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Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs
by Ranveer Kumar Singh, Madhav Sinha
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Submission summary
| Authors (as registered SciPost users): | Ranveer Singh |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2312.16296v2 (pdf) |
| Date accepted: | 2024-06-04 |
| Date submitted: | 2024-05-24 05:57 |
| Submitted by: | Singh, Ranveer |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
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Author comments upon resubmission
List of changes
1. Added a few lines in the beginning of page 7 motivating the terminology "non-chiral VOA" in response to first referee's first requested changes.
2. Added two remarks (Remark 2.1 on page 15 and Remark 5.5 on page 68) relating to Moriwaki's work in response to first referee's second requested changes.
3. Added Footnote 4 on page 4 and Footnote 5 on page 5 clarifying the notion of "maximal chiral algebra" in response to first referee's third requested changes.
4. Corrected the typo on page 10 in response to first referee's fourth requested changes.
5. Added references to Lemma 2.1, 2.2 and 2.3 by adding a line in the beginning of Lemma 2.1 on page 16 in response to second referee's third point in the pdf attached by the referee.
Published as SciPost Phys. 17, 047 (2024)