Light-cone auxiliary fields for ten-dimensional super Yang-Mills

We consider ten-dimensional super Yang-Mills in the light-cone gauge and define a set of auxiliary fields which close the light-cone super algebra off-shell. As a necessary preliminary we give a systematic discussion of the auxiliary field problem for simple super Yang-Mills in dimensions 3, 4, 6 and 10 both covariantly and in the light-cone framework. The motivation for this work is that it may prove useful in conjunction with the ideas of harmonic superspace. With this in mind we indicate how the light-cone theory in ten dimensions can be formulated in light-cone superspace using unconstrained superfields.     

Off-shell extended supergravity and central charges

We discuss the problem of field redefinition for irreducible representations of N = 3 and 4 supersymmetry in order that they reduce on-shell to the corresponding supergravities. We find that such redefinition is impossible in the Fermi sector in these cases. We conclude that central charges are essential to achieve such reduction, and that in particular they must be spin-reducing.     

Off-shell N = 8 supersymmetry with central charges

Using a new technique of dimensional reduction by Legendre transformation we derive an off-shell formulation of the N = 8 extended supersymmetry algebra, which is realised in the maximally extended supergravity theory. The theory has an Sp(8) manifest global invariance and some of the fields satisfy differential constraints.     

Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories

It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F_αβ = 0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined.     

Non-linear representations of extended supersymmetry with central charges

A new class of non-linear representations ofN extended supersymmetry is found. These non-linear realizations extend the Volkov-Akulov non-linear realizations to include central charges which can also be non-linearly realized. The general construction of the corresponding non-linear Lagrangians is presented. The coupling toN extended supergravity provides the simultaneous occurrence of the Higgs and super-Higgs effects. The corresponding formulae for spin-3/2 gravitinos and spin-1 vector boson masses are derived.     

Constraints and field equations for ten dimensional super Yang-Mills theory

We give a complete proof of the equivalence between constraint equations and field equations for thed=10,N=1 supersymmetric Yang-Mills theory, a result proposed and partially proved recently by Witten [1]. Our approach explicitly reconstructs the superconnection satisfying the constraints from the on shell component fields. A key ingredient of the method is the choice of a suitable family of gauges, effectively eliminating all gauge dependence on anti-commuting co-ordinates. As a corollary, obtained by dimensional reduction, we also deduce the equivalence of constraints and field equations for thed=4,N=4 theory, as well as ford=6,N=2.Research supported in part by the National Science and Engineering Research Council of Canada and the Israel Ministry of ScienceOn leave of absence from: Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken NJ 07030, USA     

N=2 super Yang-Mills theory in projective superspace

We constructN=2 Yang-Mills theory in projective superspace by exploiting the analogy to Ward's twistor construction of self-dual Yang-Mills fields.Work supported in part by NSF grant No. PHY 85-07627     

Yang-Mills fields of nonstationary spherical objects with big charges

We study the nonlinear electrodynamics suggested in our paper in [Russ. J. Math. Phys. 12 (3), 379–385 (2005)] by using the Yang-Mills equations. This theory is intended to describe strong fields generated by objects with large electric charges. For nonstationary sources with spherical symmetry, we find formulas for the electric field strengths. This solution generalizes our previous result related to the stationary case. The corresponding formulas for nonlinear electric fields are used to explain some puzzling properties of the Earth atmosphere.     

Towards the large N limit of pure Nu = 1 super Yang-Mills theory

We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.     

Improved Hamiltonian for Minkowski Yang-Mills theory

I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with tree level corrections from lattice spacing a beginning at O(a⁴). I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. The Lyapunov exponent has a small a limit, and the Chern-Simons number response appears to be approaching one at the finest lattices considered. In both cases the limit is within 10% of the limit found using the unimproved (Kogut-Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ between Hamiltonians by about 5%, significant at about 5σ, indicating that while a small a limit exists, its value depends on the specifics of the lattice cutoff. For Chern-Simons number the difference between Hamiltonians is within statistical errors of about 10%, which constitutes an upper bound on the lattice regulation dependence.     

BRS symmetry for Yang-Mills theory with exact renormalization group

In the exact renormalization-group (RG) flow in the infrared cutoff Λ one needs boundary conditions. In a previous paper on SU(2) Yang-Mills theory we proposed to use the nine physical relevant couplings of the effective action as boundary conditions at the physical point Λ= 0 (these couplings are defined at some non-vanishing subtraction point μ≠ 0). In this paper we show perturbatively that it is possible to appropriately fix these couplings in such a way that the full set of Slavnov-Taylor (ST) identities are satisfied. Three couplings are given by the vector and ghost wave-function normalization and the three-vector coupling at the subtraction point; three of the remaining six are vanishing (e.g. the vector mass) and the others are expressed by irrelevant vertices evaluated at the subtraction point. We follow the method used by Becchi to prove ST identities in the RG framework. There the boundary conditions are given at a non-physical point Λ = Λ′ ≠ 0, so that one avoids the need of a non-vanishing subtraction point.     

Superspace gauge theories with central charges

The superspace constraints leading to off-shell formulations of extended supersymmetric Yang-Mills theories for N = 2 and 4 are generalised to N = 6 in the abelian case. This leads to an on-shell representation of linearized N = 6 supergravity.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

Chiral U(1) anomaly in D=4 super Yang-Mills theory coupled to supergravity

We evaluate the chiral U(1) anomaly in D=4 supersymmetric Yang-Mills theory coupled to supergravity. We consider not only the minimal coupling between the gauge fields and fermions but also the interaction term which mixes the gravitino and the gaugino. We show that the mixing interaction gives new contributions to the anomaly.     

Gauge invariant geometric variables for Yang-Mills theory

In a previous publication, local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero-modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.     

Broken N=2 super Yang-Mills theories with a finite vacuum energy

It is shown that an explicit symmetry breaking of the N=2 ultra-violet finite super Yang-Mills theories through the addition of soft mass terms does not affect the finiteness of the vacuum energy above one loop. One-loop vacuum energy is finite provided the mass terms satisfy the sum rules Σ_J(2J+1)(−1)^2Jm_J^2K = 0 (K = 0, 1, 2).