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Nonrelativistic Superconformal M2-Brane Theory

Ki-Myeong Lee, Sangmin Lee, Sungjay Lee

TL;DR

This work constructs and analyzes the nonrelativistic, superconformal limit of the mass-deformed ABJM model in the symmetric phase, revealing a 3D super-Schrödinger symmetry with 14 supercharges and an operator-state framework based on a harmonic potential. The authors derive the NR ABJM Lagrangian with CS, kinetic, and interaction terms, implement Gauss-law constraints, and demonstrate a positive-definite Hamiltonian consistent with supersymmetry. They develop the representation theory of the resulting super-Schrödinger algebra, establish unitarity bounds on scaling dimension and particle number, and classify chiral primaries and their descendants, discussing implications for a NR superconformal index. The paper also discusses the role of charge-flux composites as gauge-invariant, quasi-local operators and considers potential connections to nonrelativistic holography of the ABJM construction.

Abstract

We investigate the low energy physics of particles in the symmetric phase of the N=6 mass-deformed ABJM theory in terms of the superconformal nonrelativistic field theory with 14 supercharges. They describe the certain kind of excitations on M2 branes in the background of external four-form flux. We study the nonrelativistic superconformal algebra and their representations by using the operator-state correspondence with the related harmonic oscillator Hamiltonian. We find the unitarity bounds on the scaling dimension and particle number of any local operator, and comment on subtleties in computing the superconformal Witten index that counts the chiral operators.

Nonrelativistic Superconformal M2-Brane Theory

TL;DR

This work constructs and analyzes the nonrelativistic, superconformal limit of the mass-deformed ABJM model in the symmetric phase, revealing a 3D super-Schrödinger symmetry with 14 supercharges and an operator-state framework based on a harmonic potential. The authors derive the NR ABJM Lagrangian with CS, kinetic, and interaction terms, implement Gauss-law constraints, and demonstrate a positive-definite Hamiltonian consistent with supersymmetry. They develop the representation theory of the resulting super-Schrödinger algebra, establish unitarity bounds on scaling dimension and particle number, and classify chiral primaries and their descendants, discussing implications for a NR superconformal index. The paper also discusses the role of charge-flux composites as gauge-invariant, quasi-local operators and considers potential connections to nonrelativistic holography of the ABJM construction.

Abstract

We investigate the low energy physics of particles in the symmetric phase of the N=6 mass-deformed ABJM theory in terms of the superconformal nonrelativistic field theory with 14 supercharges. They describe the certain kind of excitations on M2 branes in the background of external four-form flux. We study the nonrelativistic superconformal algebra and their representations by using the operator-state correspondence with the related harmonic oscillator Hamiltonian. We find the unitarity bounds on the scaling dimension and particle number of any local operator, and comment on subtleties in computing the superconformal Witten index that counts the chiral operators.

Paper Structure

This paper contains 19 sections, 127 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction and Concluding Remarks
  2. Nonrelativistic Limit of the Mass-deformed ABJM Model
  3. The mass-deformed ABJM model
  4. A nonrelativistic limit
  5. The nonrelativistic superconformal ABJM model
  6. Symmetries, Conserved Charges and their Algebra
  7. Internal symmetry
  8. Space-time symmetry
  9. Supersymmetry
  10. Super-Schrödinger algebra: summary
  11. Schrödinger algebra: ${\bf sch_2^{(0)}}$
  12. super Schrödinger algebra: ${\bf sch_2^{(1)}}$
  13. super Schrödinger algebra: ${\bf sch_2^{(2)}}$
  14. Comparison with other nonrelativistic super-algebras
  15. Chiral Primary Operators and States
  16. ...and 4 more sections

Figures (1)

  • Figure 1: Multiplet structure of the super-Schrödinger algebra. (a) A long multiplet consists of eight conformal primary operators. (b) A short (chiral or anti-chiral) multiplet consists of four conformal primary operators.