4,507 research outputs found
Theta-terms in nonlinear sigma-models
We trace the origin of theta-terms in non-linear sigma-models as a
nonperturbative anomaly of current algebras. The non-linear sigma-models emerge
as a low energy limit of fermionic sigma-models. The latter describe Dirac
fermions coupled to chiral bosonic fields. We discuss the geometric phases in
three hierarchies of fermionic sigma-models in spacetime dimension (d+1) with
chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres.
The geometric phases in the first two hierarchies are theta-terms. We emphasize
a relation between theta-terms and quantum numbers of solitons.Comment: 10 pages, no figures, revtex, typos correcte
Integrable systems and holomorphic curves
In this paper we attempt a self-contained approach to infinite dimensional
Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten
theory. It consists of two parts. The first one is basically a survey of
Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation
with Frobenius manifolds. We will mainly focus on the dispersionless case, with
just some hints on Dubrovin's reconstruction of the dispersive tail. The second
part deals with the relation of such systems to rational Gromov-Witten and
Symplectic Field Theory. We will use Symplectic Field theory of
as a language for the Gromov-Witten theory of a closed symplectic manifold .
Such language is more natural from the integrable systems viewpoint. We will
show how the integrable system arising from Symplectic Field Theory of
coincides with the one associated to the Frobenius structure of
the quantum cohomology of .Comment: Partly material from a working group on integrable systems organized
by O. Fabert, D. Zvonkine and the author at the MSRI - Berkeley in the Fall
semester 2009. Corrected some mistake
Integrability in non-perturbative QFT
Exact non-perturbative partition functions of coupling constants and external
fields exhibit huge hidden symmetry, reflecting the possibility to change
integration variables in the functional integral. In many cases this implies
also some non-linear relations between correlation functions, typical for the
tau-functions of integrable systems. To a variety of old examples, from matrix
models to Seiberg-Witten theory and AdS/CFT correspondence, now adds the
Chern-Simons theory of knot invariants. Some knot polynomials are already shown
to combine into tau-functions, the search for entire set of relations is still
in progress. It is already known, that generic knot polynomials fit into the
set of Hurwitz partition functions -- and this provides one more stimulus for
studying this increasingly important class of deformations of the ordinary
KP/Toda tau-functions.Comment: 10 pages, conference tal
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Platform Dependent Verification: On Engineering Verification Tools for 21st Century
The paper overviews recent developments in platform-dependent explicit-state
LTL model checking.Comment: In Proceedings PDMC 2011, arXiv:1111.006
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