2023/04/06 by Yutaka Yoshida, Yoshida, Yutaka
Physics and Astronomy 路 Mathematics 路 #Black Holes and Theoretical Physics #Algebraic structures and combinatorial models #Advanced Operator Algebra Research
paper 路 pdf 路 doi:10.1093/ptep/ptag099
Abstract We study properties of vertex (operator) algebras associated with 3D H-twisted \mathcal N=4 supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by Becchi鈥揜ouet鈥揝tora鈥揟yutin (BRST) cohomologies of currents with symplectic bosons, complex fermions, and bc-ghosts. We point out that VOAs for 3D \mathcal N=4 Abelian gauge theories are fermionic extensions of VOAs associated with toric hyper-K盲hler varieties. From this relation, it follows that the VOA associated with the 3D mirror of N-flavor U(1) SQED is a fermionic extension of a W-algebra W-N+1(\mathfrak slN, fsub). For N = 3, we explicitly compute the operator product expansion of elements in the BRST cohomology and find a new algebra that is a fermionic extension of a Bershadsky鈥揚olyakov algebra W-2(\mathfrak sl3, fsub). We also suggest an expression for the vacuum character of the fermionic extension of W-N+1(\mathfrak slN, fsub) predicted by 3D \mathcal N=4 mirror symmetry.