Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence
arXiv:1511.00995
Abstract
We explore dualities and solution-generating transformations in various contexts. Our focus is on the T-duality invariant form of supergravity known as double field theory, the -invariant M-theory extended geometry, and metrics dual under the fluid/gravity correspondence to an incompressible Navier-Stokes fluid. In double field theory (DFT), a wave solution is shown to embed both the F1 string and the pp-wave. For the former, the Goldstone mode dynamics reproduce the duality symmetric string introduced by Tseytlin. We consider solution-generating techniques in DFT in the presence of an isometry, firstly via Buscher-like transformations in the DFT string -model, and secondly via the DFT equations of motion. In the -invariant geometry, we provide a chain rule derivation of the covariant equations of motion, and present a wave solution embedding the M2 brane. Lastly, solution-generating transformations for metrics with an isometry are considered in the context of the fluid/gravity correspondence. Our focus is on the vacuum Rindler metric dual to a codimension one Navier-Stokes fluid. In particular, when there is a radially directed Killing vector, the dual fluid is found to exhibit an energy scaling invariance valid to all orders in the hydrodynamic expansion.
PhD Thesis, 113 pages, 1 figure
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