Editing Vertex operator algebra (section)

=== Twisted modules ===

Unlike ordinary rings, vertex algebras admit a notion of twisted module attached to an automorphism.  For an automorphism σ of order ''N'', the action has the form ''V'' ⊗ ''M'' → ''M''((''z''<sup>1/N</sup>)), with the following [[monodromy]] condition: if ''u'' ∈ ''V'' satisfies σ ''u'' = exp(2π''ik''/''N'')''u'', then ''u''<sub>n</sub> = 0 unless ''n'' satisfies ''n''+''k''/''N'' ∈ '''Z''' (there is some disagreement about signs among specialists).  Geometrically, twisted modules can be attached to branch points on an algebraic curve with a [[Ramification (mathematics)|ramified]] [[Galois cover]].  In the conformal field theory literature, twisted modules are called [[twisted sector]]s, and are intimately connected with string theory on [[orbifold]]s.