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Title: Modular bootstrap revisited

Abstract

We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.

Authors:
ORCiD logo [1];  [1];  [1]
  1. Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1507580
Grant/Contract Number:  
FG02-91ER40654
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Black Holes; Conformal and W Symmetry; Conformal Field Theory

Citation Formats

Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Modular bootstrap revisited. United States: N. p., 2018. Web. doi:10.1007/jhep09(2018)061.
Collier, Scott, Lin, Ying -Hsuan, & Yin, Xi. Modular bootstrap revisited. United States. doi:10.1007/jhep09(2018)061.
Collier, Scott, Lin, Ying -Hsuan, and Yin, Xi. Wed . "Modular bootstrap revisited". United States. doi:10.1007/jhep09(2018)061. https://www.osti.gov/servlets/purl/1507580.
@article{osti_1507580,
title = {Modular bootstrap revisited},
author = {Collier, Scott and Lin, Ying -Hsuan and Yin, Xi},
abstractNote = {We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.},
doi = {10.1007/jhep09(2018)061},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2018,
place = {United States},
year = {2018},
month = {9}
}

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