106,086 research outputs found

### From QCD to Dual Superconductivity to Effective String Theory

We show how an effective field theory of long distance QCD, describing a dual
superconductor, can be expressed as an effective string theory of
superconducting vortices. We use the semiclassical expansion of this effective
string theory about a classical rotating string solution in any spacetime
dimension D to obtain the semiclassical meson energy spectrum. We argue that
the experimental data on Regge trajectories along with numerical simulations of
the heavy quark potentials provide good evidence for an effective string
description of long distance QCD.Comment: Talk given at the 5th International Conference on Quark Confinement
and the Hadron Spectrum, Gargnano, Italy, September 200

### A universal solution

The phenomenon of an implicit function which solves a large set of second
order partial differential equations obtainable from a variational principle is
explicated by the introduction of a class of universal solutions to the
equations derivable from an arbitrary Lagrangian which is homogeneous of weight
one in the field derivatives. This result is extended to many fields. The
imposition of Lorentz invariance makes such Lagrangians unique, and equivalent
to the Companion Lagrangians introduced in [baker].Comment: arxiv version is already officia

### Stable divisorial gonality is in NP

Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph $G$ can be defined with help of a chip firing game on $G$. The stable
divisorial gonality of $G$ is the minimum divisorial gonality over all
subdivisions of edges of $G$.
In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer $k$ belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with $n$
vertices is bounded by $2^{p(n)}$ for a polynomial $p$

### Effective String Theory of Vortices and Regge Trajectories

Starting from a field theory containing classical vortex solutions, we obtain
an effective string theory of these vortices as a path integral over the two
transverse degrees of freedom of the string. We carry out a semiclassical
expansion of this effective theory, and use it to obtain corrections to Regge
trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in
appendix E (was previously D), added more discussion of Fig. 3, moved some
material in section 9 to a new appendi

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