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.     

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.     

N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

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.     

Operators with Large R-Charge in N=4 Yang-Mills Theory

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong-weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well-defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two-loop level that the anomalous dimension has a finite limit when the R-charge J→∞ keeps λ/J² finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.     

On the low-energy effective action of N = 2 supersymmetric Yang-Mills theory

We investigate the perturbative part of Seiberg's low-energy effective action of N = 2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on U(1)_R anomaly and non-perturbative β-function arguments.     

Noncompact N=2 supergravity

A massive spin-one multiplet with central charge is coupled to N=2 supergravity. Compared to conventional gauge fields the anomalous magnetic moment of the spin-one particles is of the opposite sign. The construction of this theory is based on an N=2 supersymmetric gauge theory associated with the noncompact group SO(2,1). As a byproduct we present a convenient expression for the N=2 Einstein-Yang-Mills lagrangian.     

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.     

N=3 supersymmetry multiplets with vanishing trace anomaly: Building blocks of the N>3 supergravities

N?3 supergravity theories with vanishing one-loop trace anomaly may be constructed fron three basic N=3 multiplets, one of which contains an antisymmetric tensor gauge field. As an example we construct the N=4 theory and discuss its relationship to ten-dimensional supergravity.     

The complete N =2, d = 10 supergravity

The alternative N = 2, d = 10 supergravity, which is not derivable by dimensional reduction from the N = 1, d = 11 theory, is constructed at the full non-linear level. The transformation laws of the component fields and the equations of motion are derived and shown to be consistent. The derivation makes use of superspace techniques and exploits the fact that the scalars belong to the coset space SU(1,1)/U(1).     

Supersymmetric gauge anomalies in 2 and 4 dimensions from generalized descent-equations

Via a supersymmetric generalization of the descent-equations we derive in Wess-Zumino gauge explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theory for space-time dimensions 2 and 4.     

The relaxed hypermultiplet: An unconstrained N = 2 superfield theory

We present an off-shell version of the hypermultiplet, without a central charge or gauge antisymmetric tensors. We give the unconstrained superfield form of the action and its coupling to N = 2 super-Yang-Mills theory. This allows an N = 2 superspace formulation of the N = 4 super-Yang-Mills theory, whose ultraviolet finiteness is then ensured by N = 2 non-renormalization theorems.     

N = 2, D = 10 non-chiral supergravity and its spontaneous compactification

The non-chiral N = 2, D = 10 supergravity theory is constructed using dimensional reduction from N = 1, D = 11 supergravity. It is shown that this theory may spontaneously compactify, yielding S⁴ × S², CP² × S² and S² × S² × S² spaces for the extra dimensions.     

N = 4 supergravity coupled to N = 4 matter and hidden symmetries

We present the N = 1 supergravity in 10 dimensions obtained by truncating the reduced N = 1 supergravity from 11 dimensions. This is further reduced to 4 dimensions to give SU(4) supergravity coupled to six SO(4) vector multiplets. As the reduction is from 10 dimensions, the theory is expected to have the symmetry SL(6R)_global×SO(6)_local, but we give a theoretical argument that this can be extended to SO(6,6)×SU(1,1)_global and SO(6)×SO(6)×U(1)_local.     

N = 8 supergravity

The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E₇ invariance, but leave the local SU(8) unaffected. Exploiting E₇ × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.     

Black holes in N=8 supergravity

Solutions of the bosonic field equations of the ungauged, N=8 supergravity which describe black holes with no scalar hairs are obtained. It is found that, in contrast to the Einstein-Maxwell theory where a uniqueness theorem exists, there are two distinct families of black holes in N=8 supergravity. There are also two distinct generalizations of Majumdar-Papapertrou solutions which describe the static equilibrium of many black holes.     

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.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.