8 problems

Let the vertex operator algebras be the algebras introduced in the paper for the eight-vertex model and its associated representations. Let the bosonization procedure mean the cons…

Let $\tilde\beta$ be the bosonic-shadow theory and $\tilde\alpha$ the corresponding fermionic anomaly theory, with a conjectural defect $\tilde z_c$ relating them. Invertibility-tr…

Let $G$ be a fermionic symmetry acting on a super modular tensor category, with anomaly $\tilde\alpha$. Let $F_{\tilde\alpha}$ be the Dijkgraaf–Witten-type theory obtained by summi…

Let a spin topological field theory be related to a bosonic theory by a bosonization procedure. Bosonization conjecture. The partition function of the spin theory can be computed v…

The regular boson and critical boson theories are dual to the critical fermion and regular fermion theories, respectively. Boson–fermion duality conjecture. The regular boson/criti…

Let $Z_\text{boson}^{w_1,w_2}[\alpha,\beta]$ denote the bosonic partition function in the sectors with spatial and temporal $\mathbb{Z}_2$ twists $w_1,w_2\in\{+,-\}$, and let…

Boson-fermion duality. The infrared duality should identify

Let $F(p_a)$ be the boson Fock space generated by the bosons $a_m^i$, $b_m^{i,j}$, and $c_m^{i,j}$ on the vectors $|p_a,p_b,p_c\rangle$ satisfying the stated vacuum and zero-mode c…