2008/06/30 by Matthias Blau, Martin O'Loughlin, Martin O’Loughlin
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Black brane #Black string #Brane #Brane cosmology #Cosmology and Gravitation Theories #Differential geometry #Dilaton #Geometry #Hyperbolic geometry #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Plane wave #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Spacetime #String theory #Theoretical physics #hep-th
paper · pdf · doi:10.1088/1126-6708/2008/09/112
published as JHEP 0809:112,2008 · 11 pages; v2 & v3: references added + minor cosmetic corrections
arxiv created 2008/08/25 · openalex publication_date 2008/09/23 · arxiv updated 2011/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a natural generalisation of the BLG multiple M2-brane action to membranes in curved plane wave backgrounds, and verify in two different ways that the action correctly captures the non-trivial space-time geometry. We show that the M2 to D2 reduction of the theory along a non-trivial direction in field space is equivalent to the D2-brane world-volume Yang-Mills theory with a non-trivial (null-time dependent) dilaton in the corresponding IIA background geometry. As another consistency check of this proposal we show that the properties of metric 3-algebras ensure the equivalence of the Rosen coordinate version of this action (time-dependent metric on the space of 3-algebra valued scalar fields, no mass terms) and its Brinkmann counterpart (constant couplings but time-dependent mass terms). We also establish an analogous result for deformed Yang-Mills theories in any dimension which, in particular, demonstrates the equivalence of the Rosen and Brinkmann forms of the plane wave matrix string action.