7,290 research outputs found
Maps on surfaces and Galois groups
A brief survey of some of the connections between maps on surfaces, permutations, Riemann surfaces, algebraic curves and Galois groups is given
Permutation combinatorics of worldsheet moduli space
52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio
Matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the
gauge where the field strength is diagonal. Twisted sectors originate, as in
Matrix string theory, from permutations of the eigenvalues around homotopically
non-trivial loops. These sectors, that must be discarded in the usual
quantization due to divergences occurring when two eigenvalues coincide, can be
consistently kept if one modifies the action by introducing a coupling of the
field strength to the space-time curvature. This leads to a generalized
Yang-Mills theory whose action reduces to the usual one in the limit of zero
curvature. After integrating over the non-diagonal components of the gauge
fields, the theory becomes a free string theory (sum over unbranched coverings)
with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to
a lattice theory with a gauge group which is the semi-direct product of S_N and
U(1)^N. By using well known results on the statistics of coverings, the
partition function on arbitrary Riemann surfaces and the kernel functions on
surfaces with boundaries are calculated. Extensions to include branch points
and non-abelian groups on the world-sheet are briefly commented upon.Comment: Latex2e, 29 pages, 2 .eps figure
Branching Data for Algebraic Functions and Representability by Radicals
The branching data of an algebraic function is a list of orders of local
monodromies around branching points. We present branching data that ensure that
the algebraic functions having them are representable by radicals. This paper
is a review of recent work by the authors and of closely related classical work
by Ritt.Comment: Submitted for publication to Banach Center Publications on April 1st,
201
On semiconjugate rational functions
We investigate semiconjugate rational functions, that is rational functions
related by the functional equation , where is a
rational function of degree at least two. We show that if and is a pair
of such functions, then either can be obtained from by a certain
iterative process, or and can be described in terms of orbifolds of
non-negative Euler characteristic on the Riemann sphere.Comment: Final version, accepted by Geom. Funct. Ana
General Solution of 7D Octonionic Top Equation
The general solution of a 7D analogue of the 3D Euler top equation is shown
to be given by an integration over a Riemann surface with genus 9. The 7D model
is derived from the 8D invariant self-dual Yang-Mills equation
depending only upon one variable and is regarded as a model describing
self-dual membrane instantons. Several integrable reductions of the 7D top to
lower target space dimensions are discussed and one of them gives 6, 5, 4D
descendants and the 3D Euler top associated with Riemann surfaces with genus 6,
5, 2 and 1, respectively.Comment: 13 pages, Latex, 3 eps.files. Minor changes, eq.(4) adde
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