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Title: Parity and the modular bootstrap

Abstract

We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation P P . Combining P P with modular inversion S S leads to a continuous family of fixed points of the SP S P transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying \beta_L \beta_R = 4\pi^2 β L β R = 4 π 2 . We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large- c c CFT _2 2 with a suitably sparse low-lying spectrum matches that of AdS _3 3 gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum and providing a new proof of the statement that the twist gap is smaller than (c-1)/12 ( c − 1 ) / 12 when c>1 c > 1 . At large c c we show that the operator dimension of the first excited primary lies in a region in the (h,\overline{h}) ( h , h ¯ ) -plane that is significantly smaller than h+\overline{h} h + h ¯ > c / 6 . Our results for the free energy and constraints on the operator spectrum extend to theories without parity symmetry through the construction of an auxiliary parity-invariant partition function.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
+ Show Author Affiliations
  1. University of British Columbia
  2. Institute for Advanced Study, Princeton University, Princeton University
  3. Cornell University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1469406
Grant/Contract Number:  
SC0016244
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 5 Journal Issue: 3; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Anous, Tarek, Mahajan, Raghu, and Shaghoulian, Edgar. Parity and the modular bootstrap. Netherlands: N. p., 2018. Web. doi:10.21468/SciPostPhys.5.3.022.
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Anous, Tarek, Mahajan, Raghu, & Shaghoulian, Edgar. Parity and the modular bootstrap. Netherlands. https://doi.org/10.21468/SciPostPhys.5.3.022
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Anous, Tarek, Mahajan, Raghu, and Shaghoulian, Edgar. Tue . "Parity and the modular bootstrap". Netherlands. https://doi.org/10.21468/SciPostPhys.5.3.022.
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@article{osti_1469406,
title = {Parity and the modular bootstrap},
author = {Anous, Tarek and Mahajan, Raghu and Shaghoulian, Edgar},
abstractNote = {We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation P P . Combining P P with modular inversion S S leads to a continuous family of fixed points of the SP S P transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying \beta_L \beta_R = 4\pi^2 β L β R = 4 π 2 . We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large- c c CFT _2 2 with a suitably sparse low-lying spectrum matches that of AdS _3 3 gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum and providing a new proof of the statement that the twist gap is smaller than (c-1)/12 ( c − 1 ) / 12 when c>1 c > 1 . At large c c we show that the operator dimension of the first excited primary lies in a region in the (h,\overline{h}) ( h , h ¯ ) -plane that is significantly smaller than h+\overline{h} h + h ¯ > c / 6 . Our results for the free energy and constraints on the operator spectrum extend to theories without parity symmetry through the construction of an auxiliary parity-invariant partition function.},
doi = {10.21468/SciPostPhys.5.3.022},
journal = {SciPost Physics},
number = 3,
volume = 5,
place = {Netherlands},
year = {Tue Sep 11 00:00:00 EDT 2018},
month = {Tue Sep 11 00:00:00 EDT 2018}
}
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https://doi.org/10.21468/SciPostPhys.5.3.022
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