Distributions in CFT. Part II. Minkowski space

Autor: Jiaxin Qiao, Petr Kravchuk, Slava Rychkov
Přispěvatelé: Institut des Hautes Etudes Scientifiques (IHES), IHES, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Champs, Gravitation et Cordes, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Jazyk: angličtina
Rok vydání: 2021
Předmět:
space: Minkowski
invariance: conformal
Nuclear and High Energy Physics
Pure mathematics
tube
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Field Theories in Higher Dimensions
QC770-798
Conformal and W Symmetry
01 natural sciences
operator product expansion
field theory: Euclidean
Conformal symmetry
Nuclear and particle physics. Atomic energy. Radioactivity
0103 physical sciences
Euclidean geometry
Minkowski space
Ising model
unitarity
correlation function
010306 general physics
Commutative property
Axiom
Physics
field theory: conformal
Conformal Field Theory
010308 nuclear & particles physics
Conformal field theory
axiomatic field theory
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
Wightman axioms
D Intuition about Lemma 4.2
16. Peace & justice
spectral
Signature (topology)
signature
Zdroj: Journal of High Energy Physics
Journal of High Energy Physics, Springer, 2021, 08, pp.094. ⟨10.1007/JHEP08(2021)094⟩
Journal of High Energy Physics, Vol 2021, Iss 8, Pp 1-131 (2021)
ISSN: 1126-6708
1029-8479
DOI: 10.1007/JHEP08(2021)094⟩
Popis: CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).
Databáze: OpenAIRE
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