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SUMMARY:Three Avatars of Mock Modularity - Atish Dabholkar (ICTP)
DTSTART:20211125T130000Z
DTEND:20211125T140000Z
UID:TALK164362@talks.cam.ac.uk
CONTACT:Chiung Hwang
DESCRIPTION:Mock theta functions were introduced by Ramanujan in his famou
 s last letter to Hardy in 1920 but were properly understood only recently 
 with the work of Zwegers in 2002. I will describe three manifestations of 
 this apparently exotic mathematics in  three important  physical contexts 
 of holography\, topology and duality where mock modularity has come to pla
 y in important role. \n \nIn particular\, I will derive  a holomorphic ano
 maly equation for the indexed partition function of a two-dimensional CFT2
  dual to AdS3 that counts the black hole degeneracies\,  and for Vafa-Witt
 en partition function for twisted four dimensional N=4 super Yang-Mills th
 eory on CP2 for the gauge group SO(3) that counts instantons.  The holomor
 phic kernel of this equation is not modular but `mock modular’ and one o
 btains correct modular properties  only after including certain `anomalous
 ’ nonholomorphic boundary contributions. This phenomenon can be related 
 to the holomorphic anomaly of  the elliptic genus of a two-dimensional non
 compact supersymmetric sigma model\, and in a simpler context of quantum m
 echanics to the Atiyah-Patodi-Singer  eta invariant. \n \nMock modularity 
 is thus essential to exhibit modular symmetries expected from the AdS3/CFT
 2 holographic equivalence in   quantum gravity  and the S-duality symmetry
   of four-dimensional quantum gauge theories.
LOCATION:Potter room/Zoom
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