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Twisted modules over vertex algebras formalize the relations among twistedvertex operators and have applications to conformal field theory andrepresentation theory. A recent generalization, called twisted logarithmicmodule, involves the logarithm of the formal variable and is related tologarithmic conformal field theory. We investigate twisted logarithmic modulesof lattice vertex algebras, reducing their classification to the classificationof modules over a certain group. This group is a semidirect product of adiscrete Heisenberg group and a central extension of the additive group of thelattice.

Twisted logarithmic modules of lattice vertex algebras