1,727 research outputs found
Time-dependent backgrounds of 2D string theory
We study possible backgrounds of 2D string theory using its equivalence with
a system of fermions in upside-down harmonic potential. Each background
corresponds to a certain profile of the Fermi sea, which can be considered as a
deformation of the hyperbolic profile characterizing the linear dilaton
background. Such a perturbation is generated by a set of commuting flows, which
form a Toda Lattice integrable structure. The flows are associated with all
possible left and right moving tachyon states, which in the compactified theory
have discrete spectrum. The simplest nontrivial background describes the
Sine-Liouville string theory. Our methods can be also applied to the study of
2D droplets of electrons in a strong magnetic field.Comment: 28 pages, 2 figures, lanlma
The algebraic structure of geometric flows in two dimensions
There is a common description of different intrinsic geometric flows in two
dimensions using Toda field equations associated to continual Lie algebras that
incorporate the deformation variable t into their system. The Ricci flow admits
zero curvature formulation in terms of an infinite dimensional algebra with
Cartan operator d/dt. Likewise, the Calabi flow arises as Toda field equation
associated to a supercontinual algebra with odd Cartan operator d/d \theta -
\theta d/dt. Thus, taking the square root of the Cartan operator allows to
connect the two distinct classes of geometric deformations of second and fourth
order, respectively. The algebra is also used to construct formal solutions of
the Calabi flow in terms of free fields by Backlund transformations, as for the
Ricci flow. Some applications of the present framework to the general class of
Robinson-Trautman metrics that describe spherical gravitational radiation in
vacuum in four space-time dimensions are also discussed. Further iteration of
the algorithm allows to construct an infinite hierarchy of higher order
geometric flows, which are integrable in two dimensions and they admit
immediate generalization to Kahler manifolds in all dimensions. These flows
provide examples of more general deformations introduced by Calabi that
preserve the Kahler class and minimize the quadratic curvature functional for
extremal metrics.Comment: 54 page
Conifold geometries, topological strings and multi-matrix models
We study open B-model representing D-branes on 2-cycles of local Calabi--Yau
geometries. To this end we work out a reduction technique linking D-branes
partition functions and multi-matrix models in the case of conifold geometries
so that the matrix potential is related to the complex moduli of the conifold.
We study the geometric engineering of the multi-matrix models and focus on
two-matrix models with bilinear couplings. We show how to solve this models in
an exact way, without resorting to the customary saddle point/large N
approximation. The method consists of solving the quantum equations of motion
and using the flow equations of the underlying integrable hierarchy to derive
explicit expressions for correlators. Finally we show how to incorporate in
this formalism the description of several group of D-branes wrapped around
different cycles.Comment: 35 pages, 5.3 and 6 revise
Self-Consistent Sources and Conservation Laws for a Super Broer-Kaup-Kupershmidt Equation Hierarchy
Based on the matrix Lie superalgebras and supertrace identity, the integrable super
Broer-Kaup-Kupershmidt hierarchy with self-consistent sources is established. Furthermore, we
establish the infinitely many conservation laws for the integrable super Broer-Kaup-Kupershmidt
hierarchy. In the process of computation especially, Fermi variables also play an important role in
super integrable systems
Unitary One Matrix Models: String Equations and Flows
We review the Symmetric Unitary One Matrix Models. In particular we discuss
the string equation in the operator formalism, the mKdV flows and the Virasoro
Constraints. We focus on the \t-function formalism for the flows and we
describe its connection to the (big cell of the) Sato Grassmannian \Gr via
the Plucker embedding of \Gr into a fermionic Fock space. Then the space of
solutions to the string equation is an explicitly computable subspace of
\Gr\times\Gr which is invariant under the flows.Comment: 20 pages (Invited talk delivered by M. J. Bowick at the Vth Regional
Conference on Mathematical Physics, Edirne Turkey: December 15-22, 1991.
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