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.     

Linearized N = 2 superfield supergravity

We present the formulation of linearized SU(2) supergravity and U(2) conformal supergravity in terms of unconstrained N = 2 superfields: the gauge superfield, compensating superfields, gauge transformations, supertensors, actions and covariant derivatives.     

Superfield currents of PoincaréN=1 supersymmetry

Starting from the algebraically reduced PoincaréN=1 superspace Noether-current, represented by four superfields obeying a conservation law, the question of further reductions is investigated. Each reduction is defined by a transformation of the four superfields leaving the conservation law as well as certain superfield currents built from them invariant. Two requirements for these superfield currents are stated and the corresponding equations are solved. An additional requirement related to, the uniqueness of the component currents is postulated.     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Dirac Superfield Quantization in Odd Superspace

We generalize the superfield method of Dirac quantization to the odd sector of superspace for N = 2 extended models. We discuss the mechanism of generating constraints in the odd sector of supersymmetric classical mechanics and then Dirac quantization in the odd superspace in superfield version. An example of supersymmetric system, defined by odd superfields, and the application of the method in the odd superspace is given.     

Goldstino and sgoldstino in microscopic models and the constrained superfields formalism

We examine the exact relation between the superconformal symmetry breaking chiral superfield (X) and the goldstino superfield in microscopic models of an arbitrary Kahler potential (K) and in the presence of matter fields. We investigate the decoupling of the massive sgoldstino and scalar matter fields and the offshell/onshell-SUSY expressions of their superfields in terms of the fermions composites. For general K of two superfields, we study the properties of the superfield X after integrating out these scalar fields, to show that in the infrared it satisfies (offshell) the condition X³=0 and X²≠0. We then compare our results to those of the well-known method of constrained superfields discussed in the literature, based on the conjecture X²=0. Our results can be used in applications, to couple offshell the (s)goldstino fields to realistic models such as the MSSM.     

Partial spontaneous breaking of two-dimensional supersymmetry

We construct low-energy Goldstone superfield actions describing various patterns of the partial spontaneous breakdown of two-dimensional N=(1,1), N=(2,0) and N=(2,2) supersymmetries, with the main focus on the last case. These nonlinear actions admit a representation in the superspace of the unbroken supersymmetry as well as in a superspace of the full supersymmetry. The natural setup for implementing the partial breaking in a self-consistent way is provided by the appropriate central extensions of D=2 supersymmetries, with the central charges generating shift symmetries on the Goldstone superfields. The Goldstone superfield actions can be interpreted as manifestly worldsheet supersymmetric actions in the static gauge of some superstrings and D1-branes in D=3 and D=4 Minkowski spaces. As an essentially new example, we elaborate on the action representing the 1/4 partial breaking pattern N=(2,2)→N=(1,0).     

Representations of N = 4 supersymmetry on superfields

We determine all of the irreducible representations (irreps) of the extended supersymmetry algebra (for N = 2 and 4) on superfields with arbitrary external spin in terms of the associated eigenvalues of suitable Casimirs of enlarged algebras. Detailed results are presented for the scalar, spinor and vector superfield cases. The component content of the corresponding irreps are also discussed by means of suitable basis functions.     

Supergraphity: (II). Manifestly covariant rules and higher-loop finiteness

We continue our discussion of the background field formalism in supersymmetric theories, deriving new covariant Feynman rules for chiral superfields. As a result, we obtain improved power-counting rules for both simple and extended supersymmetry which can be used to make the following statements: If the corresponding extended superfield formalism exist, (a) N=2 supersymmetric Yang-Mills theory is finite beyond one loop, (b) N=4 Yang-Mills is finite at all loops, and (c) N=8 supergravity is finite through six loops. We also find that in simple super-Yang-Mills the radiative corrections to the Fayet-Iliopoulos (“D”) term, which are known to vanish for higher loops, also vanish automatically at one loop for arbitrary couplings.     

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.     

The Hamiltonian structure of the N = 2 supersymmetric GNLS hierarchy

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N = 2 supersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N = 2 supersymmetric (n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n = 1, m = 1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N = 4 supersymmetry structure is uncovered.     

Towards the construction of N = 2 supersymmetric integrable hierarchies

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible N = 2 supersymmetric integrable hierarchies with N = 2 super-W_n second Hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the N = 2 supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct Hamiltonians we are led to a new definition of super-residues for degenerate N = 2 supersymmetric pseudo-differential operators. We have found a new non-polynomials Miura-like realization for N = 2 superconformal algebra in terms of two bosonic chiral-anti-chiral free superfields.     

The off-shell infrared problem in N = 1 supersymmetric yang-mills theories (II). General massless models

We prove that in a general massless N = I SYM theory off-shell Green functions exist such that Green functions of gauge invariant operators are supersymmetrically covariant. The off-shell infrared problem present in the superfield treatment of these theories is thus shown to remain a gauge artefact. The N = 2, 4 pure SYM theories are covered by this result and thus exist as N = 1 SYM theories.     

Extended supersymmetry in massless conformal higher spin theory

We propose superfield equations in tensorial N-extended superspaces to describe the N=2,4,8 supersymmetric generalizations of free conformal higher spin theories. These can be obtained by quantizing a superparticle model in N-extended tensorial superspace. The N-extended higher spin supermultiplets just contain scalar and ‘spinor’ fields in tensorial space so that, in contrast with the standard (super)space approach, no nontrivial generalizations of the Maxwell or Einstein equations to tensorial space appear when N>2. For N=4,8, the higher spin-tensorial components of the extended tensorial superfields are expressed through additional scalar and spinor fields in tensorial space which obey the same free higher spin equations, but that are axion-like in the sense that they possess Peccei-Quinn-like symmetries.     

Supercurrents

Supercurrents that provide irreducible off-shell representation of N-extended supersymmetry with maximum $\text{spin}\text{?}\text{1}\text{2}\text{N}$ are constructed as bilinears of massless on-shell superfields. The corresponding prepotentials are derived and used to construct maximally gauge-invariant field theories with maximum $\text{spin}\text{?}\text{1}\text{2}\text{N}$. The construction of non-conformal theories using these irreducible field multiplets is discussed; in particular the superfield form of massive spin 1 is given for N = 2 and compensating fields are proposed for N = 4 Poincarésupergravity. We also show how the components of supercurrents may be simply obtained with the aid of the “tableaux calculus” and we work out in detail several N = 4 and N = 8 examples.     

The N=2 Supersymmetric Matrix GNLS Hierarchies

We construct the matrix generalization of the N=2 supersymmetric GNLS hierarchies. This is done by exhibiting the corresponding matrix super Lax operators in terms of N=2 superfields in two different superfield bases. We present the second Hamiltonian structure and discrete symmetries. We then extend our discussion by conjecturing the Lax operators of different reductions of the N=2 supersymmetric matrix KP hierarchy and discuss the simplest examples.