Pith. sign in

REVIEW 3 cited by

Harmonic analysis of 2d CFT partition functions

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2107.10744 v3 pith:HJH7TEF6 submitted 2021-07-22 hep-th

Nathan Benjamin , Scott Collier , A. Liam Fitzpatrick , Alexander Maloney , Eric Perlmutter This is my paper · ORCID
classification hep-th
keywords mathbbpartitionanalysisfunctionsharmonicspacetheoriescertain
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space $\mathbb H/SL(2,\mathbb Z)$, and of target space moduli space $O(c,c;\mathbb Z)\backslash O(c,c;\mathbb R)/O(c)\times O(c)$. This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS$_3$ gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Descending into the Modular Bootstrap

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    Numerical search finds candidate modular-invariant spectra with integer degeneracies for 1 < c < 8/7 and hints at a stronger gap bound near c = 1.

  2. Properties of scalar partition functions of 2d CFTs

    hep-th 2025-05 conditional novelty 6.0 of 10

    Scalar Virasoro primaries in any 2d CFT obey a crossing equation whose high-temperature form is controlled by a modular integral and by oscillations tied to the nontrivial zeros of the Riemann zeta function.

  3. The Conformal Primon Gas at the End of Time

    hep-th 2025-02 conditional novelty 6.0 of 10

    BKL singularity dynamics are mapped to conformal quantum mechanics whose states are odd automorphic L-functions, and these L-functions are reinterpreted as partition functions of prime-labeled oscillator gases.

Pith tools