期刊
SCIPOST PHYSICS
卷 8, 期 6, 页码 -出版社
SCIPOST FOUNDATION
DOI: 10.21468/SciPostPhys.8.6.088
关键词
-
资金
- NSF [PHY-1911298]
- Ambrose Monell Foundation
- DOE [DE-SC0009988]
We consider previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [Delta - delta, Delta + delta] at asymptotically large Delta in 2d unitary modular invariant CFTs. These bounds depend on a choice of functions that majorize and minorize the characteristic function of the interval [Delta - delta, Delta + delta] and have Fourier transforms of finite support. The optimization of the bounds over this choice turns out to be exactly the Beurling-Selberg extremization problem, widely known in analytic number theory. We review solutions of this problem and present the corresponding bounds on the number of operators for any delta >= 0. When 2 delta is an element of Z(>= 0) the bounds are saturated by known partition functions with integer-spaced spectra. Similar results apply to operators of fixed spin and Virasoro primaries in c > 1 theories.
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