John Donoghue

University of Massachusetts Amherst
Time and Emergent Symmetry

In everyday life we encounter sound waves and water waves as the large scale result of atoms interacting with each other at the microscopic scales. The word "emergent" is used to describe the situation where the features that one sees at large scales are not themselves part of the more fundamental theory. In contrast, light waves are thought to be completely fundamental and present all scales, no matter how small. This project explores the possibility that light waves (and other waves in our present theory) are also emergent, manifestations of a different underlying reality. There are hints that, to make this idea work, the features of Einstein's Special Relativity must also be emergent. The work initiated in this project should help us understand better how this could occur, and provides some ideas to potentially test this framework.

In the context of potentially emergent gauge symmetries, a key question is whether time should really be unified with space to form spacetime at the fundamental level or whether this property is itself emergent. The Weinberg Witten theorem forbids the emergence of composite gauge bosons or gravitons, coupled to a conserved charge, from any initially Lorentz invariant theory. Indeed the concrete condensed matter models in which gauge theory is emergent are (3+1)D Hamiltonian systems in which space is discrete and time continuous.

This proposal contains a cluster of projects investigating the nature of time and Lorentz invariance in emergent theories. This includes the emergence of a common "speed of light" through renormalization group evolution of interacting field which do not initially have a common limiting velocity. Also studied is the question of whether the non-invariant terms could become suppressed due to the coordinate expansion of FRW cosmology. In addition, we propose to extend the (3+1)D models to 4D path integrals to see if this changes the nature of the results - an exploration of the content of the Weinberg-Witten theorem. The phenomenology of such theories will also be considered.

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