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SUMMARY:Rademacher Expansions and the Spectrum of 2d CFT - Luis Fernando A
 lday (Oxford)
DTSTART:20200130T130000Z
DTEND:20200130T140000Z
UID:TALK137155@talks.cam.ac.uk
CONTACT:Dr. Carl Turner
DESCRIPTION:A classical result from analytic number theory by Rademacher g
 ives an exact formula for the Fourier coefficients of modular forms of non
 -positive weight. We apply similar techniques to study the spectrum of two
 -dimensional unitary conformal field theories\, with no extended chiral al
 gebra and c > 1. By exploiting the full modular constraints of the partiti
 on function we propose an expression for the spectral density in terms of 
 the light spectrum of the theory. The expression is given in terms of a Ra
 demacher expansion\, which converges for spin j>0. For a finite number of 
 light operators the expression agrees with a variant of the Poincare const
 ruction developed by Maloney\, Witten and Keller. With this framework we s
 tudy the presence of negative density of states in the partition function 
 dual to pure gravity\, and propose a scenario to cure this negativity.\n\n
LOCATION:Potter Room (first floor\, Pav. B)
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