Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture (1510.07911v2)

Abstract: This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the "principle of completeness", which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim that it leads to a new motivation for (and a clarification of) the "weak gravity conjecture", which I interpret as a strengthening of this principle. This setup gives a simple example of a situation where describing low-energy bulk physics in CFT language requires knowledge of high-energy bulk physics. This contradicts to some extent the notion of "effective conformal field theory", but in fact is an expected feature of the resolution of the black hole information problem. An analogous factorization issue exists also for the gravitational field, and I comment on several of its implications for reconstructing black hole interiors and the emergence of spacetime more generally.

Overview of "Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture"

Daniel Harlow's paper addresses the complexities of reconstructing bulk gauge fields as boundary operators within the AdS/CFT duality, specifically when accounting for wormholes linked to thermofield double states of two CFTs. This paper suggests novel resolutions to existing tensions in theoretical physics, especially concerning bulk gauge fields in AdS/CFT frameworks, providing insights into reconciling microscopic Hilbert space factorization with wormhole structures.

Key Arguments and Claims

1. Splitting of Gauge Fields into Charged Constituents: Harlow proposes that the tension in the reconstruction can be mitigated by decomposing gauge fields into discrete charged elements. This idea leads to a robust argument supporting the "principle of completeness," which posits that the charge lattice in a gauge theory linked with gravity should be fully occupied.
2. Weak Gravity Conjecture Motivation: The paper introduces a new rationale for the weak gravity conjecture, interpreting it as an extension of the completeness principle. This perspective provides an avenue to understand how a gauge field's emergent nature within a quantum gravitational context strengthens theoretical frameworks around the conjecture.
3. High vs. Low-Energy Physics: The manuscript illustrates scenarios highlighting the necessity of incorporating high-energy bulk physics to accurately describe low-energy bulk phenomena in AdS/CFT terms, elucidating inconsistencies with the notion of effective conformal field theory.
4. Factorization and Bulk Quantum Gravity: By exploring analogies in gravitational fields, the paper extends the discussion to implications for black hole interior reconstruction and spacetime emergence, emphasizing that the resolution of factorization issues can imply novel insights into quantum gravity.

Numerical Results and Contradictory Claims

Harlow scrutinizes the notion of effective conformal field theory, indicating instances where low-energy physics requires knowledge of high-energy counterpart physics, which conflicts with traditional views in holography. Additionally, the formulation strengthens the weak gravity conjecture by implying necessary conditions under quantum gravity frameworks.

Practical and Theoretical Implications

Theoretical Implication: The resolution of factorization problems within gauge theories provides substantial backing for core principles like the weak gravity conjecture and completeness principle, offering new pathways in quantum gravity research.

Practical Outlook: From a practical standpoint, these insights pave the way for deeper understandings of gauge fields' role in gravitational theories and potential applications in quantum computing and theoretical models involving wormholes and entanglement scenarios.

Future Directions

Harlow's approach suggests several avenues for further research. Investigating the completeness principle's applicability in broader contexts, particularly non-string quantum gravity theories, could yield invaluable insights. Additionally, delving deeper into the black hole information problem with the factorization aspects might unlock novel paradigms in quantum mechanics and field theory.

In conclusion, Daniel Harlow's exploration of emergent gauge fields and wormhole phenomena within AdS/CFT establishes foundational advancements in theoretical physics by bridging significant conjectures with quantum gravitational dynamics. The insights derived from this work offer substantial contributions to understanding not only the intrinsic nature of gauge fields but also their broader implications in quantum field theory and holography.