On the relation between Green's functions of the SUSY theory with and without soft terms

We study possible relations between the full Green's functions of softly broken supersymmetric theories and the full Green's functions of rigid supersymmetric theories on the example of the supersymmetric quantum mechanics and find that algebraic relations can exist and can be written in a simple form. These algebraic relations between the Green's functions have been derived by transforming the path integral of the rigid theory. In this approach soft terms appear as the result of general changes of coordinates in the superspace.     

Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “Ø-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the Ø-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.     

Supersymmetric Noether Currents and Seiberg–Witten Theory

The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to derive the mass-formula for the quantized Seiberg–Witten model from the supersymmetric algebra. We check that the mass-formula of the low-energy theory agrees with that of the full theory (in the broken phase).     

Towards Higher-N Superextensions of Born–Infeld Theory

We give a brief account of supersymmetric Born–Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N = 3 supersymmetric Born–Infeld theory which admits a natural off-shell formulation in N = 3 harmonic superspace.     

Supersymmetric field theories at finite temperature

We show by explicit calculations to second and third order in perturbation theory, that finite temperature effects do not break the supersymmetry Ward-Takahashi identities for graded thermal Green functions of the Wess-Zumino model. Moreover, it is argued that this result is true to all orders in perturbation theory, and further, true for a wide class of supersymmetric theories. We point out, however, that these identities can be broken in the course of a phase transition that restores an originally broken internal symmetry.     

Perturbation theory and renormalization of supersymmetric Yang-Mills theories

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.     

Vacuum alignment in supersymmetric gauge theories

The vacuum alignment problem is analyzed in the context of supersymmetric gauge theories with dynamical symmetry breaking. Three cases are distinguished, depending on whether the vacuum expectation value of the weak gauge current superfield in vacuum characterized by the orientation Ω is zero for all Ω, for some Ω, or for no Ω. In the first case, a non-renormalization theorem is proved to all orders in the weak coupling, showing that the usual criterion of minimizing the vacuum energy density is insufficient to determine the alignment, and possible resolutions of the problem are discussed. The second case is similar, except that the possible alignments are resricted to the range of Ω giving a vanishing VEV and the weak gauge group may then be broken non-minimally. In the third case, supersymmetry is itself broken at the tree level by the weak interactions. The supersymmetric generalization of the Schwinger mechanism for dynamical mass generation is described.     

Symmetry Breaking for Matter Coupled to Linearized Supergravity from the Perspective of the Current Supermultiplet

We consider a generic supersymmetric matter theory coupled to linearized supergravity, and analyze scenarios for spontaneous symmetry breaking in terms of vacuum expectation values of components of the current supermultiplet. When the vacuum expectation of the energy momentum tensor is zero, but the scalar current or pseudoscalar current gets an expectation, evaluation of the gravitino self energy using the supersymmetry current algebra shows that there is an induced gravitino mass term. The structure of this term generalizes the supergravity action with cosmological constant to theories with CP violation. When the vacuum expectation of the energy momentum tensor is nonzero, supersymmetry is broken; requiring cancellation of the cosmological constant gives the corresponding generalized gravitino mass formula.     

Secret supersymmetry

We present new non-linear realizations of the N = 1 supergravity algebra. They allow us to build interesting realistic models of the four forces of nature. These models are different from all previous ones in that particles do not appear in (broken) supersymmetric multiplets.These new non-linear realizations also permit us to construct the effective low-energy lagrangian of an arbitrary supergravity theory in which supersymmetry is spontaneously broken. We are thus able to analyze what are the model-independent low-energy effects of supergravity. We find that the number of Higgs fields and the way they couple to quark and lepton matter is a feature which distinguishes supersymmetric theories from non-supersymmetric ones.     

New avenues in supersymmetry and supergravity

We analyze the problem of constructing supersymmetric versions of gauge theories of particles and of gravity which have a closed supersymmetric algebra. Inparticular we present the basic no-go theorems that indicate that in four dimensions it is not possible to construct suitably extended supersymmetric versions of the above theories without drastic modification of the supersymmetric algebra. Two ways past the“N=3” barrier are discussed; that of central charges involved highly constrained versions which appearn difficult to quantize effectively, while the use of light-cone variables seems to be the most promising. We give light-cone gauge versions of supersymmetric Yang-Mills theories for all extended cases of interest and briefly consider their ultraviolet divergence properties.     

More supersymmetric technicolor

We propose a supersymmetric model of particle physics in which supersymmetry is broken by strong gauge forces. Unlike previous realistic supersymmetric technicolor theories, the model contains only one extra strong gauge group, and it lends itself readily to grand unification. The model also has no light axions which can burn out stars. A variety of new particles, many weighing less than 100 GeV, are predicted. A no-go theorem due to Witten is discussed.     

Primordial supersymmetric inflation

We discuss the motivations for reconsidering cosmological inflation in supersymmetric theories as contrasted with conventional GUTs. Radiative corrections to the effective potential can be made arbitrarily small in supersymmetric GUTs, removing some of the obstacles to inflation. We analyze general renormalizable potentials at the tree level and show that the required fine-tuning of parameters becomes less acute if inflation takes place before the grand unified phase transition, a hypothesis we term primordial inflation. We show how the grand unified monopole problem can be solved in supersymmetric GUTs embodying primordial inflation.     

Supersymmetric preon models with gauged colour-flavour symmetry

We have conducted a search for globally supersymmetric preon models with gauged colour-flavour symmetries. Theories with both two- and three-preon composites, and colour-flavour groups from E₆ down to the standard model, are examined under the following conditions: asymptotically-free metacolour, anomaly-free gauged symmetries, and Pauli principle obeyed. It is found that there are no models with three or more supersymmetric families. If supersymmetry is broken, one model with four families emerges. The purely fermionic preon theories can also be considered as the light sector of a chiral supersymmetric theory, with supersymmetry breaking at the preon level.     

Spectrum of boundary states in N=1 SUSY sine-Gordon theory

We consider N=1 supersymmetric sine-Gordon theory (SSG) with supersymmetric integrable boundary conditions (boundary SSG=BSSG). We find two possible ways to close the boundary bootstrap for this model, corresponding to two different choices for the boundary supercharge. We argue that these two bootstrap solutions should correspond to the two integrable Lagrangian boundary theories considered recently by Nepomechie.     

Superconformal algebras and their relation to integrable nonlinear systems

We relate the manifold of periodic functions on a circle with values in the Grassmann algebra to extended superconformal algebras. The graded Poisson brackets of these functions give the classical realization of the corresponding superconformal algebras and determine the hamiltonian structure for a class of integrable nonlinear equations. A super-generalization of the Korteweg-de Vries equation is found among these equations. In this way an important step in the program of the quantization of the Liouville equation is realized for the supersymmetric cases which are crucial in constructing a consistent quantum string theory. The construction of Miura transformations is outlined and the results for the N = 1,2 supersymmetric cases are presented.     

Supersymmetry and the vacuum

It is shown that, in a supersymmetric theory, the sum of all vacuum diagrams vanishes identically as a consequence of compensations among contributions involving different fields of the supermultiplet. This means that the zero-point energy-momentum density is zero to all orders in the supersymmetric interaction. In an external gravitational field no cosmological term is induced through the vacuum polarization of the matter fields. The situation when supersymmetry is spontaneously broken, or softly broken is also discussed.     

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.     

Preliminary study of the scattering length from lattice QCD

Noncommutative generalizations of a supersymmetry algebra in two dimensions have been introduced earlier in Abbaspur (Int. J. Mod. Phys. A 18:855?C878, 2003; Mod. Phys. Lett. A 18:587?C599, 2003). In this paper we present a field theoretic realization for these algebras in the context of $\mathcal{N}=1$ supersymmetric U(1) gauge theories in two dimensions. We also describe a possible generalization to 4-dimensional theories.     

Supergravity,R invariance and spontaneous supersymmetry breaking

We show that in order for a U(1) gauge theory with a Fayet-Illiopoulos term to be consistently coupled to supergravity, preserving gauge invariance, the superpotential must be R invariant. A supersymmetric cosmological term and therefore an explicit mass-like term for the gravitino is forbidden by gauge invariance. This result severely constrains the possible models for non-gravitational interactions. We comment on possible mass term the gauginos induced by gravitational effects.     

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.