Wormholes, CFTs and Random Matrix Theory Reveal Quantum Gravity Links.

Research establishes a connection between the statistical properties of two-dimensional conformal field theories and calculations using techniques from three-dimensional gravity. This work constructs wormhole geometries – including those with trumpet-like boundaries – to model statistical behaviour of quantum field theory observables and facilitates direct computation of complex three-dimensional manifolds.

The interplay between gravity and quantum field theory continues to yield unexpected connections, and recent work explores a precise relationship between the geometry of three-dimensional space and the statistical properties of two-dimensional quantum field theories. Researchers are utilising techniques borrowed from mathematical surgery – the process of altering the topology of a space – to compute quantities related to the behaviour of these theories, specifically focusing on the statistical distribution of energy levels and the shapes of exotic wormholes. Jan de Boer, Joshua Kames-King, and Boris Post, from the Institute for Theoretical Physics at the University of Amsterdam and the Laboratory for Theoretical Fundamental Physics at EPFL, detail this approach in their paper, ‘Surgery and statistics in 3d gravity’, demonstrating how geometric manipulations can provide insights into the complex behaviour of quantum systems.

Mapping Quantum Fields to Spacetime Geometry via Random Matrix Theory

Recent research details a novel computational technique linking the statistical properties of Conformal Field Theories (CFTs) to the geometry of Anti-de Sitter (AdS) spacetime, furthering exploration of the AdS/CFT correspondence. This duality posits a relationship between gravitational theories in AdS space and quantum field theories residing on its boundary.

The core of the work centres on a method termed ‘RMT surgery’. This technique establishes a connection between off-shell partition functions – mathematical objects describing the probability of a particular state in a quantum system – in three-dimensional CFTs and the spectral statistics of CFT observables. Observables are measurable physical quantities within the theory.

Researchers employed calculations involving off-shell Euclidean wormholes – hypothetical tunnels connecting different regions of spacetime – to demonstrate how gravitational structures encode information about the statistical behaviour of CFT states. Specifically, calculations were performed on wormholes resembling four-punctured spheres and torus-like geometries. These calculations reveal the presence of ‘level repulsion’ within the high-energy sector of the CFT.

Level repulsion is a quantum mechanical phenomenon where energy levels of a system avoid coinciding. Its observation in this context suggests a deep connection between the geometry of spacetime and the quantum properties of the CFT. The research demonstrates that surgical methods – topological manipulations of the wormhole geometry – can simplify the calculation of Seifert manifolds, a class of three-dimensional spaces, thereby aiding in the analysis of these connections.

The work provides new computational tools for investigating the AdS/CFT correspondence and offers insights into the fundamental relationship between gravity and quantum field theory. It suggests that the geometry of spacetime is not merely a backdrop for quantum phenomena, but is intrinsically linked to the statistical properties of the quantum fields that inhabit it.