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Dyonic Instantons in 5-dim Yang-Mills Chern-Simons Theories

Seok Kim, Ki-Myeong Lee, Sungjay Lee

TL;DR

The paper analyzes dyonic instantons in five‑dimensional ${\cal N}=1$ Yang–Mills theories with a Chern–Simons term, showing that the CS term induces a background magnetic field on the instanton moduli space and yields 1/2‑BPS configurations saturating a pseudo‑BPS bound. The low‑energy dynamics of multiple instantons is captured by a one‑dimensional gauged matrix model with a background charge, and the moduli‑space dynamics acquire a first‑order magnetic term that encodes CS effects. For a single instanton, explicit ADHM constructions yield the scalar profiles, charges, and angular momentum, and the moduli‑space quantization reveals non‑abelian electric charge in the symmetric phase, with ground states described by lowest Landau levels on coset spaces and, in the noncommutative case, Calabi‑type metrics. The results connect to brane realizations, noncommutative geometry, and potential ultraviolet completions, highlighting the rich structure of solitons in 5d YMCS theories.

Abstract

We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.

Dyonic Instantons in 5-dim Yang-Mills Chern-Simons Theories

TL;DR

The paper analyzes dyonic instantons in five‑dimensional Yang–Mills theories with a Chern–Simons term, showing that the CS term induces a background magnetic field on the instanton moduli space and yields 1/2‑BPS configurations saturating a pseudo‑BPS bound. The low‑energy dynamics of multiple instantons is captured by a one‑dimensional gauged matrix model with a background charge, and the moduli‑space dynamics acquire a first‑order magnetic term that encodes CS effects. For a single instanton, explicit ADHM constructions yield the scalar profiles, charges, and angular momentum, and the moduli‑space quantization reveals non‑abelian electric charge in the symmetric phase, with ground states described by lowest Landau levels on coset spaces and, in the noncommutative case, Calabi‑type metrics. The results connect to brane realizations, noncommutative geometry, and potential ultraviolet completions, highlighting the rich structure of solitons in 5d YMCS theories.

Abstract

We consider the BPS dyonic instantons in the 5-dim supersymmetric Yang-Mills Chern-Simons theories. Its field theoretic structures and the moduli space dynamics in term of the ADHM data have been explored in detail. We find that the field theoretic Chern-Simons term leads to an effective magnetic field on instanton moduli space.

Paper Structure

This paper contains 15 sections, 135 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction and Conclusion
  2. 5-dim ${\cal N}=1$ Supersymmetric Gauge Theories
  3. the Lagrangian
  4. Brane Configuration
  5. Vacuum Moduli
  6. BPS Configurations
  7. BPS Energy Bound and BPS Equations
  8. BPS Configurations
  9. A Single Dyonic $SU(N)$ Instanton
  10. Low Energy Dynamics
  11. One-dimensional $U(K)$ Gauge Theory
  12. Moduli Space Dynamics
  13. A Single Chern-Simons Instanton Moduli Dynamics
  14. Quantization of A Single Instanton Moduli Space
  15. the ADHM Formalism and the Higgs Solutions

Figures (1)

  • Figure 1: Brane configurations for 5d supersymmetric gauge theory