Lattice setup for quantum field theory in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Physical review. D/Physical review. D. · 2021 · 47 citations

• Physics
• Mathematical physics
• Theoretical physics

Holographic conformal field theories (CFTs) are usually studied in a limit where the gravity description is weakly coupled. By contrast, lattice quantum field theory can be used as a tool for doing computations in a wider class of holographic CFTs where nongravitational interactions in AdS become strong, and gravity is decoupled. We take preliminary steps for studying such theories on the lattice by constructing the discretized theory of a scalar field in ${\mathrm{AdS}}_{2}$ and investigating its approach to the continuum limit in the free and perturbative regimes. Our main focus is on finite sublattices of maximally symmetric tilings of hyperbolic space. Up to boundary effects, these tilings preserve the triangle group as a large discrete subgroup of ${\mathrm{AdS}}_{2}$, but have a minimum lattice spacing that is comparable to the radius of curvature of the underlying spacetime. We quantify the effects of the lattice spacing as well as the boundary effects, and find that they can be accurately modeled by modifications within the framework of the continuum limit description. We also show how to do refinements of the lattice that shrink the lattice spacing at the cost of breaking the triangle group symmetry of the maximally symmetric tilings.

Near-conformal dynamics in a chirally broken system

Physical review. D/Physical review. D. · 2021 · 29 citations

• Computer Science
• Physics
• Statistical physics

Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain ${y}_{m}=1+{\ensuremath{\gamma}}^{*}=1.47(5)$ suggesting that ${N}_{f}=10$ lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the $4+6$ mass-split system exhibits near-conformal dynamics with a relatively light ${0}^{++}$ isosinglet scalar.

Lattice Gauge Theory for a Quantum Computer

Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022) · 2020 · 33 citations

• Physics
• Theoretical physics
• Quantum mechanics

The quantum link [1] Hamiltonian was introduced two decades ago a alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new microscopic representation of lattice field theories is referred as D-theory [2]. Recast as a Hamiltonian in Minkowski space for real time evolution, D-theory leads naturally to quantum Qubit algorithms. Here to explore digital quantum computing for gauge theories, the simplest example of U(1) compact QED on triangular lattice is defined and gauge invariant kernels for the Suzuki-Trotter expansions are expressed as Qubit circuits capable of being tested on the IMB-Q and other existing Noisy Intermediate Scale Quantum (NISQ) hardware. This is a modest step in exploring the quantum complexity of D-theory to guide future applications to high energy physics and condensed matter quantum field theories.