Bound states in N = 8 supergravity and N = 4 supersymmetric Yang-Mills theories

We present a study of possible bound states in N = 8 supergravity. We find evidence for the existence of multiplets of two-body bound states and expect that many-body bound states may exist as well. Our study is based on a calculation of Regge trajectories in the two-body scattering amplitudes of the lagrangian field theory. We also study Regge trajectories in N = 4 Yang-Mills theory and find evidence for a possible spin zero, SU(4) and gauge singlet, massless bound state. If such a state actually exists and supersymmetry is not broken, it may be a member of a supersymmetric multiplet which includes the graviton.     

The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories

We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.     

Low energy constraints on N = 2 supersymmetric models

We derive constraints on the masses of mirror particles in N = 2 supersymmetric theories. We consider the K_L?K_S mass difference, the π → ev/π → μv branching ratio and the anomalous magnetic moment of the muon. The K_L?K_S mass difference gives a lower bound of 15 TeV on the mirror gauge scalar and mirror gauge fermion masses, under suitable assumptions.     

Renormalization of N = 1 supersymmetric Yang-Mills theories: (II). The radiative corrections

We give a general proof of ultraviolet renormalizability relying on the methods of BRS and find that no anomaly can occur if the gauge group is assumed to be semisimple. We derive the Callan-Symanzik equation.     

From N = 1 to N = 4 extended supersymmetric Yang-Mills fields in a covariant Wess-Zumino gauge

It is assumed that N = 1 supersymmetric Yang-Mills fields coupled to chiral matter fields can be renormalized in a covariant Wess-Zumino gauge with a minimal number of subtractions so that the Ward identities of supersymmetry, ordinary gauge invariance and matter-field-flavour symmetries are satisfied. The chiral Yukawa couplings are supposed to remain unrenormalized. I show that on the basis of these assumptions an N = 4 extended manifestly O(4) invariant theory can be constructed with finite Yukawa and φ⁴ couplings. A consequence of these non-renormalizations is the vanishing of the renormalization group β function.     

N = 1 superspace formulation of N = 2 and N = 4 super-Yang-Mills models with central charge

The component models of N = 2 and N = 4 supersymmetric Yang-Mills theories of Sohnius, Stelle and West are reformulated in terms of N = 1 superfields. The non-supersymmetric constraints are supersymmetrized generalizing the linear multiplet in the presence of the non-abelian gauge superfield and (in the N = 4 case) a doublet of chiral superfields. The extended supersymmetry transformations preserving constraints are explicitly given in terms of N = 1 superfields. We are able to introduce the constraints back into the lagrangian using superfield Lagrange multipliers. The on-shell equivalence of this formulation with the formulation of Fayet with one (for N = 2) and three (for N = 4) chiral superfields is shown. The abelian N = 2 model is worked out to show the connection between full superspace treatment and the N = 1 superfield formulation.     

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.     

Instanton effects in N = 2 supersymmetric quantum mechanics

Supersymmetric quantum mechanics with several bosonic and fermionic dynamic variables is considered. Two different N = 2 supersymmetric models involving instantons are discussed in detail. Instantons fail to break supersymmetry in one of the models considered. The vacuum state is degenerate in this model which generally results in spontaneous breaking of internal left-right symmetry. In another model supersymmetry is destroyed dynamically due to special complex instanton solutions. Possible implications for SUSY field theories are discussed.     

Conformal invariance in N = 4 supersymmetric Yang-Mills theory

It is shown, by consideration of anomaly multiplets, that the maximally extended supersymmetric Yang-Mills theory is conformally invariant, assuming that the theory is supersymmetric and O(4)-invariant and that the structure of anomalies is given by the breakdown of conformal invariance in its coupling to supergravity.     

The supercurrent in N = 1 supersymmetric Yang-Mills theories: (I). The classical case

We construct, in the tree approximation, the complete off-shell supercurrent, including Faddeev-Popov fields and gauge contributions for a general supersymmetric Yang-Mills theory maintaining parity. Due to the conformally non-covariant character of the Faddeev-Popov procedure this supercurrent cannot be improved. The other currents of the superconformal group can therefore no longer be obtained by simply forming moments.     

The massless supersymmetric ladder with L rungs

We show that in the massless N=1$N=1$ supersymmetric Wess–Zumino theory it is possible to devise a computational strategy by which the x-space calculation of the ladder 4-point correlators can be carried out without introducing any regularization. As an application we derive a representation valid at all loop orders in terms of conformal invariant integrals. We obtain an explicit expression of the 3-loop ladder diagram for collinear external points.     

Renormalization of N = 1 supersymmetric Yang-Mills theories: (I). The classical theory

We investigate the classical N = 1 supersymmetric Yang-Mills theories and pay special attention to the search for the most general action fulfilling the Slavnov identity used to define the theory. It turns out that the well-known action of Ferrara, Zumino and Salam, Strathdee represents a special case, our general solution being equivalent to it through a redefinition of the gauge-fixing condition.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

The N = 2 supersymmetric generalization of the complex sine-gordon model

A two-dimensional field theoretical model endowed with a Lax pair and invariant under complex supersymmetry is written in a manifestly invariant formulation. The bosonic limit of the model reproduces the complex sine-Gordon equations [that is the reduced O(4) σ-model introduced by Pohlmeyer, Lund-Regge and Getmanov]. The supersymmetry algebra contains central charges which generalize the one found by Witten and Olive in the super sine-Gordon case.     

N = 2 supergravity action in terms of N = 1 superfields

We construct the full N = 2 supergravity action in terms of N = 1 supergravity and matter fields.     

The gauge-invariant N=2 supersymmetric σ-model with general scalar potential

We construct the supersymmetric σ-model, in six dimensions, for an arbitrary hyper-Kähler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N = 2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

The phase structure of SU(N)/Z(N) lattice gauge theories

The phase structure of pure SU(N)/Z(N) lattice gauge theories in four dimensions is discussed. The presence of ZN monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO(3) shows the presence of a very strong, may be first order, phase transition.     

The vanishing volume of N = 1 superspace

We show that the supergeometry of the new minimal formulation of N = 1 supergravity is a limiting case of the non-minimal supergeometry for which the volume of superspace vanishes. The action for supergravity in this case is then no longer the superdeterminant of the vielbein but is analogous to a special form of the Fayet-Iliopoulos term allowed only for the new minimal supergeometry. We discuss the restrictions on matter couplings imposed by the new and non-minimal supergeometries.