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Non-Abelian R-symmetry and dielectric branes

Francesco Mignosa, Diego Rodriguez-Gomez

TL;DR

This work investigates the holographic realization of the non-Abelian $SO(6)_R$ R-symmetry in $\mathcal{N}=4$ SYM by focusing on 1/2-BPS operators in the $[0,J,0]$ representation and identifying bulk symmetry operators. It shows that small-$J$ physics is governed by gravitational waves and large-$J$ physics by D3 giant gravitons, with the dielectric effect linking the two descriptions. The symmetry operators are realized by two non-BPS bulk objects—KK monopoles and D4 branes—and their equivalence is established via dielectric expansions, unifying their boundary interpretations as symmetry operations. A symmetry theory (symTh) and a symmetry TFT (symTFT) for $SO(6)_R$ are proposed from the 5d gauged supergravity sector, incorporating a CS term that encodes the self-anomaly and provides a bulk/boundary perspective on charged and symmetry operators. Overall, the results offer a concrete holographic framework for non-Abelian continuous symmetries in AdS/CFT and pave the way for further exploration of fusion, condensation, and monodromy defects in this context.

Abstract

We study the holographic realization of the $SO(6)_R$ R-symmetry of $\mathcal{N}=4$ super Yang-Mills with unitary gauge group. Focusing on 1/2 BPS states in the $[0,J,0]$ representation of $SO(6)_R$, it is known that depending on the scaling of $J$ with $N$, these are best described holographically in terms of gravitational waves ($J\ll N$) or D3 brane giant gravitons ($J\sim N$). These two descriptions are bridged by the dielectric effect, as the D3 giant can be regarded as a puffed-up configuration of gravitational waves. The natural non-BPS branes for symmetry operators are either 4-branes or non-BPS Kaluza-Klein monopoles. We show that the former can be regarded as a dielectric expansion of the latter, in parallel to the charged operators. We also propose symTh and symTFT candidates for the $SO(6)_R$ symmetry, whose operators at the boundary must correspond to the non-BPS branes.

Non-Abelian R-symmetry and dielectric branes

TL;DR

This work investigates the holographic realization of the non-Abelian R-symmetry in SYM by focusing on 1/2-BPS operators in the representation and identifying bulk symmetry operators. It shows that small- physics is governed by gravitational waves and large- physics by D3 giant gravitons, with the dielectric effect linking the two descriptions. The symmetry operators are realized by two non-BPS bulk objects—KK monopoles and D4 branes—and their equivalence is established via dielectric expansions, unifying their boundary interpretations as symmetry operations. A symmetry theory (symTh) and a symmetry TFT (symTFT) for are proposed from the 5d gauged supergravity sector, incorporating a CS term that encodes the self-anomaly and provides a bulk/boundary perspective on charged and symmetry operators. Overall, the results offer a concrete holographic framework for non-Abelian continuous symmetries in AdS/CFT and pave the way for further exploration of fusion, condensation, and monodromy defects in this context.

Abstract

We study the holographic realization of the R-symmetry of super Yang-Mills with unitary gauge group. Focusing on 1/2 BPS states in the representation of , it is known that depending on the scaling of with , these are best described holographically in terms of gravitational waves () or D3 brane giant gravitons (). These two descriptions are bridged by the dielectric effect, as the D3 giant can be regarded as a puffed-up configuration of gravitational waves. The natural non-BPS branes for symmetry operators are either 4-branes or non-BPS Kaluza-Klein monopoles. We show that the former can be regarded as a dielectric expansion of the latter, in parallel to the charged operators. We also propose symTh and symTFT candidates for the symmetry, whose operators at the boundary must correspond to the non-BPS branes.
Paper Structure (14 sections, 51 equations, 1 figure, 1 table)

This paper contains 14 sections, 51 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Charged operators
  3. Small dimension: $J\ll N$
  4. Large dimension: $J\sim N$
  5. Symmetry operators
  6. Non-BPS KK monopoles
  7. 4-branes
  8. Dielectric effect for symmetry operators
  9. Dielectric non-BPS branes
  10. Non-BPS KK monopoles from dielectric D4's
  11. The symTh/symTFT
  12. Conclusions
  13. R-symmetry from $SO(6)$ gauged supergravity
  14. The R-symmetry gauge field

Figures (1)

  • Figure 1: Cartoon of the completed brane: on the left, we show the $\mathcal{C}_{\phi}$ patch. On the right, the completion to make a fully closed surface.