The bosonic string on string-size tori from double field theory

Abstract

: We construct the effective action for toroidal compactifications of bosonicstring theory from generalized Scherk-Schwarz reductions of double field theory. The enhancedgauge symmetry arising at special points in moduli space is incorporated into thisframework by promoting the O(k, k) duality group of k-tori compactifications to O(n, n),n being the dimension of the enhanced gauge group, which allows to account for the fullmassless sector of the theory. We show that the effective action reproduces the right massesof scalar and vector fields when moving sligthly away from the points of maximal symmetryenhancement. The neighborhood of the enhancement points in moduli space can beneatly explored by spontaneous symmetry breaking. We generically discuss toroidal compactificationsof arbitrary dimensions and maximally enhanced gauge groups, and theninspect more closely the example of T2 at the SU(3)L × SU(3)R point, which is the simplestsetup containing all the non-trivialities of the generic case. We show that the entiremoduli space can be described in a unified way by considering compactifications on higherdimensional tori.