350 research outputs found
Spectral Duality in Integrable Systems from AGT Conjecture
We describe relationships between integrable systems with N degrees of
freedom arising from the AGT conjecture. Namely, we prove the equivalence
(spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N)
Gaudin model both at classical and quantum level. The former one appears on the
gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further
the Seiberg-Witten) limit while the latter one is natural on the CFT side. At
the classical level, the duality transformation relates the Seiberg-Witten
differentials and spectral curves via a bispectral involution. The quantum
duality extends this to the equivalence of the corresponding Baxter-Schrodinger
equations (quantum spectral curves). This equivalence generalizes both the
spectral self-duality between the 2x2 and NxN representations of the Toda chain
and the famous AHH duality
Space-Time Foam From Non-Commutative Instantons
We show that a U(1) instanton on non-commutative R^4 corresponds to a
supersymmetric non-singular U(1) gauge field on a commutative Kahler manifold X
which is a blowup of C^2 at a finite number of points. For instanton charge k
the manifold X can be viewed as a space-time foam. A direct connection with
integrable systems of Calogero-Moser type is established. We also make some
comments on the non-abelian case.Comment: harvmac, 22 pp; v.2, refs added, a section adde
Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double
It is shown that the elliptic Ruijsenaars-Schneider model can be obtained
from the affine Heisenberg Double by means of the Poisson reduction procedure.
The dynamical -matrix naturally appears in the construction.Comment: latex, 15 pages, a new section is added where we show that the
problem of solving the equations of motion is equivalent to the factorization
proble
On Integrable Systems and Supersymmetric Gauge Theories
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten
hypothesis are discussed. The main ingredients of the formulation of the
finite-gap solutions to integrable equations in terms of complex curves and
generating 1-differential are presented, the invariant sense of these
definitions is illustrated. Recently found exact nonperturbative solutions to
N=2 SUSY gauge theories are formulated using the methods of the theory of
integrable systems and where possible the parallels between standard quantum
field theory results and solutions to integrable systems are discussed.Comment: LaTeX, 38 pages, no figures; based on the lecture given at INTAS
School on Advances in Quantum Field Theory and Statistical Mechanics, Como,
Italy, 1996; minor changes, few references adde
The Partonic Nature of Instantons
In both Yang-Mills theories and sigma models, instantons are endowed with
degrees of freedom associated to their scale size and orientation. It has long
been conjectured that these degrees of freedom have a dual interpretation as
the positions of partonic constituents of the instanton. These conjectures are
usually framed in d=3+1 and d=1+1 dimensions respectively where the partons are
supposed to be responsible for confinement and other strong coupling phenomena.
We revisit this partonic interpretation of instantons in the context of d=4+1
and d=2+1 dimensions. Here the instantons are particle-like solitons and the
theories are non-renormalizable. We present an explicit and calculable model in
d=2+1 dimensions where the single soliton in the CP^N sigma-model can be shown
to be a multi-particle state whose partons are identified with the ultra-violet
degrees of freedom which render the theory well-defined at high energies. We
introduce a number of methods which reveal the partons inside the soliton,
including deforming the sigma model and a dual version of the Bogomolnyi
equations. We conjecture that partons inside Yang-Mills instantons hold the key
to understanding the ultra-violet completion of five-dimensional gauge
theories.Comment: 28 pages. v3: extra references and comments. Mathematica notebooks
for the figures can be downloaded from
http://www.damtp.cam.ac.uk/user/dt281/parton.htm
The Dn Ruijsenaars-Schneider model
The Lax pair of the Ruijsenaars-Schneider model with interaction potential of
trigonometric type based on Dn Lie algebra is presented. We give a general form
for the Lax pair and prove partial results for small n. Liouville integrability
of the corresponding system follows a series of involutive Hamiltonians
generated by the characteristic polynomial of the Lax matrix. The rational case
appears as a natural degeneration and the nonrelativistic limit exactly leads
to the well-known Calogero-Moser system associated with Dn Lie algebra.Comment: LaTeX2e, 14 pages; more remarks are added in the last sectio
On Hamiltonian structure of the spin Ruijsenaars-Schneider model
The Hamiltonian structure of spin generalization of the rational
Ruijsenaars-Schneider model is found by using the Hamiltonian reduction
technique. It is shown that the model possesses the current algebra symmetry.
The possibility of generalizing the found Poisson structure to the
trigonometric case is discussed and degeneration to the Euler-Calogero-Moser
system is examined.Comment: latex, 16 pages, references are adde
Hamiltonian of Tensionless Strings with Tensor Central Charge Coordinates
A new class of twistor-like string models in four-dimensional space-time
extended by the addition of six tensorial central charge (TCC) coordinates
is studied. The Hamiltonian of tensionless string in the extended
space-time is derived and its symmetries are investigated. We establish that
the string constraints reduce the number of independent TCC coordinates
to one real effective coordinate which composes an effective
5-dimensional target space together with the coordinates. We construct
the P.B. algebra of the first class constraints and discover that it coincides
with the P.B. algebra of tensionless strings. The Lorentz covariant
antisymmetric Dirac -matrix of the P.B. of the second class
constraints is constructed and its algebraic structure is further presented.Comment: 18 pages, Latex, no figure
Wall and Anti-Wall in the Randall-Sundrum Model and A New Infrared Regularization
An approach to find the field equation solution of the Randall-Sundrum model
with the extra axis is presented. We closely examine the infrared
singularity. The vacuum is set by the 5 dimensional Higgs field. Both the
domain-wall and the anti-domain-wall naturally appear, at the {\it ends} of the
extra compact axis, by taking a {\it new infrared regularization}. The
stability is guaranteed from the outset by the kink boundary condition. A {\it
continuous} (infrared-)regularized solution, which is a truncated {\it Fourier
series} of a {\it discontinuous} solution, is utilized.The ultraviolet-infrared
relation appears in the regularized solution.Comment: 36 pages, 29 eps figure file
- …