E11, generalised space-time and IIA string theory; the R-R sector

Abstract

We extend the analysis of arXiv:1009.2624, which constructed the non-linear realisation of the semi-direct product of E 11 and the l 1 representation at level zero, to level one. Thus we add to the previously considered N S ⊗ N S fields those of the R ⊗ R sector.

E11 must be a symmetry of strings and branes

“…Siegel theory [22,23], also called doubled field theory, is just a truncation of the nonlinear realisation of E 11 ⊗ s l 1 in ten dimensions to the lowest level zero [24]. The extension of Siegel theory to include the fields of the massless R-R sector of the superstring was first given in reference [25] which extended the E 11 ⊗ s l 1 non-linear realisation theory to level one. It must also be true that exceptional field theory [26], which uses the level zero and one coordinates [2] and ideas [1] of the E 11 approach, is essentially a truncation of the nonlinear realisation of E 11 ⊗ s l 1 to low levels.…”

Generalised space-time and gauge transformations

“…Doubled field theory, or more appropriately Siegel theory, described the massless fields of the NS-NS sector of the superstring, and it can be viewed as the non-linear realisation of E 11 ⊗ s l 1 in ten dimensions at level zero [23]. The extension of Siegel theory to include the Ramond-Ramond sector was first given in reference [24]; it was just the E 11 ⊗ s l 1 non-linear realisation at level one.…”

M-theory and type IIB from a duality manifest action

“…That it should be possible to treat M-theory and IIB in this similar way has been previously suggested by the E 11 framework of West et al [52][53][54][55][56][57][58][59][60][61][62][63][64] in which it is argued that both eleven-dimensional supergravity and the ten-dimensional IIA and IIB supergravities can be understood as non-linear realisations of E 11 . In particular by identifying the generators of the algebra corresponding to IIA and IIB fields, a relation between the two supergravities appears directly at the ten-dimensional level [57,59].…”

“…Indeed, the existence of an inequivalent IIB section for E 6 has already been mentioned in [51]. Eventually, one may wish to address this question using the full mechanics of E 11 where independent evidence [52][53][54][55][56][57][59][60][61][62][63][64] has shown that the full ten-dimensional IIA and IIB supergravities should be contained on an equal footing, just as in N = 2 D = 10 supersymmetric double field theory [34] for T-duality.…”