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Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence

Marcus Benna, Igor Klebanov, Thomas Klose, Mikael Smedbäck

TL;DR

The paper develops an $ ext{N}=2$ superspace framework for the BLG and ABJM theories, proving the full $SU(4)_R$ symmetry of ABJM and exploiting orbifold projections to generate non-chiral and chiral 3D quiver Chern–Simons theories. It proposes holographic duals for these quivers as M2-branes on $AdS_4 imes S^7/( Z_n imes Z_{ ilde{k}})$ backgrounds and analyzes an $SU(3)$-invariant mass deformation that drives an $ ext{N}=2$ sextic theory, potentially dual to Warner’s $U(1)_R imes SU(3)$ AdS$_4$ extremum with an 11D uplift. The work provides explicit superspace actions, demonstrates symmetry enhancements at specific normalization conditions, and connects 3D CFT dynamics to precise M-theory backgrounds via RG flows and operator spectra. Overall, it broadens the landscape of AdS$_4$/CFT$_3$ dual pairs rooted in M2-brane physics and furnishes concrete tools for exploring orbifolds and their holographic implications.

Abstract

We discuss the N=2 superspace formulation of the N=8 superconformal Bagger-Lambert-Gustavsson theory, and of the N=6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N)xU(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N)xU(N))^n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS_4 x S^7/(Z_n x Z_k) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N=8 theory flow to a N=2 superconformal gauge theory with a sextic superpotential. We conjecture that this gauge theory is dual to the U(1)_R x SU(3) invariant extremum of the N=8 gauged supergravity, which was discovered by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more recently.

Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence

TL;DR

The paper develops an superspace framework for the BLG and ABJM theories, proving the full symmetry of ABJM and exploiting orbifold projections to generate non-chiral and chiral 3D quiver Chern–Simons theories. It proposes holographic duals for these quivers as M2-branes on backgrounds and analyzes an -invariant mass deformation that drives an sextic theory, potentially dual to Warner’s AdS extremum with an 11D uplift. The work provides explicit superspace actions, demonstrates symmetry enhancements at specific normalization conditions, and connects 3D CFT dynamics to precise M-theory backgrounds via RG flows and operator spectra. Overall, it broadens the landscape of AdS/CFT dual pairs rooted in M2-brane physics and furnishes concrete tools for exploring orbifolds and their holographic implications.

Abstract

We discuss the N=2 superspace formulation of the N=8 superconformal Bagger-Lambert-Gustavsson theory, and of the N=6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N)xU(N) Chern-Simons theory. In particular, we prove the full SU(4) R-symmetry of the ABJM theory. We then consider orbifold projections of this theory that give non-chiral and chiral (U(N)xU(N))^n superconformal quiver gauge theories. We argue that these theories are dual to certain AdS_4 x S^7/(Z_n x Z_k) backgrounds of M-theory. We also study a SU(3) invariant mass term in the superpotential that makes the N=8 theory flow to a N=2 superconformal gauge theory with a sextic superpotential. We conjecture that this gauge theory is dual to the U(1)_R x SU(3) invariant extremum of the N=8 gauged supergravity, which was discovered by N. Warner 25 years ago and whose uplifting to 11 dimensions was found more recently.

Paper Structure

This paper contains 15 sections, 73 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Summary of BLG theory
  3. BLG theory in $\mathcal{N}=2$ superspace
  4. Expressions in components.
  5. Integrating out auxiliary fields.
  6. ABJM $\mathrm{U}(N)^2$ gauge theory in superspace
  7. Expressions in components.
  8. Integrating out auxiliary fields.
  9. $\mathrm{SU}(4)$ invariance.
  10. Non-chiral orbifold gauge theories
  11. Note added.
  12. Chiral orbifold gauge theories
  13. $\mathcal{N}=2$ superconformal theory with $\mathrm{SU}(3)$ symmetry and RG flow
  14. Discussion
  15. Notation

Figures (2)

  • Figure 1: Non-chiral quiver. The fields $\mathcal{Z}_\ell$ transform in $({\mathbf{N}},{\mathbf{\bar{N}}})$ representations and the fields $\mathcal{W}_\ell$ in $({\mathbf{\bar{N}}},{\mathbf{N}})$ ones. The arrows indicate under which of the $\mathrm{U}_\ell(N)$ the fields transform. For instance $\mathcal{Z}_2$ transforms under $(\mathrm{U}_{3}(N),\mathrm{U}_{2}(N))$. We close the chain by identifying $\mathrm{U}_{2n+1}(N) \equiv \mathrm{U}_{1}(N)$.
  • Figure 2: Chiral quiver. The characteristic property of the chiral quiver is that no nodes are connected by chiral fields with mutually conjugate representation (no anti-parallel arrows).