An Examination of Soft Theorems from Higher Symmetries
This paper addresses the relationship between higher symmetries and soft theorems in quantum field theories, focusing on the implications for spontaneously broken symmetries and their associated scattering amplitudes. The main contributions are the derivation of new double soft pion theorems within a framework where the symmetries are defined by a continuous 2-group, incorporating both 1-form and 0-form symmetries. The work revisits the conceptual framework of Nambu-Goldstone bosons (NGBs) and their interaction dynamics constrained by symmetries, using effective field theories (EFTs) to describe these long-range interactions.
The paper begins with a detailed review of spontaneously broken 0-form symmetries and the associated soft theorems, providing a rigorous analysis of the Adler zero in pion dynamics. The highlight here is demonstrating that soft limits are universal across a range of massless particles, including photons, gluons, and gravitons, which traditionally have required considerations beyond spontaneous symmetry breaking, such as asymptotic symmetries.
It then transitions to discussing how modern perspectives on higher symmetries, particularly 1-form symmetries, can be applied to describe photon interactions as NGB dynamics. The emergent symmetry perspective refines the understanding of soft photon theorems, traditionally ascribed to gauge invariance, by showing that these behaviors derive from robust 1-form symmetries.
The core focus of the research is on the novel derivation of a double soft pion theorem in specific theories characterized by a 2-group symmetry. The 2-group symmetry combines 0-form and 1-form symmetries, allowing for interaction terms that change particle species—between NGBs of the 0-form symmetry (pions) and those of the 1-form symmetry (photons)—in the universal soft theorems. This deepens the understanding of the scattering processes and strengthens the EFT descriptions by fundamentally including higher symmetry constraints and interactions.
The paper concludes by discussing the theoretical and practical implications for the field, hinting at further exploration into the generalized symmetries and their impact on the descriptions of massless particles in scattering matrices. Moreover, it draws connections between emergent 1-form symmetries in effective field theories, such as HQET and SCET, and factorization phenomena, indicating areas that might benefit from further investigation.
Overall, the paper presents a sophisticated examination of symmetry in theoretical physics, advancing the theoretical framework concerning higher symmetries and offering pathways for future research into soft theorems across various quantum field theories.
