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

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 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.

Half‐Maximal Supersymmetry from Exceptional Field Theory

“…It would be interesting to see whether one can generalise this to an effective approach, in which one would hope to see the full type II / heterotic dualities. Related to this, and given the recent work on gauge enhancement at self-dual tori [119][120][121] in DFT, one might wonder whether the formalism here can capture gauge enhancements of half-maximal string and M-theory compactifications.…”

Gauge symmetry enhancing-breaking from a Double Field Theory perspective

“…it is possible to show [3,44] that the scalar matrix, in the Left-Right basis C can be written as an expansion in scalar fluctuations…”

“…For instance, P = (±1, 0, ±1, 0) generates a k m (1)L and k m (1)R (where k m (1)R = 0 at 7 A systematic derivation is proposed in [44] with a modification of the generalized Lie derivative. 8 We avoid writing the dependence on moduli in order to lighten the notation.…”

“…Therefore, DFT is providing us with a generic field theory action that leads to an accurate description of string theory results even in a non trivial stringy situation of gauge symmetry enhancing-breaking when massive states with associated momenta and winding are present. As discussed in [3] for the circle case (and extended in [44] for other situations) by giving vev's to some specific scalar fields, the string broken symmetry action can be approximately obtained as an expansion in powers of the vev,s. It is worth insisting that the DFT construction we are presenting here is already producing the broken symmetry phase.…”

“…However, only recently windings were actually included in DFT. In [3] a step in this direction was performed by showing that DFT can describe the massless sector of an enhanced gauge symmetry situation with windings playing a fundamental role and where an unpaired number of Left and Right N −N = ±1 moving oscillators is implied in string theory (see also [44]). Also in [34] a generalized KK toroidal compactification (GKK) of DFT containing towers of massive states with generic windings and KK momenta was considered, for the case N −N = 0, namely with the level matching condition P 2 = 0.…”