nLab motivic multiple zeta values

Idea

Where a zeta function and multiple zeta function may be assigned to a suitable variety, so a motivic multiple zeta function is attached to the corresponding motive, like a motivic L-function is.

Where zeta functions appear in physics as expressions for vacuum amplitudes, so multiple zeta functions appear in expressions for more general scattering amplitudes. The intricate combinatorics of these becomes often more tractable when re-expressing them as motivic multiple zeta values (e.g. Schlotterer-Stieberger 12).

Related concepts

• zeta function

• multiple zeta values

• motive, motives in physics

• motivic L-function

• mixed Tate motive

References

General

• Francis Brown, On the decomposition of motivic multiple zeta values (arXiv:1102.1310v2)

• A. B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry (arXiv:math/0208144)

In physics (scattering amplitudes)

In scattering amplitudes.

Of the superstring:

• O. Schlotterer, Stephan Stieberger, Motivic Multiple Zeta Values and Superstring Amplitudes (arXiv:1205.1516)

• Stephan StiebergerMotivic superstring amplitudes, 2013 (pdf)

In N=4 D=4 super Yang-Mills theory:

• Marcus Spradlin, Anastasia Volovich, Symbols of One-Loop Integrals From Mixed Tate Motives (arXiv:1105.2024)

See also at motives in physics.