619 research outputs found
Bulk correlation functions in 2D quantum gravity
We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville
gravity with non-rational matter central charge c<1, following and comparing
two approaches. The continuous CFT approach exploits the action on the tachyons
of the ground ring generators deformed by Liouville and matter ``screening
charges''. A by-product general formula for the matter 3-point OPE structure
constants is derived. We also consider a ``diagonal'' CFT of 2D quantum
gravity, in which the degenerate fields are restricted to the diagonal of the
semi-infinite Kac table. The discrete formulation of the theory is a
generalization of the ADE string theories, in which the target space is the
semi-infinite chain of points.Comment: 14 pages, 2 figure
On the timelike Liouville three-point function
In a recent paper, D. Harlow, J. Maltz, and E. Witten showed that a
particular proposal for the timelike Liouville three-point function, originally
due to Al. Zamolodchikov and to I. Kostov and V. Petkova, can actually be
computed by the original Liouville path integral evaluated on a new integration
cycle. Here, we discuss a Coulomb gas computation of the timelike three-point
function and show that an analytic extension of the Selberg type integral
formulas involved reproduces the same expression, including the adequate
normalization. A notable difference with the spacelike calculation is pointed
out.Comment: 11 pages. v2 comments and references added. Appropriate credit is
given to Ref. arXiv:hep-th/0512346, where the Coulomb gas computation of the
c<1 theory has already been discusse
Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS)
related to the symmetric BD.I-type symmetric spaces and their reductions. We
briefly outline the direct and the inverse scattering method for the relevant
Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing
method to obtain the two-soliton solution and analyze the soliton interactions
of the MNLS equations and some of their reductions.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009
Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
We present two new families of stationary solutions for equations of
Bose-Fermi mixtures with an elliptic function potential with modulus . We
also discuss particular cases when the quasiperiodic solutions become periodic
ones. In the limit of a sinusoidal potential () our solutions model a
quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical
lattice. In the limit the solutions are expressed by hyperbolic
function solutions (vector solitons). Thus we are able to obtain in an unified
way quasi-periodic and periodic waves, and solitons. The precise conditions for
existence of every class of solutions are derived. There are indications that
such waves and localized objects may be observed in experiments with cold
quantum degenerate gases.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Scattering of Long Folded Strings and Mixed Correlators in the Two-Matrix Model
We study the interactions of Maldacena's long folded strings in
two-dimensional string theory. We find the amplitude for a state containing two
long folded strings to come and go back to infinity. We calculate this
amplitude both in the worldsheet theory and in the dual matrix model, the
Matrix Quantum Mechanics. The matrix model description allows to evaluate the
amplitudes involving any number of long strings, which are given by the mixed
trace correlators in an effective two-matrix model.Comment: 39 pages, 6 figure
On Kernel Formulas and Dispersionless Hirota Equations
We rederive dispersionless Hirota equations of the dispersionless Toda
hierarchy from the method of kernel formula provided by Carroll and Kodama. We
then apply the method to derive dispersionless Hirota equations of the extended
dispersionless BKP(EdBKP) hierarchy proposed by Takasaki. Moreover, we verify
associativity equations (WDVV equations) in the EdBKP hierarchy from
dispersionless Hirota equations and give a realization of associative algebra
with structure constants expressed in terms of residue formula.Comment: 30 pages, minor corrections, references adde
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