48 research outputs found
Hidden Conformal Symmetry in Tree-Level Graviton Scattering
We argue that the scattering of gravitons in ordinary Einstein gravity
possesses a hidden conformal symmetry at tree level in any number of
dimensions. The presence of this conformal symmetry is indicated by the dilaton
soft theorem in string theory, and it is reminiscent of the conformal
invariance of gluon tree-level amplitudes in four dimensions. To motivate the
underlying prescription, we demonstrate that formulating the conformal symmetry
of gluon amplitudes in terms of momenta and polarization vectors requires
manifest reversal and cyclic symmetry. Similarly, our formulation of the
conformal symmetry of graviton amplitudes relies on a manifestly permutation
symmetric form of the amplitude function.Comment: 35 pages, 3 figure
Conformal Extensions of the Standard Model with Veltman Conditions
Using the renormalisation group framework we classify different extensions of
the standard model according to their degree of naturality. A new relevant
class of perturbative models involving elementary scalars is the one in which
the theory simultaneously satisfies the Veltman conditions and is conformal at
the classical level. We term these extensions perturbative natural conformal
(PNC) theories. We show that PNC models are very constrained and thus highly
predictive. Among the several PNC examples that we exhibit, we discover a
remarkably simple PNC extension of the standard model in which the Higgs is
predicted to have the experimental value of the mass equal to 126 GeV. This
model also predicts the existence of one more standard model singlet scalar
boson with a mass of 541 GeV and the Higgs self-coupling to emerge radiatively.
We study several other PNC examples that generally predict a somewhat smaller
mass of the Higgs to the perturbative order we have investigated them. Our
results can be a useful guide when building extensions of the standard model
featuring fundamental scalars.Comment: 18 pages, updated to match published versio
Hot Conformal Gauge Theories
We compute the nonzero temperature free energy up to the order g^6 \ln(1/g)
in the coupling constant for vector like SU(N) gauge theories featuring matter
transforming according to different representations of the underlying gauge
group. The number of matter fields, i.e. flavors, is arranged in such a way
that the theory develops a perturbative stable infrared fixed point at zero
temperature. Due to large distance conformality we trade the coupling constant
with its fixed point value and define a reduced free energy which depends only
on the number of flavors, colors and matter representation.
We show that the reduced free energy changes sign, at the second, fifth and
sixth order in the coupling, when decreasing the number of flavors from the
upper end of the conformal window. If the change in sign is interpreted as
signal of an instability of the system then we infer a critical number of
flavors. Surprisingly this number, if computed to the order g^2, agrees with
previous predictions for the lower boundary of the conformal window for
nonsupersymmetric gauge theories. The higher order results tend to predict a
higher number of critical flavors. These are universal properties, i.e. they
are independent on the specific matter representation.Comment: RevTeX, 2-columns, 10 pages, 10 figure
Four-Fermion Limit of Gauge-Yukawa Theories
We elucidate and extend the conditions that map gauge-Yukawa theories at low
energies into time-honoured gauged four-fermion interactions at high energies.
These compositeness conditions permit to investigate theories of composite
dynamics through gauge-Yukawa theories. Here we investigate whether
perturbative gauge-Yukawa theories can have a strongly coupled limit at
high-energy, that can be mapped into a four-fermion theory. Interestingly, we
are able to precisely carve out a region of the perturbative parameter space
supporting such a composite limit. This has interesting implications on our
current view on models of particle physics. As a template model we use an
gauge theory with Dirac fermions transforming according to the
fundamental representation of the gauge group. The fermions further interact
with a gauge singlet complex Higgs that ceases to be a physical
degree of freedom at the ultraviolet composite scale, where it gives away to
the four-fermion interactions. We compute the hierarchy between the ultraviolet
and infrared composite scales of the theory and show that they are naturally
large and well separated. Our results show that some weakly coupled
gauge-Yukawa theories can be viewed, in fact, as composite theories. It is
therefore tantalising to speculate that the standard model, with its
phenomenological perturbative Higgs sector, could hide, in plain sight, a
composite theory.Comment: 20 pages, 9 figures, 10 pages Appendix, corrected typos and reference
adde
A natural Coleman-Weinberg theory explains the diphoton excess
It is possible to delay the hierarchy problem, by replacing the standard
Higgs-sector by the Coleman-Weinberg mechanism, and at the same time ensure
perturbative naturalness through the so-called Veltman conditions. As we showed
in a previous study, minimal models of this type require the introduction of an
extra singlet scalar further coupled to new fermions. In this constrained setup
the Higgs mass was close to the observed value and the new scalar mass was
below a TeV scale. Here we first extend the previous analysis by taking into
account the important difference between running mass and pole mass of the
scalar states. We then investigate whether these theories can account for the
750 GeV excess in diphotons observed by the LHC collaborations. New QCD-colored
fermions in the TeV mass range coupled to the new scalar state are needed to
describe the excess. We further show, by explicit computation of the running of
the couplings, that the model is under perturbative control till just above the
masses of the heaviest states of the theory. We further suggest related
testable signatures and thereby show that the LHC experiments can test these
models.Comment: Discussion on the perturbative limits of the model is added, Fig.1
updated and new Fig.2 is added; References update
Double-soft behavior of the dilaton of spontaneously broken conformal invariance
The Ward identities involving the currents associated to the spontaneously
broken scale and special conformal transformations are derived and used to
determine, through linear order in the two soft-dilaton momenta, the
double-soft behavior of scattering amplitudes involving two soft dilatons and
any number of other particles. It turns out that the double-soft behavior is
equivalent to performing two single-soft limits one after the other. We confirm
the new double-soft theorem perturbatively at tree-level in a -dimensional
conformal field theory model, as well as nonperturbatively by using the
"gravity dual'' of super Yang-Mills on the Coulomb branch; i.e.
the Dirac-Born-Infeld action on AdS.Comment: 48 pages, one appendi
Double-soft behavior for scalars and gluons from string theory
We compute the leading double-soft behavior for gluons and for the scalars
obtained by dimensional reduction of a higher dimensional pure gauge theory,
from the scattering amplitudes of gluons and scalars living in the world-volume
of a Dp-brane of the bosonic string. In the case of gluons, we compute both the
double-soft behavior when the two soft gluons are contiguous as well as when
they are not contiguous. From our results, that are valid in string theory, one
can easily get the double-soft limit in gauge field theory by sending the
string tension to infinity.Comment: 25 pages, 1 figur
Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String
We construct, in the closed bosonic string, the multiloop amplitude involving
tachyons and one massless particle with compactified directions,
and we show that at least for , the soft behaviors of the graviton and
dilaton satisfy the same soft theorems as at the tree level, up to one
additional term at the subsubleading order, which can only contribute to the
dilaton soft behavior and which we show is zero at least at one loop. This is
possible, since the infrared divergences due to the non-vanishing tachyon and
dilaton tadpoles do not depend on the number of external particles and are
therefore the same both in the amplitude with the soft particle and in the
amplitude without the soft particle. Therefore this leaves unchanged the soft
operator acting on the amplitude without the soft particle. The additional
infrared divergence appearing for depend on the number of external
legs and must be understood on their own.Comment: 20 p. + 23 p. appendices. New version to match the published version;
new appendix (A) added and dependence on compactification radii clarifie
The B-field soft theorem and its unification with the graviton and dilaton
In theories of Einstein gravity coupled with a dilaton and a two-form, a soft
theorem for the two-form, known as the Kalb-Ramond B-field, has so far been
missing. In this work we fill the gap, and in turn formulate a unified soft
theorem valid for gravitons, dilatons and B-fields in any tree-level scattering
amplitude involving the three massless states. The new soft theorem is fixed by
means of on-shell gauge invariance and enters at the subleading order of the
graviton's soft theorem. In contrast to the subsubleading soft behavior of
gravitons and dilatons, we show that the soft behavior of B-fields at this
order cannot be fully fixed by gauge invariance. Nevertheless, we show that it
is possible to establish a gauge invariant decomposition of the amplitudes to
any order in the soft expansion. We check explicitly the new soft theorem in
the bosonic string and in Type II superstring theories, and furthermore
demonstrate that, at the next order in the soft expansion, totally gauge
invariant terms appear in both string theories which cannot be factorized into
a soft theorem.Comment: 27 pages, 1 figur