We present a free field realisation for the vertex operator algebra associated to the genus-two, class $mathcal{S}$ superconformal field theory of type $mathfrak{a}_1$. The free field realisation is in the style of recent work by the authors, and is formulated in terms of a one-dimensional isotropic lattice vertex algebra along with two pairs of symplectic fermions. Our realisation makes manifest an enhanced ${ m USp}(4)$ outer automorphism group of the VOA that is inherited from the symplectic fermion system. This extends an ${ m SU(2)}$ outer automorphism that has been observed in recent work of Kiyoshige and Nishinaka and significantly simplifies the structure of the algebra. Along the way, we also produce a realisation of the generic subregular Drinfel'd-Sokolov $mathcal{W}$ algebra of type $mathcal{c}_2$ in terms of the generic principle $mathcal{W}$ algebra of type $mathfrak{c}_2$ and a one-dimensional isotropic lattice vertex algebra.
A geometric free field realisation for the genus-two class $mathcal{S}$ theory of type $mathfrak{a}_1$ / Beem, Christopher; Meneghelli, Carlo. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 104:6(2021). [10.1103/PhysRevD.104.065015]
A geometric free field realisation for the genus-two class $mathcal{S}$ theory of type $mathfrak{a}_1$
Meneghelli,Carlo
2021-01-01
Abstract
We present a free field realisation for the vertex operator algebra associated to the genus-two, class $mathcal{S}$ superconformal field theory of type $mathfrak{a}_1$. The free field realisation is in the style of recent work by the authors, and is formulated in terms of a one-dimensional isotropic lattice vertex algebra along with two pairs of symplectic fermions. Our realisation makes manifest an enhanced ${ m USp}(4)$ outer automorphism group of the VOA that is inherited from the symplectic fermion system. This extends an ${ m SU(2)}$ outer automorphism that has been observed in recent work of Kiyoshige and Nishinaka and significantly simplifies the structure of the algebra. Along the way, we also produce a realisation of the generic subregular Drinfel'd-Sokolov $mathcal{W}$ algebra of type $mathcal{c}_2$ in terms of the generic principle $mathcal{W}$ algebra of type $mathfrak{c}_2$ and a one-dimensional isotropic lattice vertex algebra.File | Dimensione | Formato | |
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