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 compactifications of arbitrary dimensions and maximally enhanced gauge groups, and then inspect more closely the example of T 2 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.

We show how the gauge and field structure of the tensor hierarchies in Double and E 7(7)Exceptional Field Theory fits into L ∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gaugingdependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.

We compute three-point functions for the SLð2; RÞ-WZNW model. After reviewing the case of the two-point correlator, we compute spectral flow preserving and nonpreserving correlation functions in the space-time picture involving three vertex operators carrying an arbitrary amount of spectral flow. When only one or two insertions have nontrivial spectral flow numbers, the method we employ allows us to find expressions without any constraint on the spin values. Unlike these cases, the same procedure restrains the possible spin configurations when the three vertices belong to nonzero spectral flow sectors. We perform several consistency checks on our results. In particular, we verify that they are in complete agreement with previously computed correlators involving states carrying a single unit of spectral flow.

In this article we investigate the structure of the four-point functions of the AdS 3 -WZNW model. We consider the integral expression for the unflowed four-point correlator involving at least one state in the discrete part of the spectrum derived by analytic continuation from the H + 3 -WZNW model and we show that the conformal blocks can be obtained from those with an extremal-weight state by means of an intertwining operator. We adapt the procedure for dealing with correlators with a single unit of spectral flow charge and we get a factorized integral expression for the corresponding four-point function. We finally transform the formulas back to the space-time picture.