergences can be written as the BRS variation of some functional X whereas the β-function coincides with the usual (covariant) result. In the homogeneous case we show that a non-local renormalization of the gauge field Aμa of the form A 0μ a = Z g − 1 2 A μ a − h ƒ μ a (A), A 0μ a and A μ a having identical gauge transformations, and the usual coupling constant renormalization, g0 = Zgμ2ϵg, suffice to get rid of all the UV-divergences in Γμνϱabc and the vacuum polarization tensor gPμνab.
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.
17246313
Variational Approximations for Correlation Functions in Quantum Field Theories
Abstract Applying the time-dependent variational principle of Balian and Veneroni, we derive variational approximations for multi-time correlation functions in Φ 4 field theory. We assume first that the initial state is given and characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.
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.
53310889
Conformal and non conformal dilaton gravity
A bstractThe quantum dynamics of the gravitational field non-minimally coupled to an (also dynamical) scalar field is studied in the broken phase. For a particular value of the coupling the system is classically conformal, and can actually be understood as the group averaging of Einstein-Hilbert’s action under conformal transformations. Conformal invariance implies a simple Ward identity asserting that the trace of the equation of motion for the graviton is the equation of motion of the scalar field. We perform an explicit one-loop computation to show that the DeWitt effective action is not UV divergent on shell and to find that the Weyl symmetry Ward identity is preserved on shell at that level. We also discuss the fate of this Ward identity at the two-loop level — under the assumption that the two-loop UV divergent part of the effective action can be retrieved from the Goroff-Sagnotti counterterm — and show that its preservation in the renormalized theory requires the introduction of counterterms which exhibit a logarithmic dependence on the dilaton field.
1680296
Noncommutative N = 1 super Yang-Mills, the Seiberg-Witten map and UV divergences
Classically, the dual under the Seiberg-Witten map of noncommutative U(N), = 1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a ?-deformed nonlinear realisation of the = 1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix ??? the UV divergent part of its effective action in the background-field gauge, and, for N?1, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain ?for N ? 3, the case with N = 2 being trivial? the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.