Abstract
We examine the equations of motion of double field theory and the duality manifest form of M-theory. We show the solutions of the equations of motion corresponding to null pp-waves correspond to strings or membranes from the usual spacetime perspective. A Goldstone mode analysis of the null wave solution in double field theory produces the equations of motion of the duality manifest string.
Highlights
From the eleven-dimensional supergravity perspective it was a null wave solution
We examine the equations of motion of double field theory and the duality manifest form of M-theory
Double field theory extends the dimensions of spacetime so that the off-diagonal components of the generalized metric — that is the metric of the full extended space — become the NS-NS two-form potential
Summary
In this paper we are dealing with several different spaces of various dimensions at the same time. In DFT this is the normal d-dimensional space and for the SL(5) duality invariant theory where the dimensions are split into 4+7, these are the four dimensions the U-duality group acts on, d = 4. The duals of the spacetime coordinates are denoted by xμ or xμfor DFT and yμν for the SL(5) theory. Together with the normal coordinates xμ they form a doubled or extended space of dimension D with coordinates XM and generalized metric HMN for DFT and MMN for the SL(5) theory, where M = 1, . This acts on a (D × D)-dimensional symmetric vector space whose building blocks are “vectors” of the form VMN with M, N symmetrized.
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