Research Paper#Theoretical Physics, Quantum Field Theory, S-Duality, Monopoles🔬 ResearchAnalyzed: Jan 3, 2026 06:27
S-Duality for Non-Abelian Monopoles
Analysis
This paper provides a general proof of S-duality in $\mathcal{N}=4$ super-Yang-Mills theory for non-Abelian monopoles. It addresses a significant gap in the understanding of S-duality beyond the maximally broken phase, offering a more complete picture of the theory's behavior. The construction of magnetic gauge transformation operators is a key contribution, allowing for the realization of the $H^s \times (H^{\vee})^s$ symmetry.
Key Takeaways
- •Provides a general proof of S-duality for non-Abelian monopoles.
- •Addresses the non-Abelian regime where the subgroup H contains a semisimple factor.
- •Constructs non-Abelian magnetic gauge transformation operators.
- •Realizes the $H^s \times (H^{\vee})^s$ symmetry at the level of monopole quantum mechanics.
Reference
“Each BPS monopole state is naturally labeled by a weight of the relevant $W$-boson representation of $(H^{\vee})^{s}$.”