Universal critical behavior in tensor models for four-dimensional quantum gravity
Astrid Eichhorn, Johannes Lumma, Antonio D. Pereira, Arslan Sikandar
Abstract
A bstract Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a model by employing background-independent coarse-graining techniques where the tensor size serves as a pre-geometric notion of scale. A fixed point candidate which features two relevant directions is found. The possible relevance of this result in view of universal results for quantum gravity and a potential connection to the asymptotic-safety program is discussed.
Topics & Concepts
PhysicsQuantum gravityTensor (intrinsic definition)Theoretical physicsConnection (principal bundle)Limit (mathematics)Point (geometry)QuantumStatistical physicsClassical mechanicsQuantum geometryGravitationRelevance (law)Tensor densityQuantum spacetimeTensor productQuantum information processingMathematical physicsCritical phenomenaQuantum mechanicsRandom matrixSemiclassical gravityHořava–Lifshitz gravityDual (grammatical number)Tensor contractionSpin foamNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical PhysicsStochastic processes and statistical mechanics