[Paper Review] Topics in Asymptotic Symmetries and Infrared Effects

Carlo Heissenberg|arXiv (Cornell University)|Nov 27, 2019

Black Holes and Theoretical Physics164 references4 citations

TL;DR

This thesis investigates asymptotic symmetries in gauge and gravitational theories, focusing on Yang-Mills, gravity, higher-spin, and two-form fields. Using frame-like formulations and cohomological methods, it identifies infinite-dimensional asymptotic symmetry algebras, including BMS-like structures, and establishes their connection to soft theorems and infrared physics, providing a unified framework for understanding infrared effects in quantum field theories and gravity.

ABSTRACT

Motivated by connections with observable phenomena, in particular with soft factorization theorems for scattering amplitudes and with memory effects, renewed interest has been recently shown in the subject of asymptotic symmetries at null infinity. The two main goals of this Ph.D. thesis are, first, to review the main aspects of the connection between such symmetries and observable effects in the context of gravity, electromagnetic and Yang-Mills theory in four dimensions and, second, to present results concerning the extension of this program to the case of spacetimes of arbitrary dimension, either even or odd, to the emission or absorption of soft scalar quanta, in connection with their dual description, and to theories containing massless higher-spin fields.

Motivation & Objective

• To understand the structure of asymptotic symmetries in gauge and gravitational theories beyond the standard model framework.
• To extend the understanding of soft theorems and infrared divergences to higher-spin and two-form fields.
• To unify the description of asymptotic symmetries across different field types using frame-like formulations and cohomological techniques.
• To clarify the role of infinite-dimensional symmetry algebras in organizing infrared physics and memory effects.
• To establish a systematic link between asymptotic symmetries and soft theorems in quantum field theories and gravity.

Proposed method

• Employing frame-like formulations for gauge and gravity theories to systematically describe field equations and symmetries at null infinity.
• Applying cohomological methods to classify conserved charges and asymptotic symmetries from the field equations and boundary conditions.
• Using the Batalin-Vilkovisky (BV) formalism to handle gauge symmetries and derive consistent charge algebras.
• Analyzing the structure of asymptotic symmetry algebras for Yang-Mills, gravity, and higher-spin fields, identifying BMS-like extensions.
• Deriving Ward identities and soft theorems from the algebraic structure of asymptotic symmetries.
• Studying the interplay between soft theorems and memory effects through the charge algebra and boundary dynamics.

Experimental results

Research questions

• RQ1 What is the structure of the asymptotic symmetry algebra for Yang-Mills theory in four-dimensional Minkowski spacetime?
• RQ2 How do asymptotic symmetries in gravity and higher-spin theories generalize the BMS algebra, and what is their physical significance?
• RQ3 What is the role of two-form fields in the infrared structure of quantum field theories and their relation to soft theorems?
• RQ4 How do cohomological methods and frame-like formulations enable a unified description of asymptotic symmetries across different field types?
• RQ5 To what extent do asymptotic symmetries and soft theorems constrain the dynamics of quantum fields at null infinity?

Key findings

• The asymptotic symmetry algebra for Yang-Mills theory is shown to be infinite-dimensional, extending the BMS-like structure observed in gravity.
• For gravity, the asymptotic symmetry algebra contains the BMS algebra as a subalgebra, with additional generators linked to soft graviton theorems.
• The cohomological approach successfully classifies conserved charges and their algebraic structure, confirming the consistency of the symmetry framework.
• The analysis reveals that soft theorems in gauge and gravitational theories arise as Ward identities associated with asymptotic symmetries.
• Higher-spin and two-form fields exhibit analogous asymptotic symmetry structures, suggesting a universal pattern in infrared physics.
• The frame-like formulation enables a manifestly covariant and consistent derivation of boundary symmetries and their charges across different field types.