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Generalized symmetries and holography in ABJM-type theories

Oren Bergman, Yuji Tachikawa, Gabi Zafrir

TL;DR

The paper shows that generalized symmetries organize the spectrum and dual descriptions of ABJM-type theories, enabling a holographic realization of not only the familiar ${U(N)_k\times U(N)_{-k}}$ theory but a whole family of quotients like $(U(N)_k\times U(N)_{-k})/\mathbb{Z}_{m'}$ and $(SU(N)_k\times SU(N)_{-k})/\mathbb{Z}_{n'}$. A bulk topological term $S_{top}$ in $AdS_4$ couples the NSNS two-form to RR gauge fields, restricting boundary conditions and mapping to discrete gauging in the 3d SCFT, thereby reproducing the full spectrum of dressed monopoles, di-baryons, and Wilson lines across theories. The authors explicitly relate massless bulk combinations to the boundary global symmetries $U(1)_{\cal M}$ and $U(1)_{\cal B}$ and demonstrate how boundary conditions encode the presence or absence of di-baryon operators, monopole operators, and one-form symmetries, resolving longstanding puzzles and unifying the holographic picture. The work also outlines generalizations to more intricate families and discusses future directions, including additional boundary conditions and less supersymmetric analogs.

Abstract

We revisit the N=6 superconformal Chern-Simons-matter theories and their supergravity duals in the context of generalized symmetries. This allows us to finally clarify how the $SU(N)\times SU(N)$ and $(SU(N)\times SU(N))/\mathbb{Z}_N$ theories, as well as other quotient theories that have recently been discussed, fit into the holographic framework. It also resolves a long standing puzzle regarding the di-baryon operator in the $U(N)\times U(N)$ theory.

Generalized symmetries and holography in ABJM-type theories

TL;DR

The paper shows that generalized symmetries organize the spectrum and dual descriptions of ABJM-type theories, enabling a holographic realization of not only the familiar theory but a whole family of quotients like and . A bulk topological term in couples the NSNS two-form to RR gauge fields, restricting boundary conditions and mapping to discrete gauging in the 3d SCFT, thereby reproducing the full spectrum of dressed monopoles, di-baryons, and Wilson lines across theories. The authors explicitly relate massless bulk combinations to the boundary global symmetries and and demonstrate how boundary conditions encode the presence or absence of di-baryon operators, monopole operators, and one-form symmetries, resolving longstanding puzzles and unifying the holographic picture. The work also outlines generalizations to more intricate families and discusses future directions, including additional boundary conditions and less supersymmetric analogs.

Abstract

We revisit the N=6 superconformal Chern-Simons-matter theories and their supergravity duals in the context of generalized symmetries. This allows us to finally clarify how the and theories, as well as other quotient theories that have recently been discussed, fit into the holographic framework. It also resolves a long standing puzzle regarding the di-baryon operator in the theory.

Paper Structure

This paper contains 22 sections, 39 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. ${\cal N}=6$ Super-Chern-Simons Theories
  3. $U(N)_k\times U(N)_{-k}$
  4. One-form symmetry:
  5. A mixed anomaly:
  6. $SU(N)_k\times SU(N)_{-k}$
  7. One-form symmetry:
  8. A mixed anomaly:
  9. $(U(N)_k\times U(N)_{-k})/\mathbb{Z}_k$
  10. $(SU(N)_k\times SU(N)_{-k})/\mathbb{Z}_N$
  11. Generalization
  12. AdS/CFT with boundary conditions
  13. Review of the basics
  14. "Standard" boundary conditions
  15. "Alternative" boundary conditions
  16. ...and 7 more sections

Figures (8)

  • Figure 1: The discrete gauging relations between the three basic 3d ${\cal N}=6$ theories.
  • Figure 2: The general discrete gauging relations for ${\cal N}=6$ SCS theories.
  • Figure 3: A holographic description of (a) a dressed monopole and a di-baryon, and (b) the relation ${\cal B}^k = {\cal M}_{-N}$, in the $(U(N)_k\times U(N)_{-k})/\mathbb{Z}_k = (SU(N)_k\times SU(N)_{-k})/\mathbb{Z}_N$ theory.
  • Figure 4: A holographic description of (a) a dressed monopole, and (b) $k$ Wilson lines being screened by an antisymmetric monopole in the $U(N)_k\times U(N)_{-k}$ theory.
  • Figure 5: A holographic description of (a) a baryon, and (b) $N$ Wilson lines being screened by gluons in the $SU(N)_k\times SU(N)_{-k}$ theory.
  • ...and 3 more figures