Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory

Abstract

We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4d simplicial complex with arbitrary number of simplices. We show that for a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a partition of the simplicial complex into three regions: Non-degenerate region, Type-A degenerate region and Type-B degenerate region. On both the non-degenerate and Type-A degenerate regions, the critical configuration implies a non-degenerate Euclidean geometry, while on the Type-B degenerate region, the critical configuration implies a vector geometry. Furthermore we can split the Non-degenerate and Type-A regions into sub-complexes according to the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin foam amplitude at critical configuration gives a Regge action that contains a sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with on-shell connection. The asymptotic formula of the spin foam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.

27 pages, 5 figures, references added

References in corpus (13)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Polyhedra in loop quantum gravity
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Path integral representation of spin foam models of 4d gravity
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Generalized Spinfoams
• Spinfoams in the holomorphic representation
• Emergence of gravity from spinfoams

Cited by in corpus (45)

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• Lorentzian spinfoam propagator
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Holonomy spin foam models: Asymptotic geometry of the partition function
• Group field theory condensate cosmology: An appetizer
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• Pachner moves in a 4d Riemannian holomorphic Spin Foam model
• Asymptotic analysis of spin foam amplitude with timelike triangles
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• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Relational evolution of effectively interacting GFT quantum gravity condensates
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Addendum: EPRL/FK Asymptotics and the Flatness Problem
• From spin foams to area metric dynamics to gravitons
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections
• Towards effective actions for the continuum limit of spin foams
• Emergent 4-dimensional linearized gravity from spin foam model
• Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics
• Analytic Continuation of Spin foam Models
• Bulk amplitude and degree of divergence in 4d spin foams
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• On Spinfoams Near a Classical Curvature Singularity
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• Timelike twisted geometries
• Classical dynamics for Loop Gravity: The 2-vertex model
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
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• Geometry from local flatness in Lorentzian spin foam theories
• The hessian in spin foam models
• A simpler way of imposing simplicity constraints
• Spin foam propagator: A new perspective to include a cosmological constant
• Spinfoam tunneling of quantum geometries in angle variables
• A saddle-point finder and its application to the spin foam model