The pseudo-trace isomorphism conjecture for the even symplectic fermion theory

Pseudo-trace functions define an injective linear map

$$\xi_{\mathcal{G}}: C(\mathcal{E}) \to C_1(\mathcal{V}_\mathrm{ev}).$$

Here $\mathcal{E}$ is the relevant endomorphism algebra, $C(\mathcal{E})$ denotes its space of symmetric linear forms, and $C_1(\mathcal{V}_\mathrm{ev})$ is the space of torus one-point functions for the even subalgebra $\mathcal{V}_\mathrm{ev}$ of the symplectic fermion vertex operator algebra. Pseudo-trace isomorphism conjecture. The map

$$\xi_{\mathcal{G}}: C(\mathcal{E}) \to C_1(\mathcal{V}_\mathrm{ev})$$

is an isomorphism. It is known to be injective, but it is not known whether these simpler pseudo-trace functions span the full space of torus one-point functions, even for $\mathcal{V}_\mathrm{ev}$; the conjecture asserts precisely this missing surjectivity.