P. Di Vecchia

A Supersymmetric Wess-Zumino Lagrangian in Two-Dimensions

Abstract We construct a supersymmetric version of the Wess-Zumino action in two dimensions. For a special value of the coupling constant γ 2 = 4 π / n it turns out that this theory consists of the original WZ action plus free fermions in the adjoint representation. By bosonization such a theory should be equivalent to a theory of two sets of free fermions. We study in some detail how supersymmetry is realized in these two theories. We further develop the general formalism for studying any two-dimensional quantum theory that is superconformal and super-Kac-Moody invariant, the SWZ theory and the particular free Fermi theory being examples. We generalize and apply this formalism to prove the equivalence of SWZ to a free Fermi theory.

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

Abstract We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d4x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g−12 and g6, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving A 1 4 ≌(0.11±0.02)K 1 2 , K being the SU(2) quarkless string tension. Although a larger value for A 1 4 K − 1 2 would be preferable, we are led to conclude (at least tentatively) that the UA(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.

N=2 extended superconformal theories in two dimensions

Abstract The general formalism for studying these theories is set up and some details are given concerning degenerate representations of the N=2 super Virasoro algebra in (generalized) Neveu-Schwarz and Ramond sectors. In particular the N=2 version of Kacs formula for conformal dimensions is derived.

On the Unitary Representations of N=2 Superconformal Theory

Abstract The Kac formula for superconformal dimensions (generalized to N = 2) is further developed (compared to a previous article). A list of discrete values of the central charge for which unitary representations are expected to exist is proposed. For several of these, unitarity is checked by computer. For two values, unitarity is proven by providing explicit fermionic representations. For one of those values, the N = 2 theory coincides with a sub theory of one of the known unitary N = 1 theories, thus extending a similar situation between N = 0 and N = 1.

Numerical checks of the lattice definition independence of topological charge fluctuations

Abstract The stability of our previous results on the topological charge fluctuation in SU(2) is checked against some variations of its lattice definition. The method consists of subtracting a partly computed perturbative tail to Monte Carlo data, whose high statistics are achieved by use of the icosahedral subgroup of SU(2).

Fermionic strings with boundary terms

Abstract We investigate the open fermion string (corresponding to the Neveu-Schwarz-Ramond model) by use of Polyakovs approach to the quantization problem. Supersymmetric boundary conditions on various fields are derived, and the boundary terms due to the superconformal anomaly are computed. It turns out that “supersymmetrization” of one-dimensional boundary terms induces two-dimensional terms.

Lattice CPN−1 models and their large-N behaviour

Abstract Two different lattice actions reproducing the CPN−1 model in the continuum are discussed and, in the two cases, strong and weak coupling expansions relative to different physical quantities are obtained. Large-N behaviour is analyzed by evaluating the limiting value of the two partition functions. In neither case does a smooth transition seem possible between strong and weak coupling regions for the limiting model.

The transition from the lattice to the continuum: CPN−1 models at large N

Abstract We study in detail the large N solution for the CP N −1 models on a euclidean lattice and their phase structure in D dimensions. In the two-dimensional case, we evaluate some physical quantities and discuss their behaviour in the continuum limit. In particular, for the internal energy, we found the analytic expression for the perturbative tail which, at large β, obscures the predicted renormalization group behaviour; such a tail, which, as we show, is reproduced by a mean field calculation at N =∞, must be subtracted in order to define a suitable scaling quantity. We also investigated the behaviour of the topological charge and we found no perturbative tail in agreement with previous Luschers results. Finally, some aspects of the supersymmetric case are discussed.

Effective actions in non-abelian theories

Abstract In two-dimensional U( l ) non-abelian gauge theories coupled to fermions, the fermionic sector possesses an additional, local U( l ) R ⊗ U( l ) L invariance. This chiral invariance is broken to U( l ) vector by a non-abelian axial anomaly. Using a method invented by Wess and Zumino we show that the anomaly determines the low energy effective action almost entirely. Possibilities of extending the argument to four dimensions are briefly discussed.

The anomaly term in the N=2 supersymmetric gauge theory

Abstract The Schwinger slowly varying field approximation is used to compute the terms in the effective lagrangian that reproduce the anomalies of the underlying theory. This method has been applied to extract the anomaly term in the case of pure N = 2 supersymmetric Yang-Mills theory.