Strings, branes and the self-dual solutions of Exceptional Field Theory

Abstract

It has been shown that membranes and fivebranes are wave-like or monopolelike solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional Field Theory. This solution solves the twisted self-duality constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic and Dirichlet branes and their bound states, in ten-and eleven-dimensional supergravity may all be extracted from this single solution of Exceptional Field Theory. The solution's properties such as its asymptotic behavior at the core and at infinity are investigated.

Conserved currents of double field theory

“…One reason this is interesting is that one will have duality transformations which map electric and magnetic solutions into each other (for instance, the M2 and M5). Indeed, it has been shown that for the E 7 all the familiar half-BPS solutions appear as a single self-dual solution of exceptional field theory [61]. This is unlike the case in T-duality, where we have argued that one needed different definitions of charge for electrical solutions like the F1 and magnetic solutions like the NS5.…”

“…Indeed, such a solution has recently been written down in [60], in the context of β-supergravity. It is also interesting to note that in [61] it is argued that the duality frame with coordinates (t,z, y µ ) is naturally selected as the appropriate description of the double field theory F1/pp-wave solution near the singularity at r = 0.…”

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory

“…These different solutions were not related by duality. 10 However, in higher rank duality groups one finds that all branes whose worldvolumes are only spatially extended in the internal space are unified into a single solution of the EFT [50,75]. Similarly, as one increases the rank of the duality group considered, various of the M2 and M5 brane solutions will be unified as more of the worldvolume directions fall into the internal space.…”

A Kaluza–Klein Approach to Double and Exceptional Field Theory

“…The answer is that the solution must be 'self-dual' meaning that it will be a wave in one direction and a monopole in the electromagnetic dual direction. This is reported in detail in [57] where these self-dual solutions to EFT were constructed and shown to describe the branes in M-theory and their bound states. For those familiar with the (2,0) theory in 6 dimensions where a self-dual string solution gives rise to the states in 4 dimensions that transform under the 4d SL(2) after dimensional reduction on a torus, this is analogous.…”