Scaling limit ofN=6superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories

2008/06/30 by Yoshinori Honma, Satoshi Iso, Yoske Sumitomo +1 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Coupling (piping) #Crystallography #Gauge theory #Geometry #Lambda #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Scaling #Scaling limit #hep-th

paper · pdf · doi:10.1103/physrevd.78.105011

published as Phys.Rev.D78:105011,2008 · 21 pages; v2 a subsection added to discuss Generalized Conformal Invariance; v3 discussions on gravity dual added; v4 published version in PRD

arxiv created 2008/11/07 · openalex publication_date 2008/11/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that the N=8 superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed N=6 superconformal U(N)\ifmmode×\else\texttimes\fiU(N) Chern-Simons-matter theories at level (k,\ensuremath-k). The scaling limit (and In"on"u-Wigner contraction) is to scale the trace part of the bifundamental fields as X₀\ensuremath→\ensuremathλ^\ensuremath-1X₀ and an axial combination of the two gauge fields as B_\ensuremathμ\ensuremath→\ensuremathλB_\ensuremathμ. Simultaneously, we scale the level as k\ensuremath→\ensuremathλ^\ensuremath-1k and then take \ensuremathλ\ensuremath→0 limit. Interestingly, the same constraint equation \ensuremath∂²X₀=0 is derived by imposing finiteness of the action. In this scaling limit, M2 branes are located far from the origin of C⁴/Z_k compared to their fluctuations and Z_k identification becomes a circle identification. Hence, the scaled theory describes N=8 supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent SO(8) vector X₀^I and we show that the scaled theory has a generalized conformal symmetry as well as manifest SO(8) with the transformation of the background fields X₀^I.

Citations

• Janus configurations, Chern-Simons couplings, and The θ-Angle in N = 4 super Yang-Mills theory
• D2 or M2? A Note on Membrane Scattering
• Coulomb Branch of the Lorentzian Three Algebra Theory
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• Selfdual strings and loop space Nahm equations
• Supersymmetric Yang-Mills theory from lorentzian three-algebras
• On the structure of k -Lie algebras
• Constraining maximally supersymmetric membrane actions
• A dilatonic deformation ofAdS5and its field theory dual
• NM2-branes toND2-branes
• Cubic Matrix, Nambu Mechanics and Beyond
• Multiple M2-branes and the embedding tensor
• Gauge symmetry and supersymmetry of multiple M2-branes
• Membranes on calibrations
• 𝒩 = 8 superconformal Chern-Simons theories
• D2 to D2

Cited by

• 3dN=8Lorentzian Bagger-Lambert-Gustavsson theory as a scaling limit of 3d superconformalN=6Aharony-Bergman-Jafferis-Maldacena theory
• Remark About Scaling Limit of ABJ Theory
• Multiple M2-branes and plane waves

Related

• 3dN=8Lorentzian Bagger-Lambert-Gustavsson theory as a scaling limit of 3d superconformalN=6Aharony-Bergman-Jafferis-Maldacena theory
• 𝒩 = 8 superconformal Chern-Simons theories
• 𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)
• Multiple M2-branes and the embedding tensor