20,155 research outputs found
Wall Crossing As Seen By Matrix Models
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends
on two sets of data, the BPS charges and the stability conditions. For D0 and
D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are
naturally related to the Kahler moduli space M(X). We construct unitary
one-matrix models which count such BPS states for a class of toric Calabi-Yau
manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting
on X turns out to give the topological string partition function for another
Calabi-Yau manifold Y, whose Kahler moduli space M(Y) contains two copies of
M(X), one related to the BPS charges and another to the stability conditions.
The two sets of data are unified in M(Y). The matrix models have a number of
other interesting features. They compute spectral curves and mirror maps
relevant to the remodeling conjecture. For finite 't Hooft coupling they give
rise to yet more general geometry \widetilde{Y} containing Y.Comment: 44 pages, 9 figures, published versio
Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
Quantization of the system comprising gravitational, fermionic and
electromagnetic fields is developed in the loop representation. As a result we
obtain a natural unified quantum theory. Gravitational field is treated in the
framework of Ashtekar formalism; fermions are described by two Grassmann-valued
fields. We define a -algebra of configurational variables whose
generators are associated with oriented loops and curves; ``open'' states --
curves -- are necessary to embrace the fermionic degrees of freedom. Quantum
representation space is constructed as a space of cylindrical functionals on
the spectrum of this -algebra. Choosing the basis of ``loop'' states we
describe the representation space as the space of oriented loops and curves;
then configurational and momentum loop variables become in this basis the
operators of creation and annihilation of loops and curves. The important
difference of the representation constructed from the loop representation of
pure gravity is that the momentum loop operators act in our case simply by
joining loops in the only compatible with their orientaiton way, while in the
case of pure gravity this action is more complicated.Comment: 28 pages, REVTeX 3.0, 15 uuencoded ps-figures. The construction of
the representation has been changed so that the representation space became
irreducible. One part is removed because it developed into a separate paper;
some corrections adde
Nijenhuis operator in contact homology and descendant recursion in symplectic field theory
In this paper we investigate the algebraic structure related to a new type of
correlator associated to the moduli spaces of -parametrized curves in
contact homology and rational symplectic field theory. Such correlators are the
natural generalization of the non-equivariant linearized contact homology
differential (after Bourgeois-Oancea) and give rise to an invariant Nijenhuis
(or hereditary) operator (\`a la Magri-Fuchssteiner) in contact homology which
recovers the descendant theory from the primaries. We also sketch how such
structure generalizes to the full SFT Poisson homology algebra to a (graded
symmetric) bivector. The descendant hamiltonians satisfy to recursion
relations, analogous to bihamiltonian recursion, with respect to the pair
formed by the natural Poisson structure in SFT and such bivector. In case the
target manifold is the product stable Hamiltonian structure , with
a symplectic manifold, the recursion coincides with genus topological
recursion relations in the Gromov-Witten theory of .Comment: 30 pages, 3 figure
Are ghost surfaces quadratic-flux-minimizing?
Two candidates for "almost-invariant" toroidal surfaces passing through
magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost
surfaces, use families of periodic pseudo-orbits (i.e. paths for which the
action is not exactly extremal). QFMin pseudo-orbits, which are
coordinate-dependent, are field lines obtained from a modified magnetic field,
and ghost-surface pseudo-orbits are obtained by displacing closed field lines
in the direction of steepest descent of magnetic action, . A generalized Hamiltonian definition of ghost
surfaces is given and specialized to the usual Lagrangian definition. A
modified Hamilton's Principle is introduced that allows the use of Lagrangian
integration for calculation of the QFMin pseudo-orbits. Numerical calculations
show QFMin and Lagrangian ghost surfaces give very similar results for a
chaotic magnetic field perturbed from an integrable case, and this is explained
using a perturbative construction of an auxiliary poloidal angle for which
QFMin and Lagrangian ghost surfaces are the same up to second order. While
presented in the context of 3-dimensional magnetic field line systems, the
concepts are applicable to defining almost-invariant tori in other
degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.Comment: 8 pages, 3 figures. Revised version includes post-publication
corrections in text, as described in Appendix C Erratu
Evidence for F(uzz) Theory
We show that in the decoupling limit of an F-theory compactification, the
internal directions of the seven-branes must wrap a non-commutative four-cycle
S. We introduce a general method for obtaining fuzzy geometric spaces via toric
geometry, and develop tools for engineering four-dimensional GUT models from
this non-commutative setup. We obtain the chiral matter content and Yukawa
couplings, and show that the theory has a finite Kaluza-Klein spectrum. The
value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points
on the internal four-cycle S. This relation puts a non-trivial restriction on
the space of gauge theories that can arise as a limit of F-theory. By viewing
the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the
geometry, we argue that this theory admits a holographic dual description in
the large N limit. We also entertain the possibility of constructing string
models with large fuzzy extra dimensions, but with a high scale for quantum
gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde
Photofragmentation of the H_3 molecule, including Jahn-Teller coupling effects
We have developed a theoretical method for interpretation of photoionization
experiments with the H_3 molecule. In the present study we give a detailed
description of the method, which combines multichannel quantum defect theory,
the adiabatic hyperspherical approach, and the techniques of outgoing Siegert
pseudostates. The present method accounts for vibrational and rotation
excitations of the molecule, deals with all symmetry restrictions imposed by
the geometry of the molecule, including vibrational, rotational, electronic and
nuclear spin symmetries. The method was recently applied to treat dissociative
recombination of the H_3^+ ion. Since H_3^+ dissociative recombination has been
a controversial problem, the present study also allows us to test the method on
the process of photoionization, which is understood better than dissociative
recombination. Good agreement with two photoionization experiments is obtained.Comment: 10 figure
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