How duality transformations tamed the current-algebraic orbifolds

Motivated by an original interest in permutation-invariant conformal field theories which are applicable in string theory, we discuss a broad class of H-invariant conformal field theories and their orbifolds. We derive the general Orbifold Virasoro Master Equation, whose solutions classify theories according to their stress tensors and central charges. Our approach recasts the problem of searching through all theories into a more mathematically tractable search by using current algebras. The current-algebraic approach makes it clear that symmetries of the CFT are realized as automorphisms of the algebra.