Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity

The prescription of Silva to derive superpotential equations from variational derivatives rather than from Lagrangian densities is applied to theories of gravity derived from Lovelock Lagrangians in the Palatini representation. Spacetimes are without torsion and isolated sources of gravity are minimally coupled. On a closed boundary of spacetime, the metric is given and the connection coefficients are those of Christoffel. We derive equations for the superpotentials in these conditions. The equations are easily integrated and we give the general expression for all superpotentials associated with Lovelock Lagrangians. We find, in particular, that in Einstein's theory, in any number of dimensions, the superpotential, valid at spatial and at null infinity, is that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we find a simple expression for the superpotential of Einstein-Gauss-Bonnet theories with an anti-de Sitter background: it is minus the KBL superpotential, confirming, as it should, the calculation of the total mass-energy of spacetime at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200

Metastable Vacua in Perturbed Seiberg-Witten Theories

We show that, for a generic choice of a point on the Coulomb branch of any N=2 supersymmetric gauge theory, it is possible to find a superpotential perturbation which generates a metastable vacuum at the point. For theories with SU(N) gauge group, such a superpotential can be expressed as a sum of single-trace terms for N=2 and 3. If the metastable point is chosen at the origin of the moduli space, we can show that the superpotential can be a single-trace operator for any N. In both cases, the superpotential is a polynomial of degree 3N of the vector multiplet scalar field.Comment: 22 pages, 4 figures; adding chiral ring arguments in appendix B.

The Confining N=1 Supersymmetric Gauge Theories: a Review

We give a classification and overview of the confining N=1 supersymmetric gauge theories. For simplicity we consider only theories based on simple gauge groups and no tree-level superpotential. Classification of these theories can be done according to whether or not there is a superpotential generated for the confined degrees of freedom. The theories with the superpotential include s-confining theories and also theories where the gauge fields participate in the confining spectrum, while theories with no superpotential include theories with a quantum deformed moduli space and theories with an affine moduli space.Comment: 12 pages, LaTeX. Talk presented at the 3rd Workshop on Continuous Advances in QCD, Minneapolis, MN, 16-19 April 1998. To appear in the proceeding

Direct derivation of the Veneziano-Yankielowicz superpotential from matrix model

We derive the Veneziano-Yankielowicz superpotential directly from the matrix model by fixing the measure precisely. The essential requirement here is that the effective superpotential of the matrix model corresponding to the ${\cal N}=4$ supersymmetric Yang-Mills theory vanishes except for the tree gauge kinetic term. Thus we clarify the reason why the matrix model reproduces the Veneziano-Yankielowicz superpotential correctly in the Dijkgraaf-Vafa theory.Comment: 13 pages, to appear in Phys. Lett.

Superpotential algebras and manifolds

In this paper we study a special class of Calabi-Yau algebras (in the sense of Ginzburg): those arising as the fundamental group algebras of acyclic manifolds. Motivated partly by the usefulness of `superpotential descriptions' in motivic Donaldson-Thomas theory, we investigate the question of whether these algebras admit superpotential presentations. We establish that the fundamental group algebras of a wide class of acyclic manifolds, including all hyperbolic manifolds, do not admit such descriptions, disproving Ginzburg's conjecture regarding them. We also describe a class of manifolds that do admit such descriptions, and discuss a little their motivic Donaldson-Thomas theory. Finally, some links with topological field theory are described.Comment: 31 pages, 2 figures, final version. Thanks to M. Kontsevich, V. Ginzburg, M, Van den Bergh and B. Keller for helpful comments and corrections. I've added some examples e.g. Klein bottl

Non-Perturbative Superpotentials from Membrane Instantons in Heterotic M-Theory

A formalism for calculating the open supermembrane contribution to the non-perturbative superpotential of moduli in heterotic M-theory is presented. This is explicitly applied to the Calabi-Yau (1,1)-moduli and the separation modulus of the end-of-the-world BPS three-branes, whose non-perturbative superpotential is computed. The role of gauge bundles on the boundaries of the open supermembranes is discussed in detail, and a topological criterion presented for the associated superpotential to be non-vanishing.Comment: 59 pages, latex, minor corrections adde