399 research outputs found
Unimodular Gravity and the lepton anomalous magnetic moment at one-loop
We work out the one-loop contribution to the lepton anomalous magnetic moment
coming from Unimodular Gravity. We use Dimensional Regularization and
Dimensional Reduction to carry out the computations. In either case, we find
that Unimodular Gravity gives rise to the same one-loop correction as that of
General Relativity.Comment: 16 pages, 5 figure
Unimodular Trees versus Einstein Trees
The maximally helicity violating (MHV) tree level scattering amplitudes
involving three, four or five gravitons are worked out in Unimodular Gravity.
They are found to coincide with the corresponding amplitudes in General
Relativity. This a remarkable result, insofar as both the propagators and the
vertices are quite different in both theories.Comment: 20 pages, 5 figure
Unimodular Gravity and General Relativity UV divergent contributions to the scattering of massive scalar particles
We work out the one-loop and order UV divergent
contributions, coming from Unimodular Gravity and General Relativity, to the S
matrix element of the scattering process
in a theory with mass . We show that both Unimodular
Gravity and General Relativity give rise to the same UV divergent contributions
in Dimension Regularization. This seems to be at odds with the known result
that in a multiplicative MS dimensional regularization scheme the General
Relativity corrections, in the de Donder gauge, to the beta function
of the coupling do not vanish, whereas the
Unimodular Gravity corrections, in a certain gauge, do vanish. Actually, we
show that the UV divergent contributions to the 1PI Feynman diagrams which give
rise to those non-vanishing corrections to do not contribute
to the UV divergent behaviour of the S matrix element of and this shows that any physical consequence
--such existence of asymptotic freedom due to gravitational interactions--
drawn from the value of is not physically meaningful.Comment: 13 pages, 4 figure
Quantum duality under the theta-exact Seiberg-Witten map
We show that in the perturbative regime defined by the coupling constant, the
theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with
or without Supersymmetry-- gives an ordinary gauge theory which is, at the
quantum level, dual to the former. We do so by using the on-shell DeWitt
effective action and dimensional regularization. We explicitly compute the
one-loop two-point function contribution to the on-shell DeWitt effective
action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten
map. We find that the non-local UV divergences found in the propagator in the
Feynman gauge all but disappear, so that they are not physically relevant. We
also show that the quadratic noncommutative IR divergences are gauge-fixing
independent and go away in the Supersymmetric version of the U(1) theory.Comment: 47 pages, 21 figures. Version published in JHEP under the reference:
JHEP09(2016)05
Quantum noncommutative ABJM theory: first steps
We introduce ABJM quantum field theory in the noncommutative spacetime by
using the component formalism and show that it is N=6 supersymmetric. For the
U(1)_{\kappa} x U(1)_{-\kappa} case, we compute all one-loop 1PI two and three
point functions in the Landau gauge and show that they are UV finite and have
well-defined commutative limits theta^{\mu\nu} -> 0, corresponding exactly to
the 1PI functions of the ordinary ABJM field theory. This result also holds for
all one-loop functions which are UV finite by power counting. It seems that the
quantum noncommutative ABJM field theory is free from the noncommutative IR
instabilities.Comment: 43 pages and 25 figures, corrected trivial typos, misprints,
misplaced symbols et
Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
We compute the one-loop 1PI contributions to all the propagators of the
noncommutative N=1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the
means of the theta-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then
we extract the UV divergent contributions and the noncommutative IR
divergences. We show that all the quadratic noncommutative IR divergences add
up to zero in each propagator.Comment: 55 pages, 53 figures, version published in JHE
Scattering of fermions in the Yukawa theory coupled to Unimodular Gravity
We compute the lowest order gravitational UV divergent radiative corrections
to the S matrix element of the
scattering process in the massive Yukawa theory, coupled either to Unimodular
Gravity or to General Relativity. We show that both Unimodular Gravity and
General Relativity give rise to the same UV divergent contribution in
Dimensional Regularization. This is a nontrivial result, since in the classical
action of Unimodular Gravity coupled to the Yukawa theory, the graviton field
does not couple neither to the mass operator nor to the Yukawa operator. This
is unlike the General Relativity case. The agreement found points in the
direction that Unimodular Gravity and General Relativity give rise to the same
quantum theory when coupled to matter, as long as the Cosmological Constant
vanishes. Along the way we have come across another unexpected cancellation of
UV divergences for both Unimodular Gravity and General Relativity, resulting in
the UV finiteness of the one-loop and order of the vertex
involving two fermions and one graviton only.Comment: 21 pages, 12 figure
Unimodular gravity and the gauge/gravity duality
Unimodular gravity can be formulated so that transverse diffeomorphisms and
Weyl transformations are symmetries of the theory. For this formulation of
unimodular gravity, we work out the two-point and three-point
contributions to the on-shell classical gravity action in the leading
approximation and for an Euclidean AdS background. We conclude that these
contributions do not agree with those obtained by using General Relativity due
to IR divergent contact terms. The subtraction of these IR divergent terms
yields the same IR finite result for both unimodular gravity and General
Relativity. Equivalence between unimodular gravity and General Relativity with
regard to the gauge/gravity duality thus emerges in a non trivial way.Comment: A reference adde
Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields
The enforcement of the unimodularity condition in a gravity theory by means
of a Lagrange multiplier leads, in general, to inconsistencies upon
quantization. This is so, in particular, when the classic linear splitting of
the metric between the background and quantum fields is used. To avoid the need
of introducing such a Lagrange multiplier while using the classic linear
splitting, we carry out the quantization of unimodular gravity with extra Weyl
symmetry by using Becchi-Rouet-Stora-Tyutin (BRST) techniques. Here, two gauge
symmetries are to be gauge-fixed: transverse diffeomorphisms and Weyl
transformations. We perform the gauge-fixing of the transverse diffeomorphism
invariance by using BRST transformations that involve antisymmetric ghost
fields. We show that these BRST transformations are compatible with the BRST
transformations needed to gauge-fix the Weyl symmetry, so that they can be
combined in a set of transformations generated by a single BRST operator.
Newton's law of gravitation is derived within the BRST formalism we put forward
as well as the Slavnov-Taylor equation.Comment: 24 pages, 1 table, 1 figur
The one-loop unimodular graviton propagator in any dimension
For unimodular gravity, we work out, by using dimensional regularization, the
complete one-loop correction to the graviton propagator in any space-time
dimension. The computation is carried out within the framework where unimodular
gravity has Weyl invariance in addition to the transverse diffeomorphism gauge
symmetry. Thus, no Lagrange multiplier is introduced to enforce the
unimodularity condition. The quantization of the theory is carried out by using
the BRST framework and there considering a large continuous family of
gauge-fixing terms. The BRST formalism is developed in such a way that the set
of ghost, {anti-ghost} and auxiliary fields and their BRST changes do not
depend on the space-time dimension, as befits dimensional regularization. As an
application of our general result, and at D=4, we obtain the renormalized
one-loop graviton propagator in the dimensional regularization minimal
{subtraction} scheme. We do so by considering two simplifying gauge-fixing
choices.Comment: 32 pages, 4 figure
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