• Corpus ID: 249210165

Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine $\mathfrak{sl}_2$ Gaudin model

@inproceedings{Franzini2022QuarticHA,
  title={Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine \$\mathfrak\{sl\}\_2\$ Gaudin model},
  author={Tommaso Franzini and Charles A. S. Young},
  year={2022}
}
In this work we will use a general procedure to construct higher local Hamiltonians for the affine sl2 Gaudin model. We focus on the first non-trivial example, the quartic Hamiltonians. We show by direct calculation that the quartic Hamiltonians commute amongst themselves and with the quadratic Hamiltonians which define the model. We go on to introduce a certain next-to-leading-order semi-classical limit of the model. In this limit, we are able to write down the full hierarchy of higher local… 

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References

SHOWING 1-10 OF 32 REFERENCES

Gaudin model, Bethe Ansatz and critical level

We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the

Cubic hypergeometric integrals of motion in affine Gaudin models

We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We

ODE/IQFT correspondence for the generalized affine sl(2) Gaudin model

An integrable system is introduced, which is a generalization of the sl(2) quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within

Quantization of soliton systems and Langlands duality

We consider the problem of quantization of classical soliton integrable systems, such as the KdV hierarchy, in the framework of a general formalism of Gaudin models associated to affine Kac--Moody

Quantization of the Gaudin System

In this article we exploit the known commutative family in Y(gl(n)) - the Bethe subalgebra - and its special limit to construct quantization of the Gaudin integrable system. We give explicit

Integrable sigma models at RG fixed points: quantisation as affine Gaudin models

The goal of this paper is to make first steps towards the quantisation of integrable non-linear sigma models using the formalism of affine Gaudin models, by approaching these theories through their

4D Chern–Simons theory and affine Gaudin models

  • B. Vicedo
  • Mathematics
    Letters in Mathematical Physics
  • 2021
We relate two formalisms recently proposed for describing classical integrable field theories. The first (Costello and Yamazaki in Gauge Theory and Integrability, III, 2019) is based on the action of