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A New Duality Between $\mathcal{N}=8$ Superconformal Field Theories in Three Dimensions

Nathan B. Agmon, Shai M. Chester, Silviu S. Pufu

TL;DR

The paper proposes a new duality between BLG$_3$ and ABJM$_{3,1}$, recast as BLG$_3$ being the interacting sector of ABJM$_{3,1}$ (with ABJM$_{1,1}$ as a decoupled free factor). It tests the duality by matching moduli spaces, the superconformal index, and the $S^3$ partition function, and goes further by analyzing 1d topological sectors to extract OPE coefficients, finding quantitative agreement between the two theories. The results are reinforced by bootstrap-consistent constraints from four-point data of protected operators and by explicit operator mappings of BPS multiplets. Altogether, the work provides strong evidence that the interacting sector of ABJM$_{3,1}$ is captured by the BLG$_3$ theory, offering a new perspective on M2-brane dynamics and exact localization techniques in 3d ${\cal N}=8$ SCFTs. The approach combines monopole operator analysis, localization, and 1d reductions to deliver a coherent set of cross-checked invariants supporting a novel duality in the landscape of 3d superconformal field theories.

Abstract

We propose a new duality between two 3d $\mathcal{N}=8$ superconformal Chern-Simons-matter theories: the $U(3)_1 \times U(3)_{-1}$ ABJM theory and a theory consisting of the product between the $\left(SU(2)_3\times SU(2)_{-3}\right)/\mathbb{Z}_2$ BLG theory and a free ${\cal N} = 8$ theory of eight real scalars and eight Majorana fermions. As evidence supporting this duality, we show that the moduli spaces, superconformal indices, $S^3$ partition functions, and certain OPE coefficients of BPS operators in the two theories agree.

A New Duality Between $\mathcal{N}=8$ Superconformal Field Theories in Three Dimensions

TL;DR

The paper proposes a new duality between BLG and ABJM, recast as BLG being the interacting sector of ABJM (with ABJM as a decoupled free factor). It tests the duality by matching moduli spaces, the superconformal index, and the partition function, and goes further by analyzing 1d topological sectors to extract OPE coefficients, finding quantitative agreement between the two theories. The results are reinforced by bootstrap-consistent constraints from four-point data of protected operators and by explicit operator mappings of BPS multiplets. Altogether, the work provides strong evidence that the interacting sector of ABJM is captured by the BLG theory, offering a new perspective on M2-brane dynamics and exact localization techniques in 3d SCFTs. The approach combines monopole operator analysis, localization, and 1d reductions to deliver a coherent set of cross-checked invariants supporting a novel duality in the landscape of 3d superconformal field theories.

Abstract

We propose a new duality between two 3d superconformal Chern-Simons-matter theories: the ABJM theory and a theory consisting of the product between the BLG theory and a free theory of eight real scalars and eight Majorana fermions. As evidence supporting this duality, we show that the moduli spaces, superconformal indices, partition functions, and certain OPE coefficients of BPS operators in the two theories agree.

Paper Structure

This paper contains 15 sections, 69 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction and Summary
  2. Operator Spectrum and the Superconformal Index
  3. Low-lying BPS Operator Spectrum
  4. ABJM$_{3, 1}$
  5. BLG$_3$
  6. Superconformal Index
  7. Moduli Space
  8. The $S^3$ Partition Function
  9. One-Dimensional Topological Sector
  10. ABJM$_{3, 1}$
  11. Free Sector
  12. Interacting Sector
  13. BLG$_3$
  14. Four Point Function
  15. OPE Coefficients in ${\cal O}^{(1,1)}\times {\cal O}^{(2,2)}$ and ${\cal O}^{(2,2)}\times {\cal O}^{(2,2)}$

Figures (2)

  • Figure 1: The field content of the two-gauge group description of ${\cal N} = 8$ SCFTs. The gauge group is $G_1 \times G_2$ with opposite Chern-Simons levels for the two factors. The matter content consists of two pairs of bifundamental chiral multiplets whose bottom components are denoted by $A_1$, $A_2$ and $B_1$, $B_2$. As explained in the main text, such theories have ${\cal N} = 8$ SUSY at the IR fixed point only for special values of $k$ and/or for special gauge groups $G_1$ and $G_2$.
  • Figure 2: Upper and lower bounds on $\bar{\lambda}_{2,2,2,2}^2$ and $\bar{\lambda}_{2,2,2,0}^2$ OPE coefficients in terms of the stress tensor OPE coefficient $\bar{\lambda}_{2,2,1,1}^2$, where the orange shaded regions are allowed, and the plot ranges from the supergravity limit $\bar{\lambda}_{2,2,1,1}\to0$ ($c_T\to\infty$) to the free theory $\bar{\lambda}_{2,2,1,1}^2=16$. The red dots denote the values for the interacting sector of the ABJM$_{3, 1}$ theory or for the BLG$_3$ theory, given in \ref{['OPEFinal']}. The $\bar{\lambda}_{2,2,2,2}^2$ bounds can be mapped into the $\bar{\lambda}_{2,2,2,0}^2$ bounds using \ref{['crossConstraints']}. These bounds were computed following Chester:2014fya, except with the improved parameters $j_\text{max}=88$ and $\Lambda=43$.