Modular constraints on superconformal field theories

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We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the 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 . Some of the candidate theories have been discussed by Hohn 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(3).
Publisher
SPRINGER
Issue Date
2019-01
Language
English
Article Type
Article
Citation

JOURNAL OF HIGH ENERGY PHYSICS, no.1

ISSN
1029-8479
DOI
10.1007/JHEP01(2019)209
URI
http://hdl.handle.net/10203/273994
Appears in Collection
PH-Journal Papers(저널논문)
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