## SciPost Submission Page

# Algebraic structure of classical integrability for complex sine-Gordon

### by J. Avan, L. Frappat, E. Ragoucy

### Submission summary

As Contributors: | Luc FRAPPAT |

Arxiv Link: | https://arxiv.org/abs/1911.06720v2 |

Date accepted: | 2020-02-11 |

Date submitted: | 2020-01-30 |

Submitted by: | FRAPPAT, Luc |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Mathematical Physics |

Approach: | Theoretical |

### Abstract

The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.

###### Current status:

Editorial decision:
For Journal SciPost Physics: Publish

(status: Editorial decision fixed and (if required) accepted by authors)

### List of changes

Dear Editor,

We have revised our manuscript according to the requested changes of the referee. Here are the major modifications:

- page 2, the sentence has been modified to clarify the point.

- we added three paragraphs in section 3 :

a/ page 8, a comment on an alternative procedure of quantizing the complex sine-Gordon model (with refs 23 and 24 added);

b/ page 8, a comment on the potential existence of discrete quantum systems related to CSG (with ref. 26).

c/ page 9, a final paragraph about the feasibility of the quantization itself.

In addition, the grammar and the punctuation have been revised.

Best regards,

The authors