Topology of the Real Part of Hyperelliptic Jacobian Associated with the Periodic Toda Lattice
نویسنده
چکیده
This paper concerns the topology of the isospectral real manifold of the sl(N) periodic Toda lattice consisting of 2 different systems. The solutions of those systems contain blow-ups, and the set of those singular points defines a devisor of the manifold. Then adding the divisor, the manifold is compactified as the real part of the (N − 1)dimensional Jacobi variety associated with a hyperelliptic Riemann surface of genus g = N −1. We also study the real structure of the divisor, and then provide conjectures on the topology of the affine part of the real Jacobian and on the gluing rule over the divisor to compactify the manifold based upon the sign-representation of the Weyl group of sl(N). 1. Preliminary Let us start with an infinite Toda lattice which is defined as a hamiltonian system with the hamiltonian,
منابع مشابه
On the Moduli Space of N =2 Supersymmetric G2 Gauge Theory
We apply the method of confining phase superpotentials to N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G2. Our findings are consistent with the spectral curve of the periodic Toda lattice, but do not agree with the hyperelliptic curve suggested previously in the literature. We also apply the method to theories with fundamental matter, treating both the example of SO(5...
متن کاملHill's Surfaces and Their Theta Functions by H. P. Mckean and E. Trubowitz
Preface. In this paper we continue the investigations begun in McKeanTrubowitz [1976] of infinite-genus hyperelliptic Riemann surfaces S which are constructed from the spectrum of a Hill's operator. Let q be a real infinitely differentiable function of 0 < { < 1 of period 1. The Hill's operator is Q = — d/di + q(£). The periodic and antiperiodic eigenfunctions of Q determine an infinite spectru...
متن کاملThe Finite Non-periodic Toda Lattice: a Geometric and Topological Viewpoint
In 1967, Japanese physicist Morikazu Toda published the seminal papers [78] and [79], exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the decades that followed, Toda’s system of particles has been generalized in different directions, each with its own analytic, geometric, and topological characteristics that sets it apart from the o...
متن کاملSeparation of Variables and Vacuum Structure of Massive N=2 Susy Qcd
We show how the method of separation of variables can be used to construct integrable models corresponding to curves describing vacuum structure of N = 2 SUSY Yang-Mills theories. In particular, we consider hyperelliptic curves of N = 2 SUSY QCD with even number of hypermultiplets with pairwise coinciding masses. We show that in the SU(3) case the curves correspond to the generalisations of the...
متن کاملSeparation of variables for the D n type periodic Toda lattice
We prove separation of variables for the most general (Dn type) periodic Toda lattice with 2 × 2 Lax matrix. It is achieved by finding proper normalisation for the corresponding Baker-Akhiezer function. Separation of variables for all other periodic Toda lattices associated with infinite series of root systems follows by taking appropriate limits.
متن کامل