Abstract
We construct the effective action for toroidal compactifications of bosonic string theory from generalized Scherk-Schwarz reductions of double field theory. The enhanced gauge symmetry arising at special points in moduli space is incorporated into this framework 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 full massless sector of the theory. We show that the effective action reproduces the right masses of scalar and vector fields when moving sligthly away from the points of maximal symmetry enhancement. The neighborhood of the enhancement points in moduli space can be neatly explored by spontaneous symmetry breaking. We generically discuss toroidal com-pactifications of arbitrary dimensions and maximally enhanced gauge groups, and then inspect more closely the example of T2 at the SU(3)L × SU(3)R point, which is the simplest setup containing all the non-trivialities of the generic case. We show that the entire moduli space can be described in a unified way by considering compactifications on higher dimensional tori.
Highlights
The low energy limit of string theory compactifications on string-size manifolds cannot be obtained by usual Kaluza-Klein reductions of ten-dimensional supergravity, since these do not incorporate the light modes originating from strings or branes wrapping cycles of the internal manifold
The non-Abelian gauge symmetries arising in toroidal compactifications of string theory require additional structures
We have incorporated the enhanced gauge symmetry arising at special points in the moduli space of compactifications on T k by building an O(d + n, d + n) structure, where n + n is the dimension of the left and right enhanced gauge groups
Summary
The low energy limit of string theory compactifications on string-size manifolds cannot be obtained by usual Kaluza-Klein reductions of ten-dimensional supergravity, since these do not incorporate the light modes originating from strings or branes wrapping cycles of the internal manifold. The internal piece is such that the C-bracket algebra gives rise to the G × G symmetry Plugging this generalized metric in the double field theory action and following the generalized Scherk-Schwarz reduction of [7, 8], we obtain an action that exactly reproduces the string theory three-point functions at the point of symmetry enhancement. Basic notions of laced Lie algebras and Lie groups are reviewed in appendix A, some basic facts about cocycles are contained in appendix B and the explicit discussion of symmetry breaking on T 4 is the subject of appendix C
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