M2-branes on a constant flux background

Abstract

We describe a compactified Supermembrane, or M2-brane, with 2-form fluxes generated by constant three-forms that are turned on a 2-torus of the target space $M_9\times T^2$. We compare this theory with the one describing a $11D$ M2-brane formulated on $M_9\times T^2$ target space subject to an irreducible wrapping condition. We show that the flux generated by the bosonic 3-form under consideration is in a one to one correspondence to the irreducible wrapping condition. After a canonical transformation both Hamiltonians are exactly the same up to a constant shift in one particular case. Consequently both of them, share the same spectral properties. We conclude that the Hamiltonian of the M2-brane with 2-form target space fluxes on a torus has a purely discrete spectrum with eigenvalues of finite multiplicity and it can be considered to describe a new sector of the microscopic degrees of freedom of M-theory. We also show that the total membrane momentum in the direction associated to the flux condition acquires a quantized contribution in correspondence to the flux units that have been turned on.

arXiv commentLatex, 15 pages, title changed, paper revised, results improved

References in corpus (24)

• M Theory As A Matrix Model: A Conjecture
• An SL(2,Z) Multiplet of Type IIB Superstrings
• Matrix Perturbation Theory For M-theory On a PP-Wave
• Superspace Geometry for Supermembrane Backgrounds
• Lectures on Supergravity p-branes
• Membranes Wrapped on Holomorphic Curves
• Supermembrane on the PP-wave Background
• Membranes and Three-form Supergravity
• Supermembranes with Winding
• On the Stability of Compactified D=11 Supermembranes
• Discreteness of the spectrum of the compactified D=11 supermembrane with non-trivial winding
• On The spectrum of a Noncommutative Formulation of the D=11 Supermembrane with Winding
• Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories
• D=11 Supermembrane wrapped on calibrated submanifolds
• The Spin of the M2-Brane and Spin-Spin Interactions via Probe Techniques
• Spectral properties in supersymmetric matrix models
• Matrix Theory in a Constant C Field Background
• The Supermembrane with Central Charges on a G2 Manifold
• M2-branes wrapped on holomorphic curves
• Supermembrane origin of type II gauged supergravities in 9D
• T-duality Invariance of the Supermembrane
• N=1 4D Supermembrane from 11D
• Heterotic and type I strings from twisted supermembranes
• Magnetic monopoles over topologically non trivial Riemann Surfaces

Cited by in corpus (8)

• Nonrelativistic expansion of M2 branes and M theory backgrounds
• The Massive Supermembrane on a Knot
• Type IIB parabolic ($p,q$)-strings from M2-branes with fluxes
• Spinning solutions for the bosonic M2-brane with $C_{\pm }$ fluxes
• Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes
• Supersymmetric algebra of the massive supermembrane
• The M2-brane over the twisted torus with punctures
• D2-brane with RR and NSNS fluxes and its dual M-theory origin