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     

A superspace formulation of the BV action for higher derivative theories

We first analyse the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under shift symmetry in the Batalin–Vilkovisky (BV) formalism. We show that the action for this theory can be written in a manifestly extended BRST invariant manner in superspace formalism using one Grassmann coordinate. It can also be written in a manifestly extended BRST invariant manner and on-shell manifestly extended anti-BRST invariant manner in superspace formalism using two Grassmann coordinates.     

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.     

On the renormalization of topological Yang-Mills field theory in N = 1 superspace

We discuss the renormalization aspects of topological super-Yang-Mills field theory in N = 1 superspace. Our approach makes use of the regularization-independent BRS algebraic technique adapted to the case of an N = 1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be a BRS coboundary, implying that the cohomological properties of the supertopological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik β-function of the model by employing a recently discovered supersymmetric antighost Ward identity.     

Higher derivative regulation of supersymmetric theories

The rigid N = 1 supersymmetric theories are regulated using higher derivatives, supplemented with one-loop Pauli-Villars regulator fields. This scheme preserves supersymmetry as well as background and quantum gauge invariances.     

Algebroid Yang-Mills theories

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead, they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.     

Yang-Mills string theories

It is shown that the addition of a “colored” Yang-Mills supermultiplet to the locally supersymmetric spinning string Lagrangian does not yield a viable new string model, even though supersymmetry is preserved. However, a Yang-Mills extension of the Veneziano string that yields the color singlet sector of the Bardakçi-Halpern model is constructed.     

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.     

Scale invariant d = 10 superspace and the heterotic string

The superspace formulation of the d = 10 Einstein-Yang-Mills system is presented. Our torsion constraints imply that the solution of the Bianchi identities will be expressed in terms of fields appearing naturally in the heterotic string. The scaling properties of superspace allow a formulation with all superfields dimensionless as well as one with superfields of canonical dimensions. The dimensionless formulation gives rise to a set of very simple supersymmetry transformation rules. This approach may facilitate the investigation of the effects of introducing string-induced higher derivative terms.     

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.     

Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories

We study the existence of monopole bound states saturating the BPS bound in N = 2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an L² index theorem, we prove the existence of certain BPS states predicted by Seiberg and Witten based on their study of the vacuum structure of N = 2 Yang-Mills theories.     

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).     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.