Author
Bae, J
Lee, S
Song, J
Journal title
Journal of High Energy Physics
DOI
10.1007/jhep01(2019)209
Issue
1
Volume
2019
Last updated
2022-12-19T04:30:32.927+00:00
Abstract
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title>
<jats:p>We constrain the spectrum of <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$$ \mathcal{N} $$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math>
</jats:alternatives>
</jats:inline-formula> = (1, 1) and <jats:inline-formula>
<jats:alternatives>
<jats:tex-math>$$ \mathcal{N} $$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math>
</jats:alternatives>
</jats:inline-formula> = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γ<jats:sub>
<jats:italic>θ</jats:italic>
</jats:sub> congruence subgroup of the full modular group SL(2, ℤ). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U(1) charges. Especially, the upper bounds on the twist gap for the noncurrent primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γ<jats:sub>
<jats:italic>θ</jats:italic>
</jats:sub>. Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS<jats:sub>3</jats:sub>.</jats:p>
Symplectic ID
1193953
Favourite
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Publication type
Journal Article
Publication date
28 Jan 2019
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