583 research outputs found

### Mass Formulae for Broken Supersymmetry in Curved Space-Time

We derive the mass formulae for ${\cal N}=1$, $D=4$ matter-coupled
Supergravity for broken (and unbroken) Supersymmetry in curved space-time.
These formulae are applicable to de Sitter configurations as is the case for
inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass
relations modified by the AdS curvature. We compute the mass relations both for
the potential and its derivative non-vanishing.Comment: 14 pages; v2: v2: Extended conclusions and typos correcte

### Poles of the topological zeta function associated to an ideal in dimension two

To an ideal in $\mathbb{C}[x,y]$ one can associate a topological zeta
function. This is an extension of the topological zeta function associated to
one polynomial. But in this case we use a principalization of the ideal instead
of an embedded resolution of the curve.
In this paper we will study two questions about the poles of this zeta
function. First, we will give a criterion to determine whether or not a
candidate pole is a pole. It turns out that we can know this immediately by
looking at the intersection diagram of the principalization, together with the
numerical data of the exceptional curves. Afterwards we will completely
describe the set of rational numbers that can occur as poles of a topological
zeta function associated to an ideal in dimension two. The same results are
valid for related zeta functions, as for instance the motivic zeta function.Comment: 17 pages, to be published in Mathematische Zeitschrif

### The monodromy conjecture for zeta functions associated to ideals in dimension two

The monodromy conjecture states that every pole of the topological (or
related) zeta function induces an eigenvalue of monodromy. This conjecture has
already been studied a lot; however, in full generality it is proven only for
zeta functions associated to a polynomial in two variables.
In this article we consider zeta functions associated to an ideal. First we
work in arbitrary dimension and obtain a formula (like the one of A'Campo) to
compute the 'Verdier monodromy' eigenvalues associated to an ideal. Afterwards
we prove a generalized monodromy conjecture for arbitrary ideals in two
variables.Comment: 16 pages, to appear in Ann. Inst. Fourie

### Wess-Zumino sigma models with non-Kahlerian geometry

Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations
that determine a larger class of geometries than the familiar Kahler manifolds,
in which covariantly holomorphic vectors rather than a scalar superpotential
determine the forces. Indeed, relaxing the requirement that the field equations
be derivable from an action leads to complex flat geometry. The
Batalin-Vilkovisky formalism is used to show that if one requires that the
field equations be derivable from an action, we once again recover the
restriction to Kahler geometry, with forces derived from a scalar
superpotential.Comment: 13 pages, Late

### Hypermultiplets and hypercomplex geometry from 6 to 3 dimensions

The formulation of hypermultiplets that has been developed for 5-dimensional
matter multiplets is by dimensional reductions translated into the appropriate
spinor language for 6 and 4 dimensions. We also treat the theories without
actions that have the geometrical structure of hypercomplex geometry. The
latter is the generalization of hyper-Kaehler geometry that does not require a
Hermitian metric and hence corresponds to field equations without action. The
translation tables of this paper allow the direct application of superconformal
tensor calculus for the hypermultiplets using the available Weyl multiplets in
6 and 4 dimensions. Furthermore, the hypermultiplets in 3 dimensions that
result from reduction of vector multiplets in 4 dimensions are considered,
leading to a superconformal formulation of the c-map and an expression for the
main geometric quantities of the hyper-Kaehler manifolds in the image of this
map.Comment: 18 pages; v2: several clarifications in text and formulae, version to
appear in Class.Quantum Gravit

- â€¦