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SUMMARY:Polyakov Path Integral as Modular Parametrization (?): CM Elliptic
Curves as Target Spaces
DTSTART;VALUE=DATE-TIME:20210601T070000Z
DTEND;VALUE=DATE-TIME:20210601T081500Z
DTSTAMP;VALUE=DATE-TIME:20230325T161927Z
UID:indico-contribution-5717@indico.ipmu.jp
DESCRIPTION:Speakers: Taizan Watari (Kavli IPMU\, U. Tokyo)\nAn L-function
is defined for an algebraic variety with defining equations written only
with algebraic numbers as coefficients. For some classes of such varieties
\, a correspondence between those L-functions and modular forms has been o
bserved as pure mathematics. It is a natural question whether the modular
transformation in g=1 string-theory amplitudes has something to do with th
is phenomenon. \n\nWe argue for the class of varieties called elliptic cur
ves of Shimura type (implying complex multiplication) that the modular tra
nsformation can indeed be regarded as that of the g=1 world sheet\, and th
at certain class of g=1 correlation functions yield functions on the compl
ex upper half plane\, just like the theory of modular parametrization does
. Roles played by choice of the target space metric\, arithmetic model dep
endence\, and the needs for average within the ideal class group will also
be discussed along the way. \n\nThis presentation is based on two joint
works with Satoshi Kondo: \nhttps://arxiv.org/abs/1912.13294 and https:/
/arxiv.org/abs/1801.07464\n\nhttps://indico.ipmu.jp/event/387/contribution
s/5717/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5717/
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