T-duality and Bosonization Emerge from Continuum Gauging and Disentangling, Enabling Equivalence Between Physical Regimes

Dualities represent a powerful toolkit for physicists, enabling them to connect seemingly disparate models and unlock new insights into complex physical systems. Gertian Roose and Erez Zohar, from the Racah Institute of Physics at The Hebrew University of Jerusalem and Tel Aviv University, now extend this concept to the realm of continuum field and particle physics. They demonstrate that duality transformations can be understood as a process of ‘gauging and disentangling’, a framework previously established for condensed matter systems, and successfully apply this approach to re-derive fundamental relationships like T-duality and bosonization. This work establishes a new, unifying perspective on dualities, potentially offering a pathway to discover and understand previously hidden connections within the foundations of physics.

Recently, researchers demonstrated that dualities can be understood through a gauging and disentangling procedure, represented by a finite depth quantum circuit. This work expands these concepts to the continuum, suggesting a way to derive duality transformations in continuum field theories and particle physics. The team successfully re-derived established results, such as T-duality and bosonization, using this new method, offering a fresh perspective on these well-known phenomena.

Fermion Simulation via Duality Transformation

This research explores a novel approach to simulating quantum many-body systems, particularly those described by lattice gauge theories and fermionic models. The central idea leverages duality transformations, mathematical mappings that relate seemingly different physical systems, to simplify the simulation process. The authors aim to remove the need to directly simulate computationally expensive fermionic degrees of freedom by transforming the problem into one involving only spin degrees of freedom.

Lattice gauge theory provides a discretization of continuous spacetime used to study fundamental forces. Fermions, such as electrons and quarks, obey the Pauli exclusion principle and are notoriously difficult to simulate. Duality transformations map a system with fermions to a system with spins, simplifying the simulation. Gauging introduces auxiliary degrees of freedom to enforce constraints or symmetries, preparing the system for the duality transformation. Representing the system using spin degrees of freedom, which are easier to simulate, is the ultimate goal. Matrix product operators (MPOs) efficiently represent quantum states and operators, particularly in one-dimensional systems, implementing the duality transformations and simulating the resulting spin systems. Topological order, characterized by non-local entanglement and exotic excitations, is a key area of investigation.

The process begins with a fermionic Hamiltonian describing the energy of the system. Auxiliary gauge fields are introduced to enforce local constraints and prepare the system for the duality transformation. A mathematical transformation maps the fermionic system into an equivalent system with only spin degrees of freedom. The transformed spin Hamiltonian is represented using MPOs, allowing for efficient simulation. The MPO representation simulates the spin system, effectively bypassing the need to directly simulate the fermionic degrees of freedom.

The authors propose a new duality transformation that maps fermionic systems to spin systems, enabling efficient simulation of the transformed spin system. This approach has the potential to study systems with topological order, relevant to condensed matter physics and quantum computing. The research demonstrates a pathway for using duality transformations to simplify quantum simulations of many-body systems.

In essence, this research proposes transforming a complicated puzzle with many hard-to-fit pieces (fermions) into a simpler one with fewer pieces (spins) without changing the overall solution, making it easier to solve (simulate) using a computer. This work presents a promising new approach to quantum simulation that could overcome limitations of existing methods.

Continuum Duality via Gauging and Disentangling

This research demonstrates a novel approach to understanding dualities, mathematical relationships equating seemingly different physical models, by extending concepts previously established on a lattice framework to the continuum. The team successfully reformulated duality transformations using a gauging and disentangling procedure, re-deriving established results such as T-duality and bosonization through this new method. This work interprets dual fields as gauge fields and duality relations as manifestations of Gauss’s laws.

The researchers explored the application of this method to systems with boundaries, finding that duality transformations can alter boundary conditions consistent with existing string theory predictions. Future investigations will focus on streamlining the bosonization process by potentially bypassing the intermediate lattice step, and on exploring non-Abelian bosonization from this new perspective. The team also intends to investigate whether duality transformations affect background metrics and to explore constructing emergent higher-dimensional spaces through sequential gauging of symmetries, drawing parallels with the AdS/CFT correspondence.

This work represents a significant advancement in the theoretical understanding of dualities and provides a promising new avenue for exploring complex physical systems.