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Title: Bounds on the density of states and the spectral gap in CFT 2

Abstract

We improve the recently discovered upper and lower bounds on the O(1) correction to the Cardy formula for the density of states integrated over an energy window (of width 2 δ), centered at high energy in two-dimensional unitary and modular invariant conformal field theory. We prove optimality of the lower bound for δ → 1. We prove a conjectured upper bound on the asymptotic gap between two consecutive Virasoro primaries for a central charge greater than 1, demonstrating it to be 1. Furthermore, a systematic method is provided to establish a limit on how tight the bound on the O(1) correction to the Cardy formula can be made using bandlimited functions. The techniques and the functions used here are of generic importance whenever the Tauberian theorems are used to estimate some physical quantities.

Authors:
ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States); Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
Simons Foundation; Ambrose Monell Foundation; USDOE Office of Science (SC)
OSTI Identifier:
1630791
Alternate Identifier(s):
OSTI ID: 1801928
Grant/Contract Number:  
SC0009919; SC0009988; 568420
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats

Ganguly, Shouvik, and Pal, Sridip. Bounds on the density of states and the spectral gap in CFT 2. United States: N. p., 2020. Web. doi:10.1103/PhysRevD.101.106022.
Ganguly, Shouvik, & Pal, Sridip. Bounds on the density of states and the spectral gap in CFT 2. United States. https://doi.org/10.1103/PhysRevD.101.106022
Ganguly, Shouvik, and Pal, Sridip. Tue . "Bounds on the density of states and the spectral gap in CFT 2". United States. https://doi.org/10.1103/PhysRevD.101.106022.
@article{osti_1630791,
title = {Bounds on the density of states and the spectral gap in CFT 2},
author = {Ganguly, Shouvik and Pal, Sridip},
abstractNote = {We improve the recently discovered upper and lower bounds on the O(1) correction to the Cardy formula for the density of states integrated over an energy window (of width 2 δ), centered at high energy in two-dimensional unitary and modular invariant conformal field theory. We prove optimality of the lower bound for δ → 1–. We prove a conjectured upper bound on the asymptotic gap between two consecutive Virasoro primaries for a central charge greater than 1, demonstrating it to be 1. Furthermore, a systematic method is provided to establish a limit on how tight the bound on the O(1) correction to the Cardy formula can be made using bandlimited functions. The techniques and the functions used here are of generic importance whenever the Tauberian theorems are used to estimate some physical quantities.},
doi = {10.1103/PhysRevD.101.106022},
journal = {Physical Review D},
number = 10,
volume = 101,
place = {United States},
year = {2020},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.101.106022

Citation Metrics:
Cited by: 3 works
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