English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider the parametric representation of the amplitudes of Abelian modelsin the so-called framework of rank $d$ Tensorial Group Field Theory. Thesemodels are called Abelian because their fields live on $U(1)^D$. We concentrateon the case when these models are endowed with particular kinetic termsinvolving a linear power in momenta. New dimensional regularization andrenormalization schemes are introduced for particular models in this class: arank 3 tensor model, an infinite tower of matrix models $\phi^{2n}$ over$U(1)$, and a matrix model over $U(1)^2$. For all divergent amplitudes, weidentify a domain of meromorphicity in a strip determined by the real part ofthe group dimension $D$. From this point, the ordinary subtraction program isapplied and leads to convergent and analytic renormalized integrals.Furthermore, we identify and study in depth the Symanzik polynomials providedby the parametric amplitudes of generic rank $d$ Abelian models. We find thatthese polynomials do not satisfy the ordinary Tutte's rules(contraction/deletion). By scrutinizing the "face"-structure of thesepolynomials, we find a generalized polynomial which turns out to be stable onlyunder contraction.

Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term $\sum_{s}|p_s| + \mu$