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SUMMARY:Three Avatars of Mock Modularity
DTSTART;VALUE=DATE-TIME:20210602T120000Z
DTEND;VALUE=DATE-TIME:20210602T131500Z
DTSTAMP;VALUE=DATE-TIME:20230928T045649Z
UID:indico-contribution-5726@indico.ipmu.jp
DESCRIPTION:Speakers: Atish Dabholkar (ICTP Trieste)\nMock theta functions
were introduced by Ramanujan in his famous last letter to Hardy in 1920 b
ut were properly understood only recently with the work of Zwegers in 2002
. I will describe three manifestations of this apparently exotic mathemati
cs in three important physical contexts of holography\, topology and dua
lity where mock modularity has come to play in important role. \n \nIn par
ticular\, I will derive a holomorphic anomaly equation for the indexed pa
rtition function of a two-dimensional CFT2 dual to AdS3 that counts the bl
ack hole degeneracies\, and for Vafa-Witten partition function for twiste
d four dimensional N=4 super Yang-Mills theory on CP2 for the gauge group
SO(3) that counts instantons. The holomorphic kernel of this equation is
not modular but `mock modularâ€™ and one obtains correct modular propertie
s only after including certain `anomalousâ€™ nonholomorphic boundary cont
ributions. This phenomenon can be related to the holomorphic anomaly of t
he elliptic genus of a two-dimensional noncompact supersymmetric sigma mod
el\, and in a simpler context of quantum mechanics to the Atiyah-Patodi-Si
nger eta invariant. \n \nMock modularity is thus essential to exhibit mod
ular symmetries expected from the AdS3/CFT2 holographic equivalence in q
uantum gravity and the S-duality symmetry of four-dimensional quantum ga
uge theories.\n\nhttps://indico.ipmu.jp/event/387/contributions/5726/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5726/
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