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2020

Beurling-Selberg Extremization and Modular Bootstrap at High Energies

Mukhametzhanov, Baur, Pal, Sridip

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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 $\delta \geq 0$.

Beurling-Selberg Extremization and Modular Bootstrap at High Energies · Around

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