Supersymmetric Bethe ansatz and Baxter equations from discrete Hirota dynamics

By Vladimir Kazakov, A. Sorin, A. Zabrodin. 2007

133 citations recorded by the source corpus.

Abstract We show that eigenvalues of the family of Baxter Q -operators for supersymmetric integrable spin chains constructed with the g l ( K | M ) -invariant R -matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super-spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic tool is a chain of Backlund transformations for the Hirota equation connecting quantum transfer matrices. This approach also provides a systematic way to derive the complete set of generalized Baxter equations for super-spin chains.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d6917f0564d27b3a1facb23a194ab9547e33c0a

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Citations in the corpus

T-systems and Y-systems in integrable systems (2010, background): “They are constructed from the a = 1 case [19, 22] in a way analogous to (9.”
On string S-matrix, bound states and TBA (2007, background): “As a final remark, we note that it would be interesting to understand how the derivation of the Hirota difference equations for the canonical S-matrix [72] could be extended to the “twisted” S-matrix (9.”
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation (2012, unknown): “oes to iu 1;k i 2 , u 2;k and u 3;k+ 2 . In the gauge where TL/R 0;s = T L/R a;0 = 1, the other T functions of the right and left (decoupled) SU(2j2) wings are obtained from the generating functional [37,55] W = 1 ei˚ B+(+)Q 1 B+( )Q+ 1 R (+) R ( ) D 1 ei Q++ 2 Q 1 Q 2Q + 1 R (+) R ( ) D 1 (174) ”
Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 (2014, methodology): “The second way explicitly operates with 6 parameters: 3 Dynkin labels [r1, r2, r3] of the su(4) subalgebra together with 3 Dynkin labels [q1, q2, q3] of the su(2, 2), defined with respect to the highest 54These diagrams are introduced and explained for spin chains in [32], but without specification ”