Speaker
Mr
Christoph Nega
(Bethe Center for Theoretical Physics)
Description
Using the Gelfand-Kapranov-Zelevinsk\u{\i} system for the primitive cohomology
of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop
order minus one, we completely clarify the analytic structure of all banana amplitudes with arbitrary
masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds
to the point of maximal unipotent monodromy, is determined by a novel $\widehat \Gamma$-class evaluation
in the ambient spaces of the mirror, while the imaginary part of the amplitude in this regime is determined
by the $\widehat \Gamma$-class of the mirror Calabi-Yau manifold itself. We provide simple closed all loop
formulas for the former as well as for the Frobenius $\kappa$-constants, which determine the behaviour of the amplitudes,
when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work
from three to four loops by providing for the latter case a complete set of (inhomogenous) Picard-Fuchs differential equations
for arbitrary masses. This allows to evaluate the amplitude as well as other master integrals with raised powers
of the propagators in very short time to very high numerical precision for all values of the physical
parameters. Using a recent $p$-adic analysis of the periods we determine the value of the maximal cut
equal mass four-loop amplitude at the attractor points in terms of periods of modular weight two and
four Hecke eigenforms and the quasiperiods of their meromorphic cousins.
Primary authors
Prof.
Albrecht Klemm
(Bethe Center for Theoretical Physics)
Mr
Christoph Nega
(Bethe Center for Theoretical Physics)
Mr
Fabian Fischbach
(Bethe Center for Theoretical Physics)
Mr
Kilian Bönisch
(Bethe Center for Theoretical Physics)
Mr
Reza Safari
(Bethe Center for Theoretical Physics)
