Beurling-Selberg extremization and modular bootstrap at high energies
Beurling-Selberg extremization and modular bootstrap at high energies
We consider previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [\Delta - \delta,\Delta + \delta] <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">[</mml:mo><mml:mi>Δ</mml:mi><mml:mo>−</mml:mo><mml:mi>δ</mml:mi><mml:mo>,</mml:mo><mml:mi>Δ</mml:mi><mml:mo>+</mml:mo><mml:mi>δ</mml:mi><mml:mo stretchy="false" form="postfix">]</mml:mo></mml:mrow></mml:math> at asymptotically large \Delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi></mml:math> in 2d unitary modular invariant CFTs. These bounds depend on a choice …