Lifting flat directions in lattice supersymmetry

We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the exact lattice supersymmetry. The basic idea is to modify the equations of motion of an auxiliary field, which determine the moduli space of the system. Applied to numerical calculations, the resulting improved lattice action leads to dramatically reduced violations of supersymmetric Ward identities and much more rapid approach to the continuum limit

Parallel software for lattice N=4 supersymmetric Yang--Mills theory

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional $\mathcal N = 4$ supersymmetric Yang--Mills theory with gauge group SU(N). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code, which SUSY LATTICE supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development.Comment: Code available at https://github.com/daschaich/sus

Finite-temperature study of eight-flavor SU(3) gauge theory

We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \lesssim 20$ on lattice volumes as large as $48^3 \times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.Comment: Contribution to the Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories" (SCGT15), 3--6 March 2015, Nagoya Universit

Stealth dark matter and gravitational waves

I present first results from ongoing lattice investigations into the finite-temperature dynamics of stealth dark matter, which adds to the standard model a new SU(4) gauge sector with four moderately heavy fundamental fermions. This work by the Lattice Strong Dynamics Collaboration builds on past studies of direct detection and collider searches for stealth dark matter, by analyzing the early-universe SU(4) confinement transition, which produces a stochastic background of gravitational waves if it is first order. In addition to delineating the parameter space in which a first-order transition is observed, I discuss the quantities we are analyzing in order to predict the resulting gravitational-wave spectrum.Comment: Contribution to the proceedings of Lattice 2019, June 16--22, Wuhan, Chin

Exploring conformality in lattice N=4 supersymmetric Yang--Mills

Maximally supersymmetric Yang--Mills theory (N=4 SYM) is conformal for any value of the coupling. Lattice regularization breaks conformality through the introduction of a non-zero lattice spacing and a finite lattice volume. This proceedings presents ongoing numerical computations of conformal scaling dimensions in lattice N=4 SYM, based on a lattice formulation that exactly preserves a supersymmetry sub-algebra at non-zero lattice spacing. The main targets are the non-trivial anomalous dimension of the Konishi operator, as well as a mass anomalous dimension extracted from the eigenvalue mode number of the fermion operator. The latter is expected to vanish in the conformal continuum theory, providing insight into the interplay of lattice discretization and conformality.Comment: Contribution to the proceedings of Lattice 2022, August 8--13, Bonn, German

Eight light flavors on large lattice volumes

I present first results from large-scale lattice investigations of SU(3) gauge theory with eight light flavors in the fundamental representation. Using leadership computing resources at Argonne, we are generating gauge configurations with lattice volumes up to $64^3\times128$ at relatively strong coupling, in an attempt to access the chiral regime. We use nHYP-improved staggered fermions, carefully monitoring finite-volume effects and other systematics. Here I focus on analyses of the light hadron spectrum and chiral condensate, measured on lattice volumes up to $48^3\times96$ with fermion masses as light as m=0.004 in lattice units. We find no clear indication of spontaneous chiral symmetry breaking in these observables. I discuss the implications of these initial results, and prospects for further physics projects employing these ensembles of gauge configurations

Strong dynamics and lattice gauge theory

Thesis (Ph.D.)--Boston UniversityIn this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ~ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S > 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S > 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB