Anomalous scale dimensions from time-like braiding

Abstract

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the center of the conformal covering group Z( SO(d, 2)), we explore the possibility of a timelike braiding structure consistent with the timelike ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in D=4 spacetime dimensions. Other ideas of constructions based on the AdS5-CQF T4 or the perturbative SYM approach in their relation to the present idea are briefly mentioned.

Wigner particle theory and local quantum physics

“…Since conformal theories in any dimensions (even beyond chiral theories) are "almost free" (in the sense that the only structure which distinguishes them from free massless theories is the spectrum of anomalous dimension which is related to an algebraic braid-like structure in timelike direction [38]), we believe that they also can be classified and constructed by modular methods.…”

Braided structure in 4-dimensional conformal quantum field theory

“…Whereas one expects the physical realization in the sense of Rehren's "statistics characters" [15] to continue to hold in higher dimensions, the derivation of modular identities based on Verlinde's geometric argument which led to the modular "duality" (dual temperature β → 2π β ) breaks down. This can be seen by explicitly calculating the partition function of the conformal Hamiltonian R 0 [13] which is equal to the true Hamiltonian of the associated anti-deSitter model. In the case of AdS 4 for which Fronsdal [16] computed its spectrum (i.e.…”

Facts and Fictions About Anti deSitter Spacetimes¶with Local Quantum Matter

“…But taking the compactification into consideration one realizes that all three parts are connected and the space/time-like distinction is meaningless onM . In terms of Wightman correlation functions this is equivalent to the rationality of the analytically continued Wightman functions of observable fields which includes an analytic extension into timelike Jost points [37] [18]. Therefore in order to make contact with particle physics aspects, the use of either the covering M or of more general fields (see next section) onM is very important since only in this way one can implement the pivotal property of causality together with the associated localization concepts.…”

“…where the R-matrices are determined from admissible braid group representations. For more on the timelike braid group structure in higher dimensional conformal QFT we refer to [18].…”

“…where the R-matrices are determined from admissible braid group representations. For more on the timelike braid group structure in higher dimensional conformal QFT we refer to [18]. Since the AdS-CQFT isomorphism implies a radical reprocessing on the physical side, it would be interesting to perform the timelike commutation relation analysis directly within the AdS setting.…”