相关论文: A 0-dimensional counter-example to rooting?
We present an example of a zero-dimensional $F$-space that is not strongly zero-dimensional.
We present a counterexample to the Nelson-Seiberg theorem and its extensions. The model has 4 chiral fields, including one R-charge 2 field and no R-charge 0 filed. Giving generic values of coefficients in the renormalizable superpotential,…
A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are…
We prove the geometric Bogomolov conjecture over a function field of characteristic zero.
Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero…
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an…
A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such example in dimensions lower than five. A condition weaker than…
The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
This paper is devoted to the classification problem of tree-dimensional anti-commutative(zero-potent) algebras over any base field $\mathbb{F}$ such that $Char(\mathbb{F})\neq 2$ and every element admits a square root.
Let Q_0 denote the rational numbers expanded to a "meadow", that is, after taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In this paper we consider "cancellation meadows", i.e., meadows without proper zero…
Given a 0-dimensional scheme X in a n-dimensional projective space P^n_K over an arbitrary field K, we use Liaison theory to characterize the Cayley-Bacharach property of X. Our result extends the result for sets of K-rational points given…
In this note, we illustrate how the two-dimensional theory of elasticity provides a physical example of field theory displaying scale but not conformal invariance.
Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS-NS two form B, which gives rise to space-time…
Ax gave examples of fields of cohomological dimension 1 which are not C_1-fields. Kato and Kuzumaki asked whether a weak form of the C_1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of…
We give an example of a codimension-one foliation which is transversely of class C^1 and which does not satisfy the "Local Minimal Set" property.
Counterexample models to the Nelson-Seiberg theorem have been discovered, and their features have been studied in previous literature. All currently known counterexamples have generic superpotentials respecting the R-symmetry, and more…
In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional $\phi^4$ field theory,in increasing order of sophistication. The note does not contain any new…
It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…