Fluctuating Ensemble Averages and the BTZ Threshold (2501.08257v1)

Abstract: Recent work shows fascinating links between ensemble averaging and the Swampland program. In order to break the emerging global symmetries of the ensemble averaging as dictated by the no global symmetries conjecture, one may consider fluctuations away from the average given by deviations in the Siegel-Weil formula. In this work, we investigate the physical interpretation of these fluctuations in the bulk physics and pinpoint the states giving rise to them. For this purpose, we explore an ensemble of generalised Narain CFTs and build the AdS$_{3}$ gravitational dual in the Chern-Simons (CS) framework. We study the associated charged BTZ black hole solution and assess its stability. Using the Swampland weak gravity conjecture, we show that the fluctuations of the ensemble average are below the BTZ threshold and correspond to a sublattice of superextremal states emitted by the black hole. We exploit the logarithmic density of states to derive bounds on the charged vectors of the abelian CS symmetry and introduce a novel formulation of the density function to ensure consistency with the sublattice WGC. We establish bounds that allows to distinguish heavy states contributing to the average from light states generating fluctuations around it.

• The paper distinguishes generalized Narain CFTs and explores how ensemble averaging breaks global symmetries through fluctuations, linking this to the Swampland program's no-global symmetry conjecture.
• The research constructs a gravitational dual in AdS$_{3}$ via Einstein-Chern-Simons theory to analyze charged BTZ black holes, revealing that super-extremal states below the threshold generate fluctuations consistent with the Weak Gravity Conjecture.
• The study offers insights into reconciling holography and Swampland principles by clarifying how ensemble symmetries relate to gravitational stability and the black hole spectrum, potentially influencing quantum gravity model development.

Fluctuating Ensemble Averages and the BTZ Threshold: Insights and Implications

The paper "Fluctuating Ensemble Averages and the BTZ Threshold" investigates the intricate links between ensemble averaging in Conformal Field Theories (CFTs), the Swampland program, and holography, placing a spotlight on the BTZ black hole threshold. It presents a nuanced exploration of generalised Narain CFTs, examining the physical interpretations of fluctuations around ensemble averages and their associations with global symmetries, particularly through the lens of the Swampland program.

Ensemble averages have gained prominence due to their role in breaking global symmetries, which are conjectured to be absent in any consistent theory of quantum gravity according to the Swampland hypothesis. The authors explore ensemble averaging within generalized Narain CFTs and their gravitational duals, providing insights into their bulk physics through an Abelian Chern-Simons framework in AdS$_{3}$. This setup allows the authors to probe the charged BTZ black hole solutions and their stability, effectively elucidating the interplay among holography, Chern-Simons theory, and Swampland conjectures.

Key Contributions and Findings

1. Generalised Narain CFTs:
   • The paper distinguishes between standard Narain CFTs and their generalized counterparts, highlighting differences such as lattice types and modularity constraints. This distinction is pivotal for understanding the global Asp of their moduli spaces and their respective ensemble averaging.
2. Swampland and Global Symmetries:
   • A notable contribution is the analysis of how global symmetries of ensemble averaged CFTs relate to the Swampland program. The no-global symmetry conjecture indicates that such symmetries must be broken, which is achieved through considering fluctuations around the ensemble average, leading to a connection with the Siegel-Weil deviations.
3. Gravitational Dual and Black Holes:
   • The research constructs the gravitational dual in AdS$_{3}$ space, characterized by Einstein-Chern-Simons theory. This construction enables a deeper analysis of charged BTZ black holes, which reveals that super-extremal states below the black hole threshold generate fluctuations around the ensemble average, offering a novel perspective on black hole evaporation and consistency with the Weak Gravity Conjecture (WGC).
4. Density of States and Fluctuations:
   • The paper extends the Cardy formula to explore the torus density of states in the context of ensemble averaging. It innovatively aligns the density of states with the sublattice WGC, providing a framework that categorizes heavy and light states within ensemble contributions and fluctuations.

Implications and Future Directions

The paper offers valuable insights into the reconciliation of holography with Swampland principles, particularly the interplay between ensemble symmetries and gravitational stability. One direct implication is a refined understanding of the spectrum of states contributing to the stability and evaporation of black holes in three dimensions. This positions the ensemble averaging mechanism as potentially fundamental in clarifying not just gravity, but also broader Swampland conjectures.

Practically, the research might influence the development of quantum gravity models that must satisfy both holographic principles and Swampland constraints. Theoretical implications extend to further investigations into the classification of CFTs and their gravitational duals, opening pathways to explore topological and non-topological gravity intersections.

For future research, extending this framework to different dimensional AdS spaces and exploring the impact of varying CFT parameters could offer profound insights. Integrating these findings with low-energy effective field theories that confront Swampland and holographic considerations may bridge gaps in our understanding of universality in quantum gravity frameworks.

Overall, the paper contributes significantly to the nexus of ensemble averaging, CFTs, and the Swampland program, paving the way for further exploration into the fundamental structures of quantum gravity and the properties of theoretical black holes.