A geometric free field realisation for the genus-two class S theory of type a1

Journal article

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 ${\rm USp}(4)$ outer automorphism group of the VOA that is inherited from the symplectic fermion system. This extends an ${\rm SU(2)}$ 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.

Authors: Beem, C; Meneghelli, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review D: Particles, Fields, Gravitation and Cosmology
• Volume: 104
• Article number: 065015
• Publication date: 2021-09-21
• Acceptance date: 2021-07-24
• DOI: 10.1103/PhysRevD.104.065015
• EISSN: 1550-2368
• ISSN: 1550-7998
• Language: English
• Keywords: hep-th; math.QA; math.RT; FFR