417 research outputs found
Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions
Recently a special vortex string was found [5] in a class of soliton vortices
supported in four-dimensional Yang-Mills theories that under certain conditions
can become infinitely thin and can be interpreted as a critical ten-dimensional
string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the
Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the
world-sheet theory for orientational and size moduli described by the weighted
CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a
non-compact Calabi-Yau space.
We study the above vortex string from the standpoint of string theory,
focusing on the massless states in four dimensions. In the generic case all
massless modes are non-normalizable, hence, no massless gravitons or vector
fields are predicted in the physical spectrum. However, at the selfdual point
(at strong coupling) weighted CP(2,2) admits deformation of the complex
structure, resulting in a single massless hypermultiplet in the bulk. We
interpret it as a composite "baryon."Comment: 15 pages, no figures, minor correction
-opers, the -Langlands correspondence, and quantum/classical duality
A special case of the geometric Langlands correspondence is given by the
relationship between solutions of the Bethe ansatz equations for the Gaudin
model and opers - connections on the projective line with extra structure. In
this paper, we describe a deformation of this correspondence for . We
introduce a difference equation version of opers called -opers and prove a
-Langlands correspondence between nondegenerate solutions of the Bethe
ansatz equations for the XXZ model and nondegenerate twisted -opers with
regular singularities on the projective line. We show that the
quantum/classical duality between the XXZ spin chain and the trigonometric
Ruijsenaars-Schneider model may be viewed as a special case of the
-Langlands correspondence. We also describe an application of -opers to
the equivariant quantum -theory of the cotangent bundles to partial flag
varieties.Comment: v3: 32 pages, 2 figures; minor revisions, to appear in Commun. Math.
Phy
Quantum K-theory of Quiver Varieties and Many-Body Systems
We define quantum equivariant K-theory of Nakajima quiver varieties. We
discuss type A in detail as well as its connections with quantum XXZ spin
chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit
which produces a K-theoretic version of results of Givental and Kim, connecting
quantum geometry of flag varieties and Toda lattice.Comment: v3: 33 pages, some clarifications and correction
The Zoo of Opers and Dualities
We investigate various spaces of -opers and their deformations. For
each type of such opers, we study the quantum/classical duality, which relates
quantum integrable spin chains with classical solvable many body systems. In
this context, quantum/classical dualities serve as an interplay between two
different coordinate systems on the space of opers. We also establish
correspondences between the underlying oper spaces, which recently had multiple
incarnations in symplectic duality and bispectral duality.Comment: v2: 31 pages, typos corrected, references added, to appear in IMR
Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: surfaces of bismuth tellurohalides
Spintronics is aimed at active controlling and manipulating the spin degrees
of freedom in semiconductor devices. A promising way to achieve this goal is to
make use of the tunable Rashba effect that relies on the spin-orbit interaction
(SOI) in a two-dimensional (2D) electron system immersed in an
inversion-asymmetric environment. The SOI induced spin-splitting of the
2D-electron state provides a basis for many theoretically proposed spintronic
devices. However, the lack of semiconductors with large Rashba effect hinders
realization of these devices in actual practice. Here we report on a giant
Rashba-type spin splitting in 2D electron systems which reside at
tellurium-terminated surfaces of bismuth tellurohalides. Among these
semiconductors, BiTeCl stands out for its isotropic metallic surface-state band
with the Gamma-point energy lying deep inside the bulk band gap. The giant
spin-splitting of this band ensures a substantial spin asymmetry of the
inelastic mean free path of quasiparticles with different spin orientations.Comment: 12 pages, 5 figure
- β¦