Constraints on Symmetries from Holography

In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti–de Sitter/conformal field theory correspondence. These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the nonperturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.

Figure 1

A bulk time slice. The center of this slice does not lie within the shaded entanglement wedges of the boundary regions $R_i$, so the $U(g,R_i)$ in those regions must commute with any operator there.

Figure 2

A Wilson line threading the AdS-Schwarzschild wormhole.