Exploring Spacetime Dualities: New Insights from Representation Theory

A recent paper titled "Spacetime Representation Theory: Setting the Scope of the ISE Method of Topological Redescription" by Daniel Grimmer explores the concept of spacetime dualities, which occur when two theories describe the same physical phenomena using different spatiotemporal frameworks. The paper highlights that these dualities can lead to significant differences in how states are represented topologically.

One notable example discussed is the AdS-CFT correspondence, which connects a theory in a higher-dimensional spacetime with a different theory on its boundary. Additionally, the paper introduces a new duality called the Möbius-Euclid duality, where a theory describing particles on a Euclidean plane can be reinterpreted as one describing different particles on a Möbius strip.

The implications of these findings extend into the realms of epistemology and metaphysics, raising questions about the criteria used to select topological representations of spacetime. Grimmer aims to establish a general framework for understanding these topological redescriptions, which he refers to as spacetime representation theory. This framework is intended to clarify the common core shared by dual theories and the nature of their equivalence.

The paper also discusses the ISE Equivalence Theorem, which outlines the scope of the recently developed ISE Method of topological redescription. This method could have far-reaching consequences for how physicists approach the study of spacetime and its underlying structures.

The full paper can be accessed at arXiv:2306.08110.