Year: 2013
Type: erratum
Abstract: We correct what amounts to a sign error in the proof of part (i) of theorem 3. The Plebanski sectors isolated by the linear simplicity constraints do not change—they are still the three sectors (deg), (II+) and (II−). What changes is the characterization of the continuum Plebanski two-form corresponding to the first two terms in the asymptotics of the EPRL vertex amplitude for Regge-like boundary data. These two terms do not correspond to the Plebanski sectors (II+) and (II−), but rather to the two possible signs of the product of the sign of the sector—+1 for (II+) and −1 for (II−)—and the sign of the orientation IJKL B IJ ∧ B KL determined by B IJ . This is consistent with what one would expect, as this is exactly the sign which classically relates the BF action, in the Plebanski sectors (II+) and (II−), to the Einstein–Hilbert action, whose discretization is the Regge action appearing in the asymptotics.
Source: Classical and Quantum Gravity
Author: Jonathan Engle
Institution: Florida Atlantic University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1973051272