scholarly journals Hyperelliptic Prym Varieties and Integrable Systems

2001 ◽  
Vol 221 (1) ◽  
pp. 169-196 ◽  
Author(s):  
Rui Loja Fernandes ◽  
Pol Vanhaecke
Keyword(s):  
Integrable Systems ◽  
Prym Varieties

scholarly journals Prym varieties and integrable systems

1997 ◽  
Vol 5 (2) ◽  
pp. 279-332 ◽  
Author(s):  
Yingchen Li ◽  
Mothico Mulase
Keyword(s):  
Integrable Systems ◽  
Prym Varieties

scholarly journals Dimensions of Prym varieties

2001 ◽  
Vol 26 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Amy E. Ksir
Keyword(s):  
Irreducible Representation ◽  
Galois Group ◽  
Integrable Systems ◽  
Prym Variety ◽  
Lax Pairs ◽  
Prym Varieties ◽  
Branched Cover ◽  
Witten Theory

Given a tame Galois branched cover of curvesπ:X→Ywith any finite Galois groupGwhose representations are rational, we compute the dimension of the (generalized) Prym varietyPrymρ(X)corresponding to any irreducible representationρofG. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. However, the formula is much more general and its computation and proof are entirely algebraic.

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

scholarly journals Separation of variables in AdS/CFT: functional approach for the fishnet CFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk
Keyword(s):  
Integrable Systems ◽  
Density Operator ◽  
Numerical Evaluation ◽  
Lagrangian Density ◽  
Separation Of Variables ◽  
Functional Approach ◽  
Quantum Integrable Systems ◽  
Arbitrary State ◽  
Nontrivial Coupling ◽  
The One

Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

scholarly journals Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander
Keyword(s):  
Integrable Systems ◽  
Geometric Description ◽  
Discrete Integrable Systems ◽  
Birational Maps ◽  
Base Points ◽  
Special Geometry ◽  
Low Degree ◽  
Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

Sign in / Sign up

Export Citation Format

Share Document