6 research outputs found
Noncompact SL(2,R) spin chain
We consider the integrable spin chain model - the noncompact SL(2,R) spin
magnet. The spin operators are realized as the generators of the unitary
principal series representation of the SL(2,R) group. In an explicit form, we
construct R-matrix, the Baxter Q-operator and the transition kernel to the
representation of the Separated Variables (SoV). The expressions for the energy
and quasimomentum of the eigenstates in terms of the Baxter Q-operator are
derived. The analytic properties of the eigenvalues of the Baxter operator as a
function of the spectral parameter are established. Applying the diagrammatic
approach, we calculate Sklyanin's integration measure in the separated
variables and obtain the solution to the spectral problem for the model in
terms of the eigenvalues of the Q-operator. We show that the transition kernel
to the SoV representation is factorized into a product of certain operators
each depending on a single separated variable.Comment: 29 pages, 12 figure
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Bethe Subalgebras in Twisted Yangians
We study analogues of the Yangian of the Lie algebra for the other
classical Lie algebras and . We call them twisted Yangians. They
are coideal subalgebras in the Yangian of and admit
homomorphisms onto the universal enveloping algebras and
respectively. In every twisted Yangian we construct a family of maximal
commutative subalgebras parametrized by the regular semisimple elements of the
corresponding classical Lie algebra. The images in and of
these subalgebras are also maximal commutative.Comment: 26 pages, amstex, misprints correcte
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Worldsheet Scattering in AdS_5 x S^5
We calculate the S-matrix in the gauge-fixed sigma-model on AdS_5 x S^5 to
the leading order in perturbation theory, and analyze how supersymmetry is
realized on the scattering states. A mild nonlocality of the supercharges
implies that their action on multi-particle states does not follow the Leibniz
rule, which is replaced by a nontrivial coproduct. The plane wave symmetry
algebra is thus naturally enhanced to a Hopf algebra. The scattering matrix
elements obey the classical Yang-Baxter equation modified by the existence of
the coproduct. This structure mirrors that of the large 't Hooft coupling
expansion of the S-matrix for the spin chain in the dual super-Yang-Mills
theory.Comment: 51 pages, v2: references added, v3: sign in (2.12), (6.19) and (6.21)
corrected; v4: discussion of classical YBE is considerably modifie