19 problems

Full-spectrum conjecture. By the same method, including extra logarithmic singularities, one has direct access to the full spectrum of the theory.

Let $u$ be sufficiently small, with $|u|\ll 1$, let $s$ be a positive integer, and let $a\in\{1,2,\dots,s\}$. For each positive integer $m$, let $T^{(a)}_{m}(v)$ denote the transfe…

Zamolodchikov's conjecture. The system is solved by

Magnonic pseudoenergy conjecture. Two magnonic pseudoenergies, $\varepsilon^{(1)}$ and $\varepsilon^{(2)}$, should be introduced to handle the non-diagonal nature of the kink scatt…

Zero distribution conjecture. $T^{(2)}_{n-1}(v)$ has one real zero $\zeta_{n-1}$ for $n$ even with $2\leq n\leq p_0-1$, and two real zeros $\zeta_{n-1}$ and $-\zeta'_{n-1}$ for $n$…

Let the transformed-GGE spectrum be described by the vacuum and excited-state TBA equations, with … and the corresponding solutions and energies. Transformed-GGE TBA-encoding conje…

Consider the transformed-GGE TBA equations with pseudo-energy $\epsilon(\theta)$, poles $\theta_i$, and energy $E(L)$ satisfying the stated TBA equations and pole constraints. Tran…

Consider the additional TBA solutions selected so that their contributions satisfy … where $E_0(L)$ is the ground-state energy, and add the corresponding terms to the transformed g…

Consider the TBA equations for the transformed GGE, including their ground-state and excited-state solutions. Let the additional solutions be the solutions found beyond those repro…

Consider a one-particle integrable system with scattering matrix $S(\theta)$, kernel … one-particle energy $e(R,\theta)$, and pseudo-energy $\epsilon(\theta)$. Let $\theta_i$, for…

Finite-volume thermodynamic Bethe ansatz (TBA) equations describe the thermodynamics of integrable systems in finite volumes, although it is not known in general whether such equat…

Consider a potential for which the roots of $x\widetilde V(x)=0$ are positive, distinct, and ordered as … Let the TBA equations be obtained by assuming that the logarithms of the r…

Free-energy functional conjecture. Once $Z$ is known, the free energy should be

Boundary-condition conjecture. The boundary condition … , holds universally for type $D_n$ and types $E_6$, $E_7$, and $E_8$.

Analytical-structure conjecture. The functions $\tilde{y}_n(\lambda)$ of the tilted Néel state have all the poles and zeroes corresponding to the $y$-functions of the Néel state. I…

Positive-zero conjecture. In the asymptotic analysis as $\kappa$ becomes large, only the real positive zeroes corresponding either to the vacuum or to the excited states are import…

Extended Y-system conjecture. The relevance of this relation and the other discontinuity relations introduced in the paper is not restricted to the ground state: provided the analy…

The $Z_2$ staggered vertex model has a scattering theory with $S$-matrix denoted by $S$ and particle mass $mu$ as specified in the source. Its thermodynamic Bethe Ansatz (TBA) is d…

Let $Y^\epsilon_{p,\mathbf t}(\vartheta)$ be the unique solution of the nonlinear integral equations associated with real input data…