30 problems

Form-factor isomorphism conjecture. The map $\boldsymbol{\Phi}$ is an isomorphism. This conjecture asserts that the quotient space of local operators is completely captured by the…

Let $P^{\sigma}_{l,n}$ be the functions defined by the qKZ solutions in equation, and let $j^{-}_{\sigma}$ denote the corresponding lightcone components of the Noether current in t…

Let … , the corresponding coefficients of $\widetilde I(\alpha)$ should generate the form factors of the stress-energy tensor in the sine-Gordon model. This extrapolates the establ…

The calculation uses only the bootstrap property of the S-matrix, so let a diagonal scattering theory have this property. Polynomial recursion conjecture. The problem of calculatin…

Sine-Gordon form-factor conjecture. The function defined by equation provides a form factor of some local operator in the sine-Gordon theory.

Residue cancellation conjecture.

Let $F_n^{\mathcal O}(\theta_1,\ldots,\theta_n)$ denote an $n$-particle form factor of a local operator $\mathcal O$, expressed in terms of rapidities $\theta_1,\ldots,\theta_n$. C…

Form factors are matrix elements of local or quasilocal operators between eigenstates of a quantum field theory, and the form-factor bootstrap equations are the equations determine…

Two-spinon amplitude conjecture. One has

For a particle-hole form factor, let the kinematic-pole structure be the pole behavior in which, as a particle rapidity approaches the corresponding hole rapidity, the form factor…

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…

Multi-particle form-factor conjecture. At finite coupling, the multi-particle form factor is given by the product

Form-factor proportionality conjecture. The relationship between the FFLO and the universal form factors remains true in the general $\mathfrak{gl}(m|n)$ case.

Universal form-factor conjecture. The normalized matrix element satisfies

Smirnov's conjecture. The non-trivial part of the form factor of the local operator $\boldsymbol{\texttt{O}}$ takes the form of the multiple integral

Degree-four universality conjecture. The two-loop remainder of every minimal form factor has the same degree-four part as the BPS one.

Let $T^{(1)}_{ij}[0]$ be the partial zero modes in a ${\rm GL}(N)$-invariant model. Bethe vectors and dual Bethe vectors are parametrized by sets $\bar t^k$ and cardinalities $a_k$…

The form factor axioms describe solutions corresponding to matrix elements of local operators in an integrable massive two-dimensional quantum field theory. A solution of the form…

Let ${\cal A}=\bigoplus_{l=0}^{\infty}{\cal A}_l$ be the commutative algebra generated by the oscillators $c_{-k}$, graded so that $c_{-k}$ has degree $k$, and let ${\cal\bar A}$ b…

Consider the sine-Gordon model with $0<\beta^2\leq 1$, and let $f_a(\theta_1,\ldots,\theta_N)_{1\ldots1}$ denote relative form factors whose particles are all first breathers. For…

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…

Form-factor asymptotics conjecture. This equation gives the leading asymptotic behavior of all the oscillation harmonics of the two-point function. The claim concerns the contribut…

For the form-factor differential operators, let $\Omega^{(n)}_m(N;t)$ denote the operators associated with the polynomials $C^{(n)}_m(N;t)$. A direct-sum decomposition conjecture.…

Let ${\cal A}$ and $\bar{\cal A}$ be the chiral and antichiral descendant algebras, and let $V_a^g(x)$ denote the operator associated with an element $g$ at parameter $a$. The boso…

In two-dimensional integrable quantum field theory, form factors are collections of functions satisfying the bootstrap equations, and every local operator has a set of form factors…