44,244 research outputs found
On Denominators of the Kontsevich Integral and the Universal Perturbative Invariant of 3-Manifolds
The integrality of the Kontsevich integral and perturbative invariants is
discussed. We show that the denominator of the degree part of the
Kontsevich integral of any knot or link is a divisor of .
We also show that the denominator of of the degree part of the universal
perturbative invariant of homology 3-spheres is not divisible by any prime
greater than .Comment: 27 pages, LaTeX with graphics packag
Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces
This paper transfers a randomized algorithm, originally used in geometric
optimization, to computational problems in commutative algebra. We show that
Clarkson's sampling algorithm can be applied to two problems in computational
algebra: solving large-scale polynomial systems and finding small generating
sets of graded ideals. The cornerstone of our work is showing that the theory
of violator spaces of G\"artner et al.\ applies to polynomial ideal problems.
To show this, one utilizes a Helly-type result for algebraic varieties. The
resulting algorithms have expected runtime linear in the number of input
polynomials, making the ideas interesting for handling systems with very large
numbers of polynomials, but whose rank in the vector space of polynomials is
small (e.g., when the number of variables and degree is constant).Comment: Minor edits, added two references; results unchange
Integral formula for elliptic SOS models with domain walls and a reflecting end
In this paper we extend previous work of Galleas and the author to elliptic
SOS models. We demonstrate that the dynamical reflection algebra can be
exploited to obtain a functional equation characterizing the partition function
of an elliptic SOS model with domain-wall boundaries and one reflecting end.
Special attention is paid to the structure of the functional equation. Through
this approach we find a novel multiple-integral formula for that partition
function.Comment: 31 pages, 3 figures; v2: minor improvements, reference adde
The S-Matrix of superstring field theory
We show that the classical S-matrix calculated from the recently proposed
superstring field theories give the correct perturbative S-matrix. In the proof
we exploit the fact that the vertices are obtained by a field redefinition in
the large Hilbert space. The result extends to include the NS-NS subsector of
type II superstring field theory and the recently found equations of motions
for the Ramond fields. In addition, our proof implies that the S-matrix
obtained from Berkovits' WZW-like string field theory then agrees with the
perturbative S-matrix to all orders.Comment: 19 pages, 2 figure
- …