15 problems

Sobolev regularity conjecture. For $\beta \in (0,8\pi)$,

Let ${\mathsf B}(u)$ be the operator in the sinh–Gordon model with odd ${\rm N}$, written as … where the operators ${\mathsf B}_m$, $m=0,\dots,{\rm N}$, are positive self-adjoint.…

Let $k\in\mathbb{N}$, let $G\in\mathcal{S}\big((\mathbb{R}^{1,1})^k\big)$, and let $\alpha_1,\dots,\alpha_k$ be labels of solutions to the system a)–d). For each…

Smooth multipoint representation conjecture.

Small-deviation conjecture. The limit

Lukyanov's conjecture. As $N\to+\infty$,

Teschner's ground-state scaling conjecture. In the infinite-volume limit,

Let $V_\nu$ be an exponential operator, let $k$ be a positive integer, and let $r_0$ be the short-distance cutoff. Let $F^{(n,s)}_{\nu,k}(t)$ be coefficient functions, with…

Let $\varphi$ be the sinh-Gordon field, let $V_\nu$ be a non-identity exponential operator, and consider descendants formed by applying derivatives to the field and multiplying by…

Background-charge conjecture. The sinh-Gordon model is ill-defined for $b>1$ without background charge, but is well-defined with the background charge $Q_\infty=b+1/b-2$. This prop…

Let $T_k$ and $T_{-l}$ be the positive- and negative-index currents in the complex sinh-Gordon model. Let $t(X)$ and $t^{\dagger}(Y)$ be the corresponding free-field operators, let…

Lorentz-noninvariant phase-shift conjecture. The rapidity-dependent $S$ matrices should satisfy

Let $G_a=\langle V_a\rangle$ denote the vacuum expectation value of the exponential operator $V_a$ in the sinh-Gordon or sine-Gordon model. In both cases it can be written in terms…

In the sinh-Gordon model, let $V_a(x)$ be an exponential operator and write its form factors as … where $f_a$ are the dimensionless relative form factors. Analyticity conjecture. T…

The sine-Gordon and sinh-Gordon theories admit form factors for descendant operators constructed from exponential fields, with descendants generated by the Heisenberg algebra assoc…