37 research outputs found
Yangian of AdS3/CFT2 and its deformation
We construct highest-weight modules and a Yangian extension of the centrally
extended sl(1|1)^2 superalgebra, that is a symmetry of the worldsheet
scattering associated with the AdS3/CFT3 duality. We demonstrate that the
R-matrix intertwining atypical modules is of a trigonometric type. We also
consider a quantum deformation of this superalgebra, its modules, and obtain a
quantum affine extension of the Drinfeld-Jimbo type that describes a deformed
worldsheet scattering.Comment: 21 pages, 1 figure. Final version. Accepted to J. Geom. and Phy
Reflection algebras for sl(2) and gl(1|1)
We present a generalization the G. Letzter's theory of quantum symmetric
pairs of semisimple Lie algebras for the case of quantum affine algebras. We
then study solutions of the reflection equation for the quantum affine algebras
sl(2) and gl(1|1) and their Yangian limit for singlet (diagonal) and vector
(non-diagonal) boundary conditions. We construct the corresponding quantum
affine coideal subalgebras that are based on the quantum symmetric pairs, and
the (generalized) twisted Yangians.Comment: 31 page; v2: updated versio
On boundary fusion and functional relations in the Baxterized affine Hecke algebra
We construct boundary type operators satisfying fused reflection equation for
arbitrary representations of the Baxterized affine Hecke algebra. These
operators are analogues of the fused reflection matrices in solvable half-line
spin chain models. We show that these operators lead to a family of commuting
transfer matrices of Sklyanin type. We derive fusion type functional relations
for these operators for two families of representations.Comment: 35 pages, 3 figure
Yangian symmetry of the Y=0 maximal giant graviton
We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from
boundaries with no degrees of freedom. We present the generalized twisted
boundary Yangian of open strings ending on boundaries which preserve only a
subalgebra h of the bulk algebra g, where (g,h) is a symmetric pair. This is
realized by open strings ending on the D3 brane known as the Y=0 maximal giant
graviton in AdS_5 x S^5. We also consider the Yangian symmetry of the boundary
which preserves an su(1|2) subalgebra only.Comment: 17 pages, v2: minor correction made, accepted for publication in JHE
Algebraic Bethe ansatz for spinor R-matrices
© 2022 V. Regelskis. Published by the SciPost Foundation. This work is licensed under the Creative Commons Attribution 4.0 International License.We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector Rmatrices. These R-matrices are then used to construct transfer matrices for Uq2(so2n+1)- and Uq(so2n+2)-symmetric closed spin chains. Their eigenvectors and eigenvalues are computed.Peer reviewe
Integrable open spin-chains in AdS3/CFT2 correspondences
We study integrable open boundary conditions for d(2,1;\alpha)^2 and
psu(1,1|2)^2 spin-chains. Magnon excitations of these open spin-chains are
mapped to massive excitations of type IIB open superstrings ending on D-branes
in the AdS_3 x S^3 x S^3 x S^1 and AdS_3 x S^3 x T^4 supergravity geometries
with pure R-R flux. We derive reflection matrix solutions of the boundary
Yang-Baxter equation which intertwine representations of a variety of boundary
coideal subalgebras of the bulk Hopf superalgebra. Many of these integrable
boundaries are matched to D1- and D5-brane maximal giant gravitons.Comment: v1: 61 pages, 6 figures; v2: minor changes and reference added; v3:
minor changes, 60 pages, version accepted to journa
Vertex Representations for Yangians of Kac-Moody algebras
30 pagesUsing vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the PBW property for simply laced affine Yangians.Peer reviewe
Drinfeld J Presentation of Twisted Yangians
We present a quantization of a Lie coideal structure for twisted half-loop
algebras of finite-dimensional simple complex Lie algebras. We obtain algebra
closure relations of twisted Yangians in Drinfeld J presentation for all
symmetric pairs of simple Lie algebras and for simple twisted even half-loop
Lie algebras. We provide the explicit form of the closure relations for twisted
Yangians in Drinfeld J presentation for the Lie algebra
Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
We present a nested algebraic Bethe ansatz for one-dimensional so2n- and sp2n-symmetric
open spin chains with diagonal boundary conditions. The monodromy matrix of these spin
chains satisfies the defining relations on the extended twisted Yangians X_\rho(so2n; so2n^\rho)^tw and
X_\rho(sp2n; sp2n^\rho)^tw, respectively. We use a generalisation of the De Vega and Karowski approach
allowing us to relate the spectral problem of so2n- or sp2n-symmetric open spin chain to that
of gln-symmetric open spin chain studied by Belliard and Ragoucy. We explicitly derive
the structure of Bethe vectors, their eigenvalues and the nested Bethe equations. We also
provide a proof of Belliard and Ragoucy's trace formula for Bethe vectors of gln-symmetric
open spin chains