Since the M-theory U-duality groups are defined over the integers, one can go a long way even before invoking the full set of rationals.

U-duality groups such as E8(8)(Z) and E7(7)(Z) are discrete groups inducing integer shifts on the charge lattice. Schroeder gives a nice overview of discrete U-duality groups in hep-th/9909157.

From the Jordan algebra perspective, E7(7)(Z) arises from the Freudenthal triple system defined over the Jordan algebra of 3×3 Hermitian matrices over the split-octonions (with integer coefficients).

]]>What do you think of the AMS monograph on Motivic Cohomology based on Voevodsky’s lecture notes?

]]>Number theoretical universality of physics is a really fascinating idea. Especially so, when one asks seriously what would be the interpretation of say p-adic physics with a particular value of prime p. Second fascination is that number theoretic constraints such as algebraic number character of S-matrix elements provide immensely powerful constraints on theory.

Best,

Matti

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