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SUMMARY:Modular forms and black holes in N=4 string theories - Justin Davi
 d (Indian Institute of Science)
DTSTART:20231025T120000Z
DTEND:20231025T133000Z
UID:TALK206143@talks.cam.ac.uk
DESCRIPTION:We review the role of modular forms in counting the microscopi
 c degeneracies&nbsp\; of 1/4 BPS black holes in a class of&nbsp\; N=4 stri
 ng theories known as CHL models.&nbsp\; We focus on the following 3 key as
 pects.&nbsp\;\nFor a given CHL model\,&nbsp\; the 1/4 BPS index of these s
 tates&nbsp\; are Fourier coefficients of an inverse&nbsp\; Siegel modular 
 form.&nbsp\; These Siegel modular forms are associated with the elliptic g
 enera of K3 twisted by a Z_N automorphism\, each labelled by the conjugacy
  classes of the Mathieu group M_24.&nbsp\;\nWe discuss the expansion of th
 e inverse Siegel modular form in terms&nbsp\; of Mock-modular forms to obt
 ain the&nbsp\; index of single centred black holes\, and how spherical sym
 metry of the black hole horizon dictates the sign of this index.&nbsp\;\nF
 inally we&nbsp\; obtain&nbsp\; the modular transform of the Siegel&nbsp\; 
 form which captures the large charge expansion of the index and its agreem
 ent with the Hawking-Bekenstein-Wald entropy.
LOCATION:Seminar Room 2\, Newton Institute
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