Parity and the modular bootstrap
We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation $P$. Combining $P$ with modular inversion $S$ leads to a continuous family of fixed points of the $SP$ transformation. A particular subset of this locus of fixed points exists along t...
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doaj-400be07e87254ad18884aceb0dcdd15a2020-11-25T00:55:06ZengSciPostSciPost Physics2542-46532018-09-015302210.21468/SciPostPhys.5.3.022Parity and the modular bootstrapTarek Anous, Raghu Mahajan, Edgar ShaghoulianWe consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation $P$. Combining $P$ with modular inversion $S$ leads to a continuous family of fixed points of the $SP$ transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying $\beta_L \beta_R = 4\pi^2$. We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-$c$ CFT$_2$ with a suitably sparse low-lying spectrum matches that of AdS$_3$ 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 $(c-1)/12$ when $c>1$. At large $c$ we show that the operator dimension of the first excited primary lies in a region in the $(h,\overline{h})$-plane that is significantly smaller than $h+\overline{h}<c/6$. 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.https://scipost.org/SciPostPhys.5.3.022 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Tarek Anous, Raghu Mahajan, Edgar Shaghoulian |
spellingShingle |
Tarek Anous, Raghu Mahajan, Edgar Shaghoulian Parity and the modular bootstrap SciPost Physics |
author_facet |
Tarek Anous, Raghu Mahajan, Edgar Shaghoulian |
author_sort |
Tarek Anous, Raghu Mahajan, Edgar Shaghoulian |
title |
Parity and the modular bootstrap |
title_short |
Parity and the modular bootstrap |
title_full |
Parity and the modular bootstrap |
title_fullStr |
Parity and the modular bootstrap |
title_full_unstemmed |
Parity and the modular bootstrap |
title_sort |
parity and the modular bootstrap |
publisher |
SciPost |
series |
SciPost Physics |
issn |
2542-4653 |
publishDate |
2018-09-01 |
description |
We consider unitary, modular invariant, two-dimensional CFTs which are
invariant under the parity transformation $P$. Combining $P$ with modular
inversion $S$ leads to a continuous family of fixed points of the $SP$
transformation. A particular subset of this locus of fixed points exists along
the line of positive left- and right-moving temperatures satisfying $\beta_L
\beta_R = 4\pi^2$. We use this fixed locus to prove a conjecture of Hartman,
Keller, and Stoica that the free energy of a large-$c$ CFT$_2$ with a suitably
sparse low-lying spectrum matches that of AdS$_3$ 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 $(c-1)/12$ when $c>1$. At large $c$ we show that the operator
dimension of the first excited primary lies in a region in the
$(h,\overline{h})$-plane that is significantly smaller than
$h+\overline{h}<c/6$. 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. |
url |
https://scipost.org/SciPostPhys.5.3.022 |
work_keys_str_mv |
AT tarekanousraghumahajanedgarshaghoulian parityandthemodularbootstrap |
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1725232045974618112 |