Quantum Yang-Mills theory: an overview of a programme

TL;DR

This paper outlines a program to understand low-energy quantum Yang-Mills physics using quantum information tools, introducing a tensor network ansatz that interpolates between coupling regimes and facilitates observable computations.

Contribution

It introduces a novel tensor network ansatz for Yang-Mills ground states, inspired by lattice gauge theory and quantum information, bridging weak and strong coupling regimes.

Findings

Developed a nonabelian generalization of laplace interpolation.

Constructed a tensor network state for Yang-Mills ground state.

Enabled efficient computation of local observables and Wilson loops.

Abstract

We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\mathbb{Z}/2\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. Finally, the continuum limit of our ansatz as the lattice regulator is removed is then described. This paper is intended as an abstract for an ongoing programme: there are still many open problems.