Yang-Mills Theory In Terms Research Articles

Poisson brackets of normal-ordered Wilson loops

We formulate Yang–Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of ℏ) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum operators, we find, using ideas closely related to topological graph theory, that these two Poisson algebras are, roughly speaking, the same. More precisely speaking, there exists an invertible Poisson morphism between them.

Partially Dual Variables in SU(2) Yang-Mills Theory

We propose a reformulation of SU(2) Yang-Mills theory in terms of new variables, appropriate for describing the theory in its infrared limit. These variables suggest a dual picture of the Yang-Mills theory where the short distance limit describes asymptotically free, massless point gluons and the large distance limit describes extended, massive knotlike solitons.

WILSON LOOPS IN 2D YANG-MILLS: EULER CHARACTERS AND LOOP EQUATIONS

We give a simple diagrammatic algorithm for writing the chiral large N expansion of intersecting Wilson loops in 2D SU(N) and U(N) Yang-Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of branched covering maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral YM 2 partition functions. We briefly discuss finite N, the nonchiral expansion, and higher-dimensional lattice models.

The one-loop effective super-potential and non-holomorphicity

We calculate the Kählerian and the lowest order non-Kählerian contributions to the one-loop effective superpotential using super-Feynman graphs in the massless Wess-Zumino model, the massive Wess-Zumino model and N = 1, U(I) gauge theory. We also calculate the Kählerian term in Yang-Mills theory for a general gauge group. Using this latter result we find the one-loop Kählerian contribution for N = 2 Yang-Mills theory in terms of N = 1 superfields and we show that it can only come from non-holomorphic contributions to the N = 2 effective potential.

POISSON ALGEBRA OF WILSON LOOPS IN FOUR-DIMENSIONAL YANG-MILLS THEORY

We formulate the canonical structure of Yang-Mills theory in terms of Poisson brackets of gauge-invariant observables analogous to Wilson loops. This algebra is nontrivial and tractable in a light cone formulation. For U (N) gauge theories the result is a Lie algebra while for SU (N) gauge theories it is a quadratic algebra. We also study the identities satisfied by the gauge-invariant observables. We suggest that the phase space of a Yang-Mills theory is a coadjoint orbit of our Poisson algebra; some partial results in this direction are obtained.

FOUR-DIMENSIONAL YANG-MILLS THEORY IN LOCAL GAUGE INVARIANT VARIABLES

The general method that allows to formulate 4-D SU(N) Yang-Mills theory in terms of only local gauge invariant variables is presented. For the case N=2, that is discussed in details, this gauge invariant formulation appears to be very similar to R2-gravity.

BRS and anti-BRS symmetry in topological Yang-Mills theory

We incorporate both BRS symmetry and anti-BRS symmetry into the quantisation of topological Yang-Mills theory. This refines previous treatments which consider only the BRS symmetry. Our formalism brings out very clearly the geometrical meaning of topological Yang-Mills theory in terms of connections and curvatures in an enlarged superspace; and its simple relationship to the geometry of ordinary Yang-Mills theory. We also discover a certain SU(3) triality between physical space-time, and the two ghost directions of superspace. Finally, we demonstrate how to recover the usual gauge-fixed topological Yang-Mills action from our formalism.

Three dimensional Yang-Mills theory in gauge invariant variables

A formulation of three dimensional SU (2) and SO (1,2) Yang-Mills theories in terms of the gauge invariant tensor G ij= − 1 2 tr ∗F i ∗F j is presented. The resulting equations are three dimensional Einstein equations with a simple right-hand side, where G ij plays the role of the metric.

N = 4 Yang-Mills theory in terms of N = 3 and N = 2 light-cone superfields

The N = 4 Yang-Mills theory is truncated to an N = 3 Yang-Mills theory and to an N = 2 Yang-Mills theory coupled to an N = 2 Wess-Zumino field. The whole procedure is performed in the light-cone gauge. It is then shown that these theories are unique even if we only insist on N = 3 or N = 2 supersymmetry respectively. Finally we show in detail how the introduction of the fermionic Wess-Zumino field renders the one-loop self-energy finite.

Ten-dimensional supersymmetric Yang-Mills theory in terms of four-dimensional superfields

We show that the usual formulation of the N = 4 supersymmetric Yang-Mills theory in terms of N = 1 superfields can be generalized to describe the full ten-dimensional theory.

The gauge field as chiral field on the path and its integrability

It is shown that the gauge theory is equivalent to the chiral theory on the path. As a consequence the results obtained for chiral theory inD-space-time dimension may be carried over for gauge fields inD+1 dimensions. In particular, this leads to the integrability of the classical 3-dimensional Yang-Mills theory in terms of the path variables.

Failure of Bartel's scheme of applying Reggeon field theory to a spontaneously broken Yang-Mills theory

The recently proposed scheme of Bartels of studying the high-energy behavior of Yang-Mills theory in terms of Reggeon field theory fails, becausem in twelfth order or higher, not all transverse diagrams contribute to the leading power of ln s.

Spontaneously Broken Gauge Symmetries. II. Perturbation Theory and Renormalization

The second paper in this series is devoted to the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories). In Sec. II, we reformulate the renormalization prescription for massless Yang-Mills theories in terms of gauge-invariant renormalization counterterms in the action. Section III gives a group-theoretic discussion of Higgs phenomena. We discuss the possibility that an asymmetric vacuum is stable, and show how the symmetry of the physical vacuum determines the mass spectrum of the gauge bosons. We show further that in a special gauge ($U$ gauge), all unphysical fields can be eliminated. Section IV discusses the quantization of a spontaneously broken gauge theory in the $R$ gauge, where, as we show in Sec. V, Green's functions are made finite by the renormalization counterterms of the symmetric theory (in which the gauge invariance is not spontaneously broken). The $R$-gauge formulation makes use of redundant fields for the sake of renormalizability. Section VI is a discussion of the low-energy limits of propagators in the $R$-gauge formulation. In Sec. VII we show that the particles associated with redundant fields peculiar to the $R$-gauge formulation are unphysical, i.e., they do not contribute to the sum over intermediate states.