Abstract
Abstract
Enhanced tensor field theories (eTFTs) have dominant graphs that differ from the melonic diagrams of conventional tensor field theories. They therefore describe pertinent candidates to escape the so-called branched polymer phase, the universal geometry found for tensor models. For generic order d of the tensor field, we compute the perturbative β-functions at one-loop of two just-renormalizable quartic eTFT coined by + or ×, depending on their vertex weights. The models + has two quartic coupling constants
(
λ
,
λ
+
)
, and two 2-point couplings (mass, Za
). Meanwhile, the model × has two quartic coupling constants
(
λ
,
λ
×
)
and three 2-point couplings (mass, Za
,
Z
2
a
). At all orders, both models have a constant wave function renormalization: Z = 1 and therefore no anomalous dimension. Despite such peculiar behavior, both models acquire nontrivial radiative corrections for the coupling constants. The RG flow of the model + exhibits a particular asymptotic safety:
λ
+
is marginal without corrections thus is a fixed point of arbitrary constant value. All remaining couplings determine relevant directions and get suppressed in the UV. Concerning the model ×,
λ
×
is marginal and again a fixed point (arbitrary constant value), λ, µ and Za
are all relevant couplings and flow to 0. Meanwhile
Z
2
a
is a marginal coupling and becomes a linear function of the time scale. This model can neither be called asymptotically safe or free.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics