On membrane interaction in matrix theory

Abstract

We compute the interaction potential between two parallel transversely boosted wrapped membranes (with fixed momentum $p_{-}$) in D=11 supergravity with compact light-like direction. We show that the supergravity result is in exact agreement with the potential following from the all-order Born-Infeld-type action conjectured to be the leading planar infra-red part of the quantum super Yang-Mills effective action. This provides a non-trivial test of consistency of the arguments relating Matrix theory to a special limit of type II string theory. We also find the potential between two (2+0) D-brane bound states in D=10 supergravity (corresponding to the case of boosted membrane configuration in 11-dimensional theory compactified on a space-like direction). We demonstrate that the result reduces to the SYM expression for the potential in the special low-energy ($\a'\to 0$) limit, in agreement with previous suggestions. In appendix we derive the action obtained from the D=11 membrane action by the world-volume duality transformation of the light-like coordinate $x^{-}$ into a 3-vector.

18 pages, latex. v2: Some clarifying remarks and references added. v3: Further minor corrections and references

References in corpus (8)

• Why is the Matrix Model Correct?
• Higher Order Graviton Scattering in M(atrix) Theory
• A Two-Loop Test of M(atrix) Theory
• Interactions of type IIB D-branes from D-instanton matrix model
• Membrane Scattering with M-Momentum Transfer
• Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem
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• Non-holomorphic Corrections from Threebranes in F Theory
• Gravity and compactified branes in matrix models
• Non-perturbative membrane spin-orbit couplings in M/IIA theory
• Higher Derivative Terms from Threebranes in F Theory
• Emergence of the fuzzy horizon through gravitational collapse
• Probing a D6 + D0 state with D6-branes: SYM - Supergravity correspondence at subleading level
• Are M-atrix theory and Maldacena's conjecture related?
• Some comments about Schwarzschield black holes in Matrix theory
• Dynamical Aspects on Duality between SYM and NCOS from D2-F1 Bound State