Polynomial Relations for q-Characters via the ODE/IM Correspondence

Abstract

Abstract. Let U q (b) be the Borel subalgebra of a quantum affine algebra of type X (1) n (X = A, B, C, D). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the q-characters of certain representations of U q (b).

ODE/IM correspondence and the Argyres-Douglas theory

“…The correspondence between (7) and (27) was also confirmed by using other functional relations such as Baxter's T-Q relations and the quantum Wronskians [34,36].…”

“…Let us compare this 2d integrable model (27) obtained from the ODE/IM correspondence with the 2d CFT obtained by the 4d/2d correspondence. The chiral algebra corresponding to AD theories (with no flavor symmetry) engineered from the M5 branes have been classified in [9].…”

“…Here we focus on the AD theory without flavor symmetry. For the A n -type AD theories where n is even, the corresponding 2d CFT is the coset CFT (27).…”

“…We propose that the (g, A m )-type quantum spectral curve is given by the ODE associated with the conformal limit of the modified affine Toda field equations associated for the affine Lie algebraĝ ∨ . For a classical Lie algebra g the ODEs have been constructed by [19,27,22]. Let us consider the linear problem for the modified affine Toda field equation forĝ of a simply laced Lie algebra g of rank n. In the conformal limit [20,22,24], it takes the form:…”

“…The ordinary differential equations for the integrable models associated with the Bethe equations of a classical Lie algebra g have been proposed in [19]. For a general Lie algebra g, it is obtained from the conformal limit of the linear problem for the modified affine Toda field equations associated withĝ ∨ , while the full linear problem describes the massive version of the ODE/IM correspondence [20,21,22,23,24,25,26] (see also [27] for a classical Lie algebra case). Hereĝ denotes the untwisted affine Lie algebra of g andĝ ∨ the Langlands dual ofĝ.…”