Exponentiation of leading infrared divergences in massless Yang-Mills theories

In the Coulomb gauge, the leading infrared divergences of massless theories occur in external line self-energy parts only. This fact, together with the gauge invariance of S-matrix elements, leads to a simple proof of exponentiation.     

Cancellation of infrared divergences in non-Abelian gauge theories

We investigate the infrared problem for non-Abelian gauge fields. Specifically, we show that the transition rate for fermion-fermion scattering suitably averaged over the colors of the fermions is infrared finite to lowest non-trivial order. The finite radiative correction due to soft bosons is given explicitly.     

Asymptotic states and infrared divergences in non-abelian theories

We give a general definition of a class of asymptotic states in non-abelian gauge theories. We argue, using unitarity, that they give infrared-finite S-matrix elements. We discuss the energy of the soft gluons in these states.     

Combining infrared and low-temperature asymptotes in Yang-Mills theories

We demonstrate that the powerlike nonperturbative behavior of gluon and ghost propagators in the infrared limit of Yang-Mills theories can provide at finite temperatures T a negative T4 contribution to the pressure and energy density. The existence of a mass gap then implies new relations between the infrared critical exponents of gluon and ghost propagators.     

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of S?o Paulo.     

On decoupling of massless modes in NCOS theories

We revisit the decoupling phenomenon of massless modes in non-commutative open string (NCOS) theories. We check the decoupling by explicit computation in (2+1) or higher dimensional NCOS theories and recapitulate the validity of the decoupling to all orders in perturbation theory. Received: 23 April 2002 / Published online: 25 October 2002 RID="a" ID="a" e-mail: hyun@phya.yonsei.ac.kr RID="b" ID="b" e-mail: sangmin@newton.skku.ac.kr RID="c" ID="c" e-mail: hshin@kias.re.kr     

Renormalization group and infrared behaviour in theories with coupled massless fields

The renormalization-group method is applied to investigate the infrared singularities in gauge theories with Abelian or non-Abelian symmetry, involving both massive and massless fermions. In the Abelian gauge model the infrared structures of massive and massless fermion propagators and of a massive fermion form factor are found. In the non-Abelian gauge model (quantum chromodynamics) the infrared behaviour of a massless gluon propagator and a massive quark form factor is considered in the logarithmic approximation.     

On the dynamical mass generation in confining Yang-Mills theories

The dynamical mass generation for gluons is discussed in Euclidean Yang-Mills theories supplemented with a renormalizable mass term. The mass parameter is not free, being determined in a self-consistent way through a gap equation which obeys the renormalization group. The example of the Landau gauge is worked out explicitly at one-loop order. The issues of the unitarity and of the gauge invariance are also addressed.     

On the functional integration measure of supersymmetric Yang-Mills theories

For the simplest N = 1 supersymmetric Yang-Mills theory, we construct a bosonic field transformation which linearizes the Yang-Mills action in each topological sector and whose jacobian equals the product of Fadeev-Popov and Matthews-Salam determinants up to cubic order at least. Some possible implications of this result for the maximally extended N = 4 theory are discussed.     

Reggeization in Yang-Mills theories

We calculate the high energy fermion-fermion scattering amplitude in Yang-Mills field theory through sixth order in the coupling constant, and find that the amplitude Reggeizes. Our result is simpler than and qualitatively different from an earlier published calculation.     

Stability in Yang-Mills theories

At a solution of the Yang-Mills equations onS ⁴, or the Yang-Mills-Higgs equation on ?³, the hessian of the action functional defines a natural second order, elliptic operator. The number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge. The proof of this assertion requires a relative index theorem for Dirac-type operators on ? ⁿ ,n≧3.     

Quadratic divergences in gauge theories

Quadratic divergences are analysed using dimensional regularisation in gauge theories in general and the standard model in particular. We give a prediction (under dubious assumptions) thatm _t ≈115 GeV andm _H ≈180 GeV.     

Separation of non-renormalizable divergences of the massive Yang-Mills Lagrangian

The non-renormalizable divergences of the massive Yang-Mills Lagrangian are separated explicitly as determinant factors. The implications of this for the renormalizability of the theory are discussed.     

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.     

Diffraction scattering in Yang-Mills theories

The infrared problem in Yang-Mills theories is studied in order to elucidate aspects of high energy behavior. The integro-differential equation of Cornwall and Tiktopoulos is used to investigate quark-quark scattering in the limit λ → 0 (λ being the gluon regulator mass), s → ∞ with t fixed. The solution displays the infrared factors explicitly. When this formula is expanded in power series and the leading log is extracted one recovers the perturbation theory calculations to sixth order.     

Nontrivial quadratic gauge-fixing in Yang-Mills theories

We study renormalizability of a quadratic gauge-fixing choice involving gauge fields. We show that this can be renormalized simultaneously maintaining the BRS invariance since this respects the underlying global SU(n) invariance. However, this choice, too, induces quartic ghost terms in conformity with our earlier results. Physics Publication No. 81-099     

Self duality in super Yang-Mills theories

The self dual condition in superspace is analysed forN=1,2,4 super Yang-Mills theories. A complete solution of all the constraints in terms of a light cone superfieldJ is presented, where the only equation thatJ satisfies is a SUSY generalization of the Yang equation. By reduction of that equation we obtain various two dimensional SUSY models. We introduce the associated linear problem in terms ofJ, whose integrability condition gives us back the super Yang equation and allows us to obtain the Kac-Moody algebra structure of the theory.     

The pressure in lattice Yang-Mills theories

A simple proof is given that the infinite volume limit for the pressure of a lattice Yang-Mills theory exists and is a continuous function of .