Non-supersymmetric AdS and the Swampland (1610.01533v3)

Abstract: We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions.

• The paper posits that non-supersymmetric AdS vacua are unstable due to imbalances between gravitational and gauge forces as predicted by the weak gravity conjecture.
• It employs detailed analysis of BPS versus non-BPS states and holographic dual instabilities to substantiate the claim of inherent instability.
• The research highlights the necessity of supersymmetry or precise flux configurations to ensure stability in viable quantum gravity theories.

An Analysis of Non-supersymmetric AdS Vacua and the Weak Gravity Conjecture

The paper, "Non-supersymmetric AdS and the Swampland" by Hirosi Ooguri and Cumrun Vafa, addresses key conjectures in string theory and quantum gravity, particularly focusing on the implications of the Weak Gravity Conjecture (WGC) for non-supersymmetric Anti-de Sitter (AdS) vacua. The paper posits that non-supersymmetric AdS vacua supported by fluxes must inherently be unstable and offers evidence and theoretical developments that reinforce this assertion.

Context and Main Conjectures

The WGC suggests that in any consistent theory of quantum gravity, gravity should be the weakest force. This conjecture has far-reaching implications for the construction of low-energy effective theories and their potential UV completions, placing certain low-energy solutions into what is termed the "swampland"—a set of theories that cannot be embedded into a consistent quantum gravity framework.

This paper offers a sharpened version of the WGC with a specific focus on AdS vacua. The authors conjecture that non-supersymmetric AdS vacua are unstable, owing to the saturation conditions of gravity and gauge interactions. They further propose that these spaces cannot be part of a consistent quantum theory of gravity unless supported by specific flux configurations between which the gravitational and electromagnetic interactions are perfectly balanced, a condition naturally met by supersymmetric settings.

Evidence and Examples

The paper provides mathematical and theoretical evidence supporting their conjecture, grounded in string theory and M-theory frameworks:

1. BPS and Non-BPS States: The authors explore the role of BPS states, within which gravitational force is precisely counter-balanced by electric or brane forces. Non-supersymmetric configurations lack such states, leading to the proposed instability due to the dominance of Coulomb repulsion over gravitational attraction in non-BPS scenarios.
2. Gravitational Dual Instabilities: Utilizing the holographic principle, the paper posits that non-supersymmetric AdS cannot have a stable holographic dual. Any attempt to construct such a dual results in inconsistencies or instabilities detectable even within the dual conformal field theories.
3. Instanton Solutions and Non-perturbative Effects: The paper discusses instanton solutions that demonstrate the decay of non-supersymmetric AdS spaces to nothing, reinforcing the claim of inherent instability.
4. Dimensional Reduction and Strong Coupling Tests: The authors explore the implications of compactification and dimensional reduction on the WGC, arguing that non-supersymmetric setups fail to meet the conjecture’s criteria under such transformations.

Implications and Future Directions

The conclusions drawn in this paper hold significant implications for theoretical physics, particularly in the fields of quantum gravity and cosmology. The instability of non-supersymmetric AdS vacua challenges existing models in condensed matter physics and quantum information systems that rely on AdS/CFT correspondence—even suggesting limits to their applicability when non-supersymmetric elements are involved.

This work strengthens the argument for stability criteria rooted in supersymmetry and promotes further examination of the swampland conditions for theoretical constructs within string theory frameworks. Going forward, exploration of alternative conjectures or refined definitions of stability in non-supersymmetric scenarios may provide additional insights.

Additionally, the paper encourages further empirical and mathematical investigation into the subtle interplay between different forces in quantum gravity to delineate more clearly between "landscape" (viable theories) and "swampland" constructs. This future work is essential for validating or challenging existing conjectures in the quest for a coherent understanding of the universe at fundamental scales.