Abstract
We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in five and eleven dimensions and find the dynamical equations it predicts at low levels. Restricting these results to contain only the usual fields of supergravity and the generalised space-time to be the usual space-time we find the equations of motion of the five and eleven dimensional maximal supergravity theories. Since this non-linear realisation contains effects that are beyond the supergravity approximation and are thought to be present in an underlying theory we conclude that the low energy effective action of string and branes must possess an E11 symmetry.
Highlights
It has been conjectured that the low energy effective action for strings and branes is the non-linear realisation of the semi-direct product of E 11 and its vector (l1 ) representation, denoted E 11 ⊗s l1[1,2]
To understand why the non-linear realisation leads to equations of motion one just has to realise that the group element of equation (1.1) contains the fields of the theory which depend on the generalised space–time
In writing the group element g E we have used the local symmetry of the non-linear realisation of equation (1.2) to gauge away all terms that involve negative level generators in g E
Summary
It has been conjectured that the low energy effective action for strings and branes is the non-linear realisation of the semi-direct product of E 11 and its vector (l1 ) representation, denoted E 11 ⊗s l1. A more systematic approach was used to constructing the equations of motion of the E 11 ⊗s l1 non-linear realisation in eleven [15] and four [16] dimensions by including both the higher level generalised coordinates and local symmetries in I c ( E 11 ). To understand why the non-linear realisation leads to equations of motion one just has to realise that the group element of equation (1.1) contains the fields of the theory which depend on the generalised space–time. In writing the group element g E we have used the local symmetry of the non-linear realisation of equation (1.2) to gauge away all terms that involve negative level generators in g E. In equation (2.20) no vielbeins are used to convert the indices on the fields, that is, the fields that appear, which come from the group element, have their indices replaced, for example a is replaced by μ
Published Version (Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have