# Twisted logarithmic modules of free field algebras

@article{Bakalov2016TwistedLM, title={Twisted logarithmic modules of free field algebras}, author={Bojko Bakalov and McKay Sullivan}, journal={arXiv: Quantum Algebra}, year={2016} }

Given a non-semisimple automorphism $\varphi$ of a vertex algebra $V$, the fields in a $\varphi$-twisted $V$-module involve the logarithm of the formal variable, and the action of the Virasoro operator $L_0$ on such module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spaces when $V$ is generated by free fields. Specifically, we consider the cases of symplectic fermions (odd superbosons), free fermions, and $\beta\gamma$-system (even superfermions…

## 6 Citations

Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras.

- Mathematics
- 2017

SULLIVAN, STEVEN MCKAY. Twisted Logarithmic Modules of Free Field and Lattice Vertex Algebras. (Under the direction of Bojko Bakalov.) Vertex algebras formalize the relations between vertex operators…

Associative algebras for (logarithmic) twisted modules for a vertex operator algebra

- MathematicsTransactions of the American Mathematical Society
- 2018

We construct two associative algebras from a vertex operator algebra $V$ and a general automorphism $g$ of $V$. The first, called $g$-twisted zero-mode algebra, is a subquotient of what we call…

Twisted logarithmic modules of lattice vertex algebras

- MathematicsTransactions of the American Mathematical Society
- 2018

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called…

Logarithmic Vertex Algebras

- Mathematics
- 2021

We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a…

Free Field Realisations in Logarithmic Conformal Field Theory

- Mathematics
- 2019

Invariances of conformal field theories (CFTs) would seem to suggest that correlation functions behave as power laws. However, logarithms also exhibit conformal invariance. When logarithms are…

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

## References

SHOWING 1-10 OF 55 REFERENCES

Twisted Modules over Lattice Vertex Algebras

- Mathematics
- 2004

For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of…

Twisted Logarithmic Modules of Vertex Algebras

- Mathematics
- 2015

Motivated by logarithmic conformal field theory and Gromov–Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism.…

A $$\mathbb{Z}_{2}$$-orbifold model of the symplectic fermionic vertex operator superalgebra

- Mathematics
- 2007

We give an example of an irrational C2-cofinite vertex operator algebra whose central charge is −2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex…

Representation theory of the vertex algebraW1+∞

- Mathematics
- 1996

In our paper [KR] we began a systematic study of representations of the universal central extension of the Lie algebra of differential operators on the circle. This study was continued in the paper…

Modular-Invariance of Trace Functions¶in Orbifold Theory and Generalized Moonshine

- Mathematics
- 1997

Abstract: The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of the theory of rational orbifold models in conformal field theory, in other words the…

Quasifinite Representations of Classical Lie Subalgebras of W1

- Mathematics
- 1998

We show that there are precisely two, up to conjugation, anti-involutionsσ±of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible…

Affine Orbifolds and Rational Conformal Field Theory Extensions of
W1+∞

- Mathematics
- 1996

Abstract:Chiral orbifold models are defined as gauge field theories with a finite gauge group Γ. We start with a conformal current algebra associated with a connected compact Lie group G and a…

Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function

- Mathematics
- 2001

Abstract:We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this…

Representations of affine Kac-Moody algebras, bosonization and resolutions

- Mathematics
- 1990

We study boson representations of the affine Kac-Moody algebras and give an explicit description of primary fields and intertwining operators, using vertex operators. We establish the resolution of…