We derive a universal soft theorem for every scattering amplitude with at least one massless particle in an arbitrary theory of scalars. Our results follow from the geometry of field space and are valid for any choice of mass spectrum, potential terms, and higher-derivative interactions. For a vanishing potential, the soft limit of every amplitude is equal to the field-space covariant derivative of an amplitude with one fewer particle. Furthermore, the Adler zero and the dilaton soft theorem are special cases of our results. We also discuss more exotic scenarios in which the soft limit is non-trivial but still universal. Last but not least, we derive new theorems for multiple-soft limits which directly probe the field-space curvature, as well as on-shell recursion relations applicable to two-derivative scalar field theories exhibiting no symmetries whatsoever.
CERN（欧洲核子研究组织）；Institute for Fundamental Science University of Oregon（俄勒冈大学基础科学研究所）；Department of Mathematics and Physics University of Stavanger（斯塔万格大学数学与物理系）
This chapter reviews the construction of ``soft-collinear gravity'', the effective field theory which describes the interaction of collinear and soft gravitons with matter (and themselves), to all orders in the soft-collinear power expansion, focusing on the essential concepts. Among them are an emergent soft background gauge symmetry, which lives on the light-like trajectories of energetic particles and allows for a manifestly gauge-invariant representation of the interactions in terms of a soft covariant derivative and the soft Riemann tensor, and a systematic treatment of collinear interact…
We generalize soft theorems of the nonlinear sigma model beyond the $\mathcal{O} (p^2)$ amplitudes and the coset of $\text{SU} (N) \times \text{SU} (N) / \text{SU} (N) $. We first discuss the universal flavor ordering of the amplitudes for the Nambu-Goldstone bosons, so that we can reinterpret the known $\mathcal{O} (p^2)$ single soft theorem for $\text{SU} (N) \times \text{SU} (N) / \text{SU} (N) $ in the context of a general symmetry group representation. We then investigate the special case of the fundamental representation of $\text{SO} (N)$, where a special flavor ordering of the "pair ba…
We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form o…
Electromagnetism contains an infinite dimensional symmetry group of large gauge transformations. This gives rise to an infinite number of conserved quantities called "soft charges" via Noether's theorem. When charged particles scatter, the conservation of soft charge constrains the overall amount of radiation emitted per angle. Here we describe the physical consequences of soft charge conservation and give fresh accounts of the roles of spacelike and timelike infinity in these conservation laws. We conclude by exploring the possibility of creating a dual boundary theory of electromagnetism.
Soft theorems can be recast as Ward identities of asymptotic symmetries. We review such relation for the leading and subleading soft graviton theorems in arbitrary even dimensions. While soft theorems are trivially generalized to dimensions higher than four, the charges of asymptotic symmetries are plagued by divergences requiring a renormalization. We argue that the renormalized charges of these symmetries can be determined by rewriting soft theorems as Ward identities. In order to show that the charges of such identities generate asymptotic symmetries, we propose a suitable commutation relat…
We demonstrate that the tree level amplitudes and the explicit formulas of soft factors can be uniquely determined by soft theorems and the universality of soft factors. By imposing the soft theorems and the universality, as well as the assumption of double copy, we reconstruct single trace Yang-Millsscalar amplitudes and pure Yang-Mills amplitudes, in the expanded formulas. The explicit formulas of soft factors for the bi-adjoint scalar and gluon are also determined. The expansions of Yang-Mills-scalar and Yang-Mills amplitudes can be extended to Einstein-Yang-Mills and gravitational amplitud…
In this paper, we initiate the study of multi-flavor Galileon theories using the methods of scattering amplitudes. We explore this topic from different perspectives and extend the techniques employed so far mainly in the single-flavor case. This includes soft theorems, generalized soft theorems with non-trivial right-hand side, Galileon dualities, soft bootstrap and bonus relations. We demonstrate new properties on two examples, the multi-flavor U(N) Galileon and the three-flavor U(2)/U(1) Galileon.
University of British Columbia（不列颠哥伦比亚大学）；Institut des Hautes Études Scientifiques（高等科学研究所）；Walter Burke Institute for Theoretical Physics, Caltech（加州理工学院沃尔特·伯克理论物理研究所）
We summarize recent results regarding single and double soft theorems of two different particles named dilatons, the Nambu-Goldstone boson of the spontaneously broken conformal field theories and the massless scalar particle of the closed string theories. Similarities and differences between the soft theorems of these two particles are discussed as well as their connections with the symmetries of the theories.
We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on $\mathbb{CP}^{k-1}$. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for $k=3$ but we show how they generalise to arbitrary $k$. We have explicit analytic results, for any…
