The geometry of the modular bootstrap
Journal
Journal of High Energy Physics
Journal Volume
2024
Journal Issue
2
Start Page
209
ISSN
1029-8479
Date Issued
2024-02-26
Author(s)
Abstract
We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment curves on R+⊗ℤ, with boundaries characterized by the total positivity of generalized Hankel matrices. We phrase the Hankel constraints as a semi-definite program, which has several advantages, such as the validity of bounds irrespective of spin truncation. We derive bounds on the gap, twist-gap, and the space of Taylor coefficients themselves. We find that if the gap is above ∆gap∗, where c−112<Δgap∗[removed]
Subjects
AdS-CFT Correspondence
Conformal and W Symmetry
Field Theories in Lower Dimensions
Publisher
Springer Science and Business Media LLC
Type
journal article