An invitation to the world of strings; where mathematics meets physics

08.06.2016, 14:00  –  Haus 9, Raum 2.22

Johannes Brödel, Valentina Forini

-- 14:00 Uhr Johannes Brödel(HU Berlin)

"String theory: a perfect laboratory for iterated integrals and multiple zeta values"

-- 15:00 Uhr coffee break

-- 15:30 Uhr Valentina Forini (HU Berlin) 

"Functional determinants in string theory"


"String theory: a perfect laboratory for iterated integrals and multiple zeta values"

String theory, a theory where particles are promoted to one-dimensional "strings", allows to bridge the gap between conventional quantum field theory and mathematics. Due to the high degree of symmetry in string theory, the problem of calculating observables neatly connects to well-known objects and problems within mathematics. 

Observables -- string scattering amplitudes -- require the calculation of iterated integrals on surfaces of various genera. I will explain the origin of those integrals for genus zero and genus one and show, in which way they are linked to current problems in number theory, in particular to different versions of multiple zeta values.

"Functional determinants in string theory"

As strings move in space-time, they describe surfaces which according to the equations of motion are of minimal area.  Functional determinants arise naturally when quantizing strings. A first approximation of a quantized string is viewed as a fluctuation around a solution of the classical equations of motion. Finding the regularization procedure that gives results compatible with the symmetries of the specific problem turns out to be a highly non-trivial task, which I will discuss in a relevant example comparing  zeta- and heat-kernel regularized determinants."

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