Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras

Atsuo Kuniba; Junji Suzuki

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Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras

Atsuo Kuniba, Junji Suzuki

High Energy Physics - Theory · Submitted 25 Aug 1994

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The authors' main claim Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.

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arXiv IDhep-th/9408135 (version 1)

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CitationAtsuo Kuniba, Junji Suzuki. "Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras." arXiv:hep-th/9408135 (1994). https://pith.science/paper/DHJGFKQD

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Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras $U_q(X^{(\kappa)}_n)$ where $X^{(\kappa)}_n = A^{(2)}_n, D^{(2)}_n, E^{(2)}_6$ and $D^{(3)}_4$. Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras $U_q(X^{(\kappa)}_n)$ where $X^{(\kappa)}_n = A^{(2)}_n, D^{(2)}_n, E^{(2)}_6$ and $D^{(3)}_4$.	contribution 0.98	0.87	0.33	asserted 0.82
s1	Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.	result 0.90	0.84	0.33	speculative 0.58

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Original abstract

Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras $U_q(X^{(\kappa)}_n)$ where $X^{(\kappa)}_n = A^{(2)}_n, D^{(2)}_n, E^{(2)}_6$ and $D^{(3)}_4$. Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.

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7 arXiv papers cite this in 17 sentences

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Builds on it 1 paper

The reduction procedures in this section is an extension of the methods to derive the Bethe ansatz equations and T-functions for twisted quantum affine algebras from the ones for non-twisted quantum affine algebras [ref] (see also [ref] ).

Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains · Reductions of T- and Q-functions · 0.94

Compares with it 1 paper

Here we summarize expressions which are necessary for precise comparison of our results and those of [ref] (and [ref] ).

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system · Note added [This note is not included in the journal version (Nuclear Physics B 972 (2021) 115563). There is no change i · 1.00

Cites it as background 3 papers

Originally, the T-systems are systems of relations among the Kirillov–Reshetikhin modules [ref] in the Grothendieck rings of modules over quantum affine algebras and Yangians [ref] .

T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras · Introduction · 0.97
The T-system was proposed for quantum integrable systems associated with quantum affine algebras (or Yangians) [ref] (see also [ref] for $U_q(A_1^(1))$ case) and superalgebras [ref] .

Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system · Introduction · 1.00
Some partial results have already been obtained in the previous papers [ref] , but the whole picture is still unclear, which contrasts with the well-understood non-superalgebra cases [ref] .

Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains · Concluding remarks · 0.88

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