Selfdual strings and loop space Nahm equations

By Andreas Gustavsson. 2008

312 citations recorded by the source corpus.

We give two independent arguments why the classical membrane fields should be take values in a loop algebra. The first argument comes from how we may construct selfdual strings in the M5 brane from a loop space version of the Nahm equations. The second argument is that there appears to be no infinite set of finite-dimensional Lie algebras (such as su(N) for any N) that satisfies the algebraic structure of the membrane theory.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7de50374623ccc5fba26d0b208762e6e04570ceb

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Citations in the corpus

Fractional M2-branes (2008, background): “Motivated by the work of Bagger and Lambert [1] (see also [2-4]), there has recently been great interest in studying three dimensional superconformal field theories and their relation to the low-energy theory on M2-branes.”
N=4 Superconformal Chern-Simons Theories with Hyper and Twisted Hyper Multiplets (2008, background): “A family of abelian theories are identified with those proposed earlier in the context of the M-crystal model for M2-branes probing (C2/Zn) 2 orbifolds.”
Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry (2008, background): “In [16℄ it was proposed that these xed points ould bereformulated in a more useful dual formulation analogous to a Seiberg dual.”
Ghost-free superconformal action for multiple M2-branes (2008, background): “Bagger and Lambert [1, 2, 3], as well as Gustavsson [4, 5] discovered the general rules for constructing an action for a three-dimensional theory with OSp(8|4) superconformal symmetry.”
M5-brane in three-form flux and multiple M2-branes (2008, unknown): “28 98 1 e-mail address: pmho@phys.ntu.edu.tw 2 e-mail address: imamura@hep-th.phys.s.u-tokyo.ac.jp 3 e-mail address: matsuo@phys.s.u-tokyo.ac.jp 4 e-mail address: shiba@hep-th.phys.s.u-tokyo.ac.jp”
M2 to D2 revisited (2008, methodology): “12 02 We present two derivations of the multiple D2 action from the multiple M2brane model proposed by Bagger-Lambert and Gustavsson.”
M2-branes, 3-Lie algebras and Plucker relations (2008, background): “Later it was supersymmetrized by Gustavsson in [4], see also [5].”
n-ary algebras: a review with applications (2010, background): “It turned out that this determined completely the finite 3-Lie algebra [34, 35, 265] to be the simple euclidean A4 one; of course, it is also possible to have a direct sum of multiple A4 copies and trivial one-dimensional algebras, as conjectured in [56, 266].”
N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds (2008, unknown): “The idea was crystalized by Bagger and Lambert [2–4] and Gustavsson [5, 6] (BLG) who proposed an N = 8 Chern-Simons theory based on 3-algebra, and gave an explicit example with SO(4) = SU(2) × SU(2) gauge group.”
Lie 3-Algebra and Multiple M2-branes (2008, background): “A weaker form of the conjecture has already been studied in [22].”
Bagger-Lambert Theory for General Lie Algebras (2008, background): “[ 9 , 10]. 3 Earlier studies of 3-algebras for Lorentzian metrics can be found in [11].”