TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.047
TI  - Non-chiral vertex operator algebra associated to Lorentzian lattices and Narain CFTs
PY  - 2024/08/12
UR  - https://scipost.org/SciPostPhys.17.2.047
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 047
A1  - Singh, Ranveer Kumar
AU  - Sinha, Madhav
AB  - Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature $(m,n)$ assuming the validity of a technical result about automorphisms of the lattice. We finally show that Narain conformal field theories in physics are examples of non-chiral VOA. Our formalism helps us to identify the chiral algebra of Narain CFTs in terms of a particular sublattice and give us the decomposition of its partition function into sum of characters.
ER  -

@Article{10.21468/SciPostPhys.17.2.047,
	title={{Non-chiral vertex operator algebra associated to Lorentzian lattices and Narain CFTs}},
	author={Ranveer Kumar Singh and Madhav Sinha},
	journal={SciPost Phys.},
	volume={17},
	pages={047},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.047},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.047},
}