26 research outputs found
Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting
In this paper, we use the exact renormalisation in the context of tensor
models and tensorial group field theories. As a byproduct, we rederive Gaussian
universality for random tensors and provide a general power counting for
Abelian tensorial field theories with a closure constraint, leading us to a
only five renormalizable theories.Comment: 22 pages, 4 figure
Exact Renormalisation Group Equations and Loop Equations for Tensor Models
In this paper, we review some general formulations of exact renormalisation
group equations and loop equations for tensor models and tensorial group field
theories. We illustrate the use of these equations in the derivation of the
leading order expectation values of observables in tensor models. Furthermore,
we use the exact renormalisation group equations to establish a suitable
scaling dimension for interactions in Abelian tensorial group field theories
with a closure constraint. We also present analogues of the loop equations for
tensor models
Composite Leptons at the LHC
In some models of electro-weak interactions the W and Z bosons are considered
composites, made up of spin-one-half subconstituents. In these models a spin
zero counterpart of the W and Z boson naturally appears, whose higher mass can
be attributed to a particular type of hyperfine spin interaction among the
various subconstituents. Recently it has been argued that the scalar state
could be identified with the newly discovered Higgs (H) candidate. Here we use
the known spin splitting between the W/Z and H states to infer, within the
framework of a purely phenomenological model, the relative strength of the
spin-spin interactions. The results are then applied to the lepton sector, and
used to crudely estimate the relevant spin splitting between the two lowest
states. Our calculations in many ways parallels what is done in the SU(6) quark
model, where most of the spin splittings between the lowest lying baryon and
meson states are reasonably well accounted for by a simple color hyperfine
interaction, with constituent (color-dressed) quark masses.Comment: 12 pages, footnotes added. Conforms to published versio
Inconsistencies from a Running Cosmological Constant
We examine the general issue of whether a scale dependent cosmological
constant can be consistent with general covariance, a problem that arises
naturally in the treatment of quantum gravitation where coupling constants
generally run as a consequence of renormalization group effects. The issue is
approached from several points of view, which include the manifestly covariant
functional integral formulation, covariant continuum perturbation theory about
two dimensions, the lattice formulation of gravity, and the non-local effective
action and effective field equation methods. In all cases we find that the
cosmological constant cannot run with scale, unless general covariance is
explicitly broken by the regularization procedure. Our results are expected to
have some bearing on current quantum gravity calculations, but more generally
should apply to phenomenological approaches to the cosmological vacuum energy
problem.Comment: 34 pages. Typos fixed, references added, one section expande
Power counting ans scaling for tensor models
International audienceRandom tensors are natural generalisations of matrix models related to random geometries of dimension D. Here, we revisit the large N limit of tensor models and the power counting of tensorial group field theories using a renormalisation group equation
Wheeler-DeWitt Equation in 3 + 1 Dimensions
Physical properties of the quantum gravitational vacuum state are explored by
solving a lattice version of the Wheeler-DeWitt equation. The constraint of
diffeomorphism invariance is strong enough to uniquely determine the structure
of the vacuum wave functional in the limit of infinitely fine triangulations of
the three-sphere. In the large fluctuation regime the nature of the wave
function solution is such that a physically acceptable ground state emerges,
with a finite non-perturbative correlation length naturally cutting off any
infrared divergences. The location of the critical point in Newton's constant
, separating the weak from the strong coupling phase, is obtained, and it
is inferred from the structure of the wave functional that fluctuations in the
curvatures become unbounded at this point. Investigations of the vacuum wave
functional further suggest that for weak enough coupling, , a
pathological ground state with no continuum limit appears, where configurations
with small curvature have vanishingly small probability. One is then lead to
the conclusion that the weak coupling, perturbative ground state of quantum
gravity is non-perturbatively unstable, and that gravitational screening cannot
be physically realized in the lattice theory. The results we find are in
general agreement with the Euclidean lattice gravity results, and lend further
support to the claim that the Lorentzian and Euclidean lattice formulations for
gravity describe the same underlying non-perturbative physics.Comment: 44 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1207.375
One-loop beta-functions of quartic enhanced tensor field theories
Enhanced tensor field theories (eTFT) 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 of the
tensor field, we compute the perturbative -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 , and two 2-point couplings(mass, ). Meanwhile, the model
has two quartic coupling constants and
three 2-point couplings (mass, , ). At all orders, both models
have a constant wave function renormalization: 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: 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 , is marginal and again a fixed
point (arbitrary constant value), , and are all relevant
couplings and flow to 0. Meanwhile is a marginal coupling and becomes
a linear function of the time scale. This model can neither be called
asymptotically safe or free.Comment: 48 pages, 20 figures, scaling dimensions corrected, some statements
corrected, typos fixe
Classification of higher grade graphs for multi-matrix models
We studied in [Ann. Inst. Henri Poincar\'e D 9, 367-433, (2022)], a complex
multi-matrix model with symmetry, and
whose double scaling limit where simultaneously the large- and large-
limits were taken while keeping the ratio finite and fixed. In
this double scaling limit, the complete recursive characterization of the
Feynman graphs of arbitrary genus for the leading order grade was
achieved. In this current study, we classify the higher order graphs in .
More specifically, and with arbitrary genus, in addition to a
specific class of two-particle-irreducible (2PI) graphs for higher but with genus zero. Furthermore, we demonstrate that counting the
2PI graphs with a single -loop corresponds to enumerating the
alternating knots using the Rolsen's table results, performing a connected sum,
or Tait flyping moves on them.Comment: 61 pages, 75 figure
Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term
We consider the parametric representation of the amplitudes of Abelian models
in the so-called framework of rank Tensorial Group Field Theory. These
models are called Abelian because their fields live on . We concentrate
on the case when these models are endowed with particular kinetic terms
involving a linear power in momenta. New dimensional regularization and
renormalization schemes are introduced for particular models in this class: a
rank 3 tensor model, an infinite tower of matrix models over
, and a matrix model over . For all divergent amplitudes, we
identify a domain of meromorphicity in a strip determined by the real part of
the group dimension . From this point, the ordinary subtraction program is
applied and leads to convergent and analytic renormalized integrals.
Furthermore, we identify and study in depth the Symanzik polynomials provided
by the parametric amplitudes of generic rank Abelian models. We find that
these polynomials do not satisfy the ordinary Tutte's rules
(contraction/deletion). By scrutinizing the "face"-structure of these
polynomials, we find a generalized polynomial which turns out to be stable only
under contraction.Comment: 69 pages, 35 figure