8 problems

Let $W_K$ denote the higher-rank free-field algebra associated with the Toda theory under consideration, and consider free-field correlators in the large $N$ limit whose integratio…

OSP(5|2) duality conjecture. The deformed sigma model defined by $\widetilde{\mathcal{L}}^{(1)}_{\operatorname{OSP}(5|2)}$ is dual to the Toda QFT…

Yukawa-coupling conjecture. The Yukawa-like massive terms are

Dual Toda description conjecture. Any quantum integrable $\eta$-deformed sigma model admits a dual Toda theory description.

The Wakimoto–fermionic duality conjecture. This commutation requirement can be satisfied by choosing the exponents $\boldsymbol{\beta}_r$ and $\boldsymbol{\alpha}^{\pm}_r$ accordin…

Connection-constant conjecture. The analog of the connection-constant product formula should hold: the product of two connection constants equals the ratio of three-point functions…

The fully packed loop model is described at long distances by a time-like Toda field theory with $W_3$ symmetry and continuous primary spectrum. Its generic purely electric operato…

Let $N$ be a positive integer, let $boldsymbol{ inecalpha}1,boldsymbol{ inecalpha}2,boldsymbol{ inecalpha}3$ be the parameters entering the Weyl-invariant structure constants, let…