Supersymmetric Yang-Mills theories with local coupling: The supersymmetric gauge

Supersymmetric pure Yang-Mills theory is formulated with a local, i.e. space-time dependent, complex coupling in superspace. Super-Yang-Mills theories with local coupling have an anomaly, which has been first investigated in the Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a manifest supersymmetric formulation the anomaly appears in two other identities: The first one describes the non-renormalization of the topological term, the second relates the renormalization of the gauge coupling to the renormalization of the complex supercoupling. Only one of the two identities can be maintained in perturbation theory. We discuss the two versions and derive the respective beta function of the local supercoupling, which is non-holomorphic in the first version, but directly related to the coupling renormalization, and holomorphic in the second version, but has a non-trivial, i.e.anomalous, relation to the beta function of the gauge coupling.Comment: References correcte

Coexistence of long-range order for two observables at finite temperatures

We give a criterion for the simultaneous existence or non existence of two long-range orders for two observables, at finite temperatures, for quantum lattice many body systems. Our analysis extends previous results of G.-S. Tian limited to the ground state of similar models. The proof involves an inequality of Dyson-Lieb-Simon which connects the Duhamel two-point function to the usual correlation function. An application to the special case of the Holstein model is discussed.Comment: 12 pages, accepted for publication in J. of Phys.

SU(m|n) supersymmetric Calogero-Sutherland model confined in harmonic potential

In this work, we study a continuous quantum system of a mixture of bosons and fermions with the supersymmetry SU(m|n). The particles are confined in a harmonic well and interact with each other through the 1/r2 interaction. The ground state wavefunction is constructed explicitly for the most general SU(m|n) case, with the ground state energy given explicitly. The full energy spectrum of excitations in the SU(m|n) model is also equal spaced. In the limiting case where there are no bosons in the system, our results reduce to those obtained previously.Comment: 9 pages, preprint of ETH-Lausanne (August 1996

Constructive algebraic renormalization of the abelian Higgs-Kibble model

We propose an algorithm, based on Algebraic Renormalization, that allows the restoration of Slavnov-Taylor invariance at every order of perturbation expansion for an anomaly-free BRS invariant gauge theory. The counterterms are explicitly constructed in terms of a set of one-particle-irreducible Feynman amplitudes evaluated at zero momentum (and derivatives of them). The approach is here discussed in the case of the abelian Higgs-Kibble model, where the zero momentum limit can be safely performed. The normalization conditions are imposed by means of the Slavnov-Taylor invariants and are chosen in order to simplify the calculation of the counterterms. In particular within this model all counterterms involving BRS external sources (anti-fields) can be put to zero with the exception of the fermion sector.Comment: Jul, 1998, 31 page

Finiteness in N=1 SYM Theories

I present a criterion for all-order finiteness in N=1 SYM theories. Three applications are given; they yield all-order finite N=1 SYM models with global symmetries of the superpotential.Comment: 3 pages, plain LaTex, no figure

Algebraic Properties of BRST Coupled Doublets

We characterize the dependence on doublets of the cohomology of an arbitrary nilpotent differential s (including BRST differentials and classical linearized Slavnov-Taylor (ST) operators) in terms of the cohomology of the doublets-independent component of s. All cohomologies are computed in the space of local integrated formal power series. We drop the usual assumption that the counting operator for the doublets commutes with s (decoupled doublets) and discuss the general case where the counting operator does not commute with s (coupled doublets). The results are purely algebraic and do not rely on power-counting arguments.Comment: Some explanations enlarged, references adde

Off-diagonal long-range order and meissner effect for lattice systems

We study some general properties of a strongly correlated electron system defined on a lattice. Assuming that the system exhibits off-diagonal long-range order, we show that this assumption implies the Meissner effect. This extends to lattice systems previous results obtained for the continuous cas