nLab number theory and physics

Idea

number theory and physics

Examples

• Riemann hypothesis and physics

• Langlands duality

• p-adic physics

  • p-adic string theory

  • p-adic AdS-CFT

References

The relation between string theory with its scattering amplitudes on Riemann surfaces and the theory of automorphic forms was maybe first highlighted in

• Edward Witten, Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. Volume 113, Number 4 (1988), 529-700 (Euclid)

Reviews include

• Matthew Watkins, Number theory and physics archive

• Michael Atiyah, Robbert Dijkgraaf, Nigel Hitchin Geometry and physics, Phil. Trans. R. Soc. A 2010 368, doi: 10.1098/rsta.2009.0227 (pdf)

  (despite the title, this is really mostly about number theory/enumerative geometry and physics)