Higher representations on the lattice: numerical simulations. SU(2) with adjoint fermions

Abstract: We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present in detail the implementation of the HMC/RHMC algorithm for simulating dynamical fermions. We discuss the validation of the implementation through an extensive set of tests, and the stability of simulations by monitoring the distribution of the lowest eigenvalue of the Wilson-Dirac operator. Working with two flavors of Wilson fermions in the adjoint representation, benchmark results for realistic lattice simulations are presented. Runs are performed on different lattice sizes ranging from 4^3x8 to 24^3x64 sites. For the two smallest lattices we also report the measured values of benchmark mesonic observables. These results can be used as a baseline for rapid cross-checks of simulations in higher representations. The results presented here are the first steps towards more extensive investigations with controlled systematic errors, aiming at a detailed understanding of the phase structure of these theories, and of their viability as candidates for strong dynamics beyond the Standard model.

• The paper introduces a generalized Dirac operator for handling fermions in higher representations and validates its effectiveness via eigenvalue distribution tests.
• The paper employs HMC and RHMC algorithms to rigorously control systematic errors and maintain stability across various lattice sizes.
• The paper presents preliminary results that benchmark phase structures in SU(2) gauge theory, offering insights into potential BSM and technicolor models.

Numerical Simulations of Higher Representations on the Lattice: SU(2) with Adjoint Fermions

The paper addresses the formulation and implementation of lattice gauge theories, particularly those involving fermions in arbitrary representations of the color group. It emphasizes the SU(2) gauge theory with adjoint fermions, highlighting the challenges and strategies involved in simulating such systems using lattice techniques.

The authors concentrate on the Hamiltonian Hybrid Monte Carlo (HMC) and Rational Hybrid Monte Carlo (RHMC) algorithms, which are pivotal for handling dynamical fermions in lattice simulations. They provide an in-depth discussion on the adaptation of these algorithms to accommodate fermions in higher representations, specifically outlining the development of a generalized Dirac operator capable of acting on vectors of arbitrary dimensions in color space. Implementations are validated through robustness tests, including the distribution of the lowest eigenvalue of the Wilson-Dirac operator to assess simulation stability.

Preliminary results for the SU(2) gauge theory with two flavors of Wilson fermions in the adjoint representation are presented. These results cover different lattice sizes from $4^3 \times 8$ to $24^3 \times 64$. Numerical outcomes serve as benchmarks for future simulations and are crucial for understanding the phase structure of these theories and evaluating their viability as candidates for dynamics beyond the Standard Model.

Key numerical results include calculations on smaller lattices to identify scaling behaviors and stability of the algorithms. For instance, the paper highlights consistent eigenvalue distributions of the Hermitian Dirac operator, which demonstrate algorithmic stability and controlled systematic errors. The authors also explore autocorrelation times, ensuring that the statistical measures of the simulations remain reliable towards phenomenological analyses.

By simulating the SU(2) gauge theory, the paper contributes to the broader effort of studying strongly-interacting theories beyond Quantum Chromodynamics (QCD). These studies are integral to exploring technicolor models and their potential as frameworks for beyond Standard Model (BSM) physics, particularly focusing on nonperturbative phenomena. The results align with extensive Monte Carlo studies aimed at pinning down systematic errors in lattice gauge theories, thus paving the way for rigorous nonperturbative analysis. The methodologies and findings can impact LHC phenomenology by providing reliable lattice results to test candidate theories for strong electroweak symmetry breaking.

In the future, this research could be extended to larger lattice sizes and varied representation parameters to achieve results closer to the continuum and chiral limits, thus refining our understanding of such BSM theories. Advancements in computational techniques and resources will further enhance our capability to simulate complex lattice systems, providing deeper insights into technicolor dynamics and other strongly-interacting models.