String geometry and the noncommutative torus

We construct a new gauge theory on a pair of d-dimensional noncommutative t ori. The latter comes from an intimate relationship between the noncommutat ive geometry associated with a lattice vertex operator algebra A and the no ncommutative torus. We show that the tachyon algebra of A is naturally isom orphic to a class of twisted modules representing quantum deformations of t he algebra of functions on the torus. We construct the corresponding real s pectral triples and determine their Morita equivalence classes using string duality arguments, These constructions yield simple proofs of the O(d, d; Z) Morita equivalences between d-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duali ty group of toroidally compactified string theory. We classify the automorp hisms of the twisted modules and construct the most general gauge theory wh ich is invariant under the automorphism group. We compute bosonic and fermi onic actions associated with these gauge theories and show that they are ex plicitly duality-symmetric. The duality-invariant gauge theory is manifestl y covariant but contains highly non-local interactions. We show that it als o admits a new sort of particle-antiparticle duality which enables the cons truction of instanton field configurations in any dimension, The duality no n-symmetric on-shell projection of the field theory is shown to coincide wi th the standard non-abelian Yang-Mills gauge theory minimally coupled to ma ssive Dirac fermion fields.