15 problems

Consider the Sine–Gordon model with action … Here $\beta>0$ is the coupling constant, $g$ is the interaction cutoff, and the massless model has solitons and anti-solitons. The mass…

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…

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

Let $\Omega\subset\mathbb{R}^2$ be a bounded, simply connected domain, let $\alpha:\overline{\Omega}\to\mathbb{R}^2$ be a smooth vector field of the form $\alpha=\nabla V$, and let…

Metastable random-walk conjecture. As $\epsilon\to0$, the rescaled process approaches a symmetric simple random walk on

Global well-posedness conjecture. The renormalized sine-Gordon model is globally well-posed on the support of the Gibbs measure $\vec{\rho}$ for $\beta^2 < 6\pi$.

The sine-Gordon model is the Euclidean, massless quantum field theory formally described by the measure … where $\mu\in\mathbb{R}$, $\beta>0$, the integrals are over $\mathbb{R}^2$…

Let $\beta<8\pi$, and consider the formally massless continuum sine-Gordon model in the limit $L\to\infty$ and $m^2\to 0$ with nonzero coupling parameter $z\neq 0$. Its equilibrium…

Consider the dynamical Sine-Gordon equation on the two-dimensional torus, whose parameter satisfies $\beta^2\in[4\pi,\frac{16}{3}\pi)$. Criticality conjecture for the dynamical Sin…

Consider the sine-Gordon model with purely imaginary coupling, whose Lagrangian density is … where $\beta,\mu\in\mathbb{R}$, $\phi$ is a scalar field, and…

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…

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…

Let $f^{(1,1)}_a(\theta_1,\ldots,\theta_N)$ and $f^{(2)}_a(\theta_1,\ldots,\theta_N)$ be the level-two descendant form factors defined from the basis elements $c_{-1}^2$ and…

Let ${\cal F}_n$ be the level $n$ subspace of the Fock module ${\cal F}$, and let ${\cal P}_n$ be the space of order $n$ polynomials $p(\xi_1,\ldots,\xi_n|\eta_1,\ldots,\eta_n)$ wh…