2021
DOI: 10.1088/1361-6382/abf897
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Addendum to ‘EPRL/FK asymptotics and the flatness problem’

Abstract: We show that, when an approximation used in this prior work is removed, the resulting improved calculation yields an alternative derivation, in the particular case studied, of the accidental curvature constraint of Hellmann and Kaminski. The result is at the same time extended to apply to almost all non-degenerate Regge-like boundary data and a broad class of face amplitudes. This resolves a tension in the literature.

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Cited by 20 publications
(11 citation statements)
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References 22 publications
(57 reference statements)
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“…The accidental flatness constraint is consistent with the above argument about over-constrained equations, and it has been demonstrated explicitly in the example well-studied in, e.g., [12,36]. If one only considers the real critical point for the dominant contribution to A(K), Eq.…”
Section: Complex Critical Point and Effective Dynamicssupporting
confidence: 76%
“…The accidental flatness constraint is consistent with the above argument about over-constrained equations, and it has been demonstrated explicitly in the example well-studied in, e.g., [12,36]. If one only considers the real critical point for the dominant contribution to A(K), Eq.…”
Section: Complex Critical Point and Effective Dynamicssupporting
confidence: 76%
“…The same conclusion can also be derived using saddle point techniques, and Poisson resummation [43]. We preferred to follow the singular support argument to demystify the result of [23] because it focuses more on the holonomies than the geometries.…”
Section: Extended Eprl Spin Foam Amplitudesmentioning
confidence: 89%
“…The "naive" flatness problem [40,41,42,23,43] claims that, at fixed triangulation, the amplitude is dominated in the large (boundary) spin limit by flat geometries. For a path integral formulation of a quantum theory, the amplitude is exponentially suppressed if and only if the boundary data is inconsistent with the classical equation of motions.…”
Section: Extended Eprl Spin Foam Amplitudesmentioning
confidence: 99%
“…The EPRL-FK model [1,2] (we will refer to it as just EPRL for brevity) is the stateof-the-art spin foam model. There is a large consensus in the community [3][4][5][6][7] that the classical continuum theory can be recovered with a double limit of finer discretization and vanishing h. This observation is supported by the emergence of Regge geometries and the Regge action in the asymptotics of the 4-simplex vertex amplitude for large quantum numbers [8,9] and the recent study of many vertices transition amplitudes.…”
Section: Introductionmentioning
confidence: 97%