2,162 research outputs found
Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups
We consider noncommutative GUT inspired field theories formulated within the
enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our
theories have only gauge fields and fermions, and we compute the UV divergent
part of the one-loop background-field effective action involving two fermionic
fields at first order in the noncommutativity parameter theta. We show that, if
the second-degree Casimir has the same value for all the irreps furnished by
the fermionic multiplets of the model, then, that UV divergent part can be
renormalised by carrying out multiplicative renormalisations of the coupling
constant, theta and the fields, along with the inclusion of theta-dependent
counterterms which vanish upon imposing the equations of motion. These
theta-dependent counterterms have no physical effect since they vanish
on-shell. This result along with the vanishing of the UV divergent part of the
fermionic four-point functions leads to the unexpected conclusion that the
one-loop matter sector of the background-field effective action of these
theories is one-loop multiplicatively renormalisable on-shell. We also show
that the background-field effective action of the gauge sector of the theories
considered here receives no theta-dependent UV divergent contributions at
one-loop. We thus conclude that these theories are on-shell one-loop
multiplicatively renormalisable at first order in theta.Comment: 20 pages, 3 figure
Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
Classically, the dual under the Seiberg-Witten map of noncommutative U(N),
{\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge
symmetry whose fields carry, however, a \theta-deformed nonlinear realisation
of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter
theory we work out at one-loop and first order in the noncommutative parameter
matrix \theta^{\mu\nu} the UV divergent part of its effective action in the
background-field gauge, and, for N>=2, we show that for finite values of N the
gauge sector fails to be renormalisable; however, in the large N limit the full
theory is renormalisable, in keeping with the expectations raised by the
quantum behaviour of the theory's noncommutative classical dual. We also obtain
--for N>=3, the case with N=2 being trivial-- the UV divergent part of the
effective action of the SU(N) noncommutative theory in the enveloping-algebra
formalism that is obtained from the previous ordinary U(N) theory by removing
the U(1) degrees of freedom. This noncommutative SU(N) theory is also
renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3:
New types of field redefinitions were considered, which make the large N U(N)
and the SU(N) theories renormalisable. The conclusions for U(N) with finite N
remain unchanged. Version 4: Corrected mistyped equations, minor revision
Shift versus no-shift in local regularizations of Chern-Simons theory
We consider a family of local BRS-invariant higher covariant derivative
regularizations of Chern-Simons theory that do not shift the value of
the Chern-Simons parameter to k+\,{\rm sign}(k)\,\cv at one loop.Comment: phyzzx, 6 pages, FTUAM 94/8, NIKHEF-H 94/14 and UPRF 93/39
Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism
We consider noncommutative gauge theory defined by means of Seiberg-Witten
maps for an arbitrary semisimple gauge group. We compute the one-loop UV
divergent matter contributions to the gauge field effective action to all
orders in the noncommutative parameters . We do this for Dirac fermions
and complex scalars carrying arbitrary representations of the gauge group. We
use path-integral methods in the framework of dimensional regularisation and
consider arbitrary invertible Seiberg-Witten maps that are linear in the matter
fields. Surprisingly, it turns out that the UV divergent parts of the matter
contributions are proportional to the noncommutative Yang-Mills action where
traces are taken over the representation of the matter fields; this result
supports the need to include such traces in the classical action of the gauge
sector of the noncommutative theory.Comment: 7 page
The Effective Potential, the Renormalisation Group and Vacuum Stability
We review the calculation of the the effective potential with particular
emphasis on cases when the tree potential or the
renormalisation-group-improved, radiatively corrected potential exhibits
non-convex behaviour. We illustrate this in a simple Yukawa model which
exhibits a novel kind of dimensional transmutation. We also review briefly
earlier work on the Standard Model. We conclude that, despite some recent
claims to the contrary, it can be possible to infer reliably that the tree
vacuum does not represent the true ground state of the theory.Comment: 23 pages; 5 figures; v2 includes minor changes in text and additional
reference
Fibre Inflation: Observable Gravity Waves from IIB String Compactifications
We introduce a simple string model of inflation, in which the inflaton field
can take trans-Planckian values while driving a period of slow-roll inflation.
This leads naturally to a realisation of large field inflation, inasmuch as the
inflationary epoch is well described by the single-field scalar potential . Remarkably, for a broad class of vacua
all adjustable parameters enter only through the overall coefficient , and
in particular do not enter into the slow-roll parameters. Consequently these
are determined purely by the number of \e-foldings, , and so are not
independent: . This implies similar
relations among observables like the primordial scalar-to-tensor amplitude,
, and the scalar spectral tilt, : . is
itself more model-dependent since it depends partly on the post-inflationary
reheat history. In a simple reheating scenario a reheating temperature of
GeV gives , corresponding to and , within reach of future observations. The model is
an example of a class that arises naturally in the context of type IIB string
compactifications with large-volume moduli stabilisation, and takes advantage
of the generic existence there of Kahler moduli whose dominant appearance in
the scalar potential arises from string loop corrections to the Kahler
potential. The inflaton field is a combination of Kahler moduli of a K3-fibered
Calabi-Yau manifold. We believe there are likely to be a great number of models
in this class -- `high-fibre models' -- in which the inflaton starts off far
enough up the fibre to produce observably large primordial gravity waves.Comment: Extended calculations beyond the leading approximations, including
numerical integrations of multi-field evolution; Display an example with ; Simplify the discussion of large fields; Corrected minor errors and
typos; Added references; 41 pages LaTeX, 25 figure
Addendum to "Superimposed Oscillations in the WMAP Data?"
We elaborate further on the possibility that the inflationary primordial
power spectrum contains superimposed oscillations. We study various effects
which could influence the calculation of the multipole moments in this case. We
also present the theoretical predictions for two other cosmological
observables, the matter power spectrum and the EE polarization channel.Comment: 4 pages, 3 figures, uses RevTex4, matches published versio
Dirac Born Infeld (DBI) Cosmic Strings
Motivated by brane physics, we consider the non-linear Dirac-Born-Infeld
(DBI) extension of the Abelian-Higgs model and study the corresponding cosmic
string configurations. The model is defined by a potential term, assumed to be
of the mexican hat form, and a DBI action for the kinetic terms. We show that
it is a continuous deformation of the Abelian-Higgs model, with a single
deformation parameter depending on a dimensionless combination of the scalar
coupling constant, the vacuum expectation value of the scalar field at
infinity, and the brane tension. By means of numerical calculations, we
investigate the profiles of the corresponding DBI-cosmic strings and prove that
they have a core which is narrower than that of Abelian-Higgs strings. We also
show that the corresponding action is smaller than in the standard case
suggesting that their formation could be favoured in brane models. Moreover we
show that the DBI-cosmic string solutions are non-pathological everywhere in
parameter space. Finally, in the limit in which the DBI model reduces to the
Bogomolnyi-Prasad-Sommerfield (BPS) Abelian-Higgs model, we find that DBI
cosmic strings are no longer BPS: rather they have positive binding energy. We
thus argue that, when they meet, two DBI strings will not bind with the
corresponding formation of a junction, and hence that a network of DBI strings
is likely to behave as a network of standard cosmic strings.Comment: 25 pages, 12 figure
A model for gelation with explicit solvent effects: Structure and dynamics
We study a two-component model for gelation consisting of -functional
monomers (the gel) and inert particles (the solvent). After equilibration as a
simple liquid, the gel particles are gradually crosslinked to each other until
the desired number of crosslinks has been attained. At a critical crosslink
density the largest gel cluster percolates and an amorphous solid forms. This
percolation process is different from ordinary lattice or continuum percolation
of a single species in the sense that the critical exponents are new. As the
crosslink density approaches its critical value , the shear viscosity
diverges: with a nonuniversal
concentration-dependent exponent.Comment: 6 pages, 9 figure
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