Constraints on symmetry from holography (1810.05337v2)

Abstract: In this letter we use the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence to establish a set of old conjectures about symmetries in quantum gravity. These 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 non-perturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.

• The paper shows that quantum gravity forbids global symmetries using holographic methods.
• The paper employs AdS/CFT duality and entanglement wedge reconstruction to link bulk gauge symmetries with boundary representations.
• The paper demonstrates that enforcing compact internal gauge groups is crucial for a consistent holographic quantum gravity framework.

Overview of "Constraints on Symmetry from Holography"

The paper "Constraints on Symmetry from Holography" by Daniel Harlow and Hirosi Ooguri rigorously investigates conjectures regarding symmetries within the framework of quantum gravity, specifically focusing on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. This research explores three conjectural constraints: the impossibility of global symmetries, the requirement of dynamical objects for all irreducible representations of any internal gauge symmetry, and the necessity for these symmetries to be compact. The significance of this paper stems from exploring these hypotheses that are deeply rooted in theoretical physics, yet are not inherently evident when viewed from a bulk perspective.

Key Findings

The paper reviews classical arguments based on black hole physics, which traditionally support these conjectures but have notable exceptions and loopholes, such as discrete global symmetries and assumptions regarding short-distance physics. The researchers leverage the AdS/CFT correspondence to eliminate these gaps, utilizing the intricacies of this duality to demonstrate that these symmetry constraints apply within this theoretical framework. The use of entanglement wedge reconstruction and the Ryu-Takayanagi (RT) formula substantiates the mechanism by which these conjectures hold in the holographic context.

1. No Global Symmetries: The research supports the conjecture that quantum gravity prohibits global symmetries, arguing through entanglement wedge reconstruction that such symmetries would be incompatible with the structure of holography.
2. Completeness of Gauge Representations: It is demonstrated that any valid bulk long-range gauge symmetry must reflect a splittable global symmetry on the boundary. The authors reference established representation theory arguments to confirm the need for complete representation of gauge symmetries.
3. Compactness of Internal Symmetries: The paper posits the compactness of internal gauge symmetry groups by incorporating assumptions about the completeness of operator algebras in CFTs. This argument is expanded upon by considering finiteness in generated symmetry representations and their implications on compactness.

Implications and Future Directions

The theoretical implications of the paper extend to deeper understanding in fields where quantum gravity and gauge theories intersect, demanding that any proposed model comply with these criteria of symmetry constraints. The practical ramifications may affect how researchers build models for quantum gravity that consider holographic properties. A significant insight presented involves treating non-perturbative elements as critical to establishing these symmetry properties, stressing the role of the AdS/CFT correspondence in understanding quantum gravitational theories.

Future research could explore extending these constraints beyond the AdS/CFT framework to other holographic theories and general spacetimes, challenging prevailing structures in theoretical physics. Moreover, there remains interest in solidifying bounds on the masses of charged objects alluded to in these discussions. Efforts to resolve the potential scale of approximate global symmetries not covered in this work suggest avenues ripe for both analytical and numerical exploration within string theory contexts.

In conclusion, the paper clarifies longstanding conjectures by applying insights from holography, enforcing a stringent framework that aligns quantum gravitational behavior with gauge symmetries, ultimately offering a more cohesive understanding of symmetries in quantum gravity.