The Z2 -Orbifold of the W3 -Algebra

Abstract

The Zamolodchikov W3-algebra W3c with central charge c has full automorphism group Z2. It was conjectured in the physics literature over 20 years ago that the orbifold (W3c)Z2 is of type W(2 , 6 , 8 , 10 , 12) for generic values of c. We prove this conjecture for all c≠559±77665795, and we show that for these two values, the orbifold is of type W(2 , 6 , 8 , 10 , 12 , 14). This paper is part of a larger program of studying orbifolds and cosets of vertex algebras that depend continuously on a parameter. Minimal strong generating sets for orbifolds and cosets are often easy to find for generic values of the parameter, but determining which values are generic is a difficult problem. In the example of (W3c)Z2, we solve this problem using tools from algebraic geometry.