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CATEGORIES:Quantum Fields and Strings Seminars
SUMMARY:Three Avatars of Mock Modularity - Atish Dabholkar
(ICTP)
DTSTART;TZID=Europe/London:20211125T130000
DTEND;TZID=Europe/London:20211125T140000
UID:TALK164362AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/164362
DESCRIPTION:Mock theta functions were introduced by Ramanujan
in his famous last letter to Hardy in 1920 but wer
e properly understood only recently with the work
of Zwegers in 2002. I will describe three manifest
ations of this apparently exotic mathematics in t
hree important physical contexts of holography\,
topology and duality where mock modularity has com
e to play in important role. \n \nIn particular\,
I will derive a holomorphic anomaly equation for
the indexed partition function of a two-dimensiona
l CFT2 dual to AdS3 that counts the black hole deg
eneracies\, and for Vafa-Witten partition functio
n for twisted four dimensional N=4 super Yang-Mill
s theory on CP2 for the gauge group SO(3) that cou
nts instantons. The holomorphic kernel of this eq
uation is not modular but `mock modularâ€™ and one o
btains correct modular properties only after incl
uding certain `anomalousâ€™ nonholomorphic boundary
contributions. This phenomenon can be related to t
he holomorphic anomaly of the elliptic genus of a
two-dimensional noncompact supersymmetric sigma m
odel\, and in a simpler context of quantum mechani
cs to the Atiyah-Patodi-Singer eta invariant. \n
\nMock modularity is thus essential to exhibit mod
ular symmetries expected from the AdS3/CFT2 hologr
aphic equivalence in quantum gravity and the S-
duality symmetry of four-dimensional quantum gaug
e theories.
LOCATION:Potter room/Zoom
CONTACT:Chiung Hwang
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