Populations of solutions of the 𝑋𝑋𝑋 Bethe equations associated to Kac-Moody algebras

2005 ◽  
pp. 95-102 ◽  
Author(s):  
E. Mukhin ◽  
A. Varchenko
Keyword(s):  
Bethe Equations

scholarly journals A REVIEW OF INTEGRABLE DEFORMATIONS IN AdS/CFT

2007 ◽  
Vol 22 (13) ◽  
pp. 915-930 ◽  
Author(s):  
IAN SWANSON
Keyword(s):  
String Theory ◽  
Bethe Ansatz ◽  
Energy Spectra ◽  
Yang Mills ◽  
Twisted String ◽  
Pp Wave ◽  
Integrable Deformations ◽  
Type Iib String Theory ◽  
Bethe Equations ◽  
Wave Limit

Marginal β deformations of [Formula: see text] super-Yang–Mills theory are known to correspond to a certain class of deformations of the S5 background subspace of type IIB string theory in AdS5×S5. An analogous set of deformations of the AdS5 subspace is reviewed here. String energy spectra computed in the near-pp-wave limit of these backgrounds match predictions encoded by discrete, asymptotic Bethe equations, suggesting that the twisted string theory is classically integrable in this regime. These Bethe equations can be derived algorithmically by relying on the existence of Lax representations, and on the Riemann–Hilbert interpretation of the thermodynamic Bethe ansatz. This letter is a review of a seminar given at the Institute for Advanced Study, based on research completed in collaboration with McLoughlin.

scholarly journals Inner products in integrable Richardson-Gaudin models

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Pieter W. Claeys ◽  
Dimitri Van Neck ◽  
Stijn De Baerdemacker
Keyword(s):  
Domain Wall ◽  
Integrable Models ◽  
Partition Functions ◽  
Dual Representation ◽  
Determinant Formula ◽  
Quadratic Equations ◽  
Conserved Charges ◽  
Inner Products ◽  
Gaudin Models ◽  
Bethe Equations

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

scholarly journals On quantum corrections to spinning strings and Bethe equations

2005 ◽  
Vol 629 (2-4) ◽  
pp. 102-110 ◽  
Author(s):  
N. Beisert ◽  
A.A. Tseytlin
Keyword(s):  
Quantum Corrections ◽  
Bethe Equations

CANONICAL BÄCKLUND TRANSFORMATION — A NEW DISCRETE INTEGRABLE SYSTEM AND BETHE ANSATZ

2005 ◽  
Vol 20 (18) ◽  
pp. 4355-4361
Author(s):  
SUPRIYA MUKHERJEE ◽  
A. ROY CHOWDHURY ◽  
A. GHOSE CHOUDHURY
Keyword(s):  
Explicit Form ◽  
Integrable System ◽  
Canonical Variable ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
R Matrix ◽  
Discrete Integrable System ◽  
Lax Operator ◽  
Bethe Equations ◽  
Quantization Problem

A new discrete Lax operator involving discrete canonical variable is introduced which generate new integrable system, and is analyzed in the light of the new concept of canonical Bäcklund transformation and classical r-matrix. The generating function of the transformation is explicitly deduced. The second half of the paper deals with the quantization problem where an explicit form of the Bethe equations are deduced.

scholarly journals On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS3×S3×T4

2016 ◽  
Vol 50 (2) ◽  
pp. 024004 ◽  
Author(s):  
Riccardo Borsato ◽  
Olof Ohlsson Sax ◽  
Alessandro Sfondrini ◽  
Bogdan Stefański ◽  
Alessandro Torrielli
Keyword(s):  
Bethe Equations ◽  
Yangian Symmetry

scholarly journals Quantum strings and Bethe equations

2005 ◽  
Vol 53 (7-8) ◽  
pp. 846-851 ◽  
Author(s):  
G. Arutyunov
Keyword(s):  
Bethe Equations

scholarly journals Bethe equations `on the wrong side of the equator'

1999 ◽  
Vol 32 (12) ◽  
pp. 2333-2340 ◽  
Author(s):  
G P Pronko ◽  
Yu G Stroganov
Keyword(s):  
Wrong Side ◽  
Bethe Equations
Sign in / Sign up

Export Citation Format

Share Document