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

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 $D$-dimensional conformal field theory model, as well as nonperturbatively by using the "gravity dual'' of ${\cal{N}}=4$ super Yang-Mills on the Coulomb branch; i.e. the Dirac-Born-Infeld action on AdS${}_5 \times S^5$.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 $N$ tachyons and one massless particle with $26 -D$ compactified directions, and we show that at least for $D>4$, 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 $D \leq 4$ 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