Generalized Narain theories $\mathfrak{decoded}$: $\mathfrak{d}$iscussions on $\mathfrak{E}$isenstein series, $\mathfrak{c}$haracteristics, $\mathfrak{o}$rbifolds, $\mathfrak{d}$iscriminants &amp; $\mathfrak{e}$nsembles in any $\mathfrak{d}$imension

Ashwinkumar, Meer; Leedom, Jacob M.; Yamazaki, Masahito; Kidambi, Abhiram

Preprint

PUBDB-2023-06429

Generalized Narain theories $\mathfrak{decoded}$: $\mathfrak{d}$iscussions on $\mathfrak{E}$isenstein series, $\mathfrak{c}$haracteristics, $\mathfrak{o}$rbifolds, $\mathfrak{d}$iscriminants & $\mathfrak{e}$nsembles in any $\mathfrak{d}$imension

Ashwinkumar, M. ; Kidambi, A. (Corresponding author) ; Leedom, J. M.DESY* ; Yamazaki, M.

2023

[10.3204/PUBDB-2023-06429]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-06429

Report No.: DESY-23-170; arXiv:2311.00699

Abstract: We study a class of newly-introduced CFTs associated with even quadratic forms of generalsignature, which we call generalized Narain theories. We first summarize the properties ofthese theories. We then consider orbifolds of these theories, thereby obtaining a large classof non-supersymmetric CFTs with exactly marginal deformations. We then discuss ensembleaverages of such theories over their moduli space, and obtain a modular form associated withthe quadratic form and an element of the discriminant group. The modular form can bewritten as a Poincar´e series, which contains novel invariants of lens spaces and suggests theinterpretation of the holographic bulk as a theory of anyons.

Keyword(s): field theory, conformal ; deformation, marginal ; orbifold ; modular ; moduli space ; Poincare ; signature