arXiv subjects

David Schaich

Publications and source records attributed to David Schaich.

At least 19 recordsLinked to original sources

arXiv2026

Lattice Studies of Two-Dimensional Maximally Supersymmetric Yang-Mills Theory for Tests of Gauge-Gravity Duality

We present our ongoing work on two-dimensional maximally supersymmetric Yang-Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional ${\mathcal N} = 4$ supersymmetric Yang-Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge-gravity duality and investigate related non-perturbative phenomena.

hep-lat↗

arXiv2026

Holography on the lattice: Evidence from 3D supersymmetric Yang--Mills theory

We present new results from our lattice investigations of maximally supersymmetric Yang--Mills theory in three dimensions, focusing on its nonperturbative phase diagram. Using a lattice formulation that preserves part of the supersymmetry algebra at finite lattice spacing, we study the spatial deconfinement transition, which holography relates to the transition between localized and homogeneous black branes in the dual gravity theory. Our analysis employs $N_L^2 \times N_T$ lattices with $N = 8$ colors in the SU($N$) gauge group, considering $N_T = 8$, $10$ and $12$, in each case with aspect ratios $\alpha = N_L/N_T \leq 3$. The resulting transition temperatures are consistent with the holographic low-temperature, large-$N$ prediction $T_c \propto \alpha^3$, providing further evidence for the gauge--gravity correspondence in this setting.

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arXiv2026

Simulating Supersymmetric Quantum Mechanics Using Variational Quantum Algorithms

The study of spontaneous supersymmetry breaking (SSB) on the lattice is obstructed by a severe sign problem. Quantum computing provides a promising alternative approach. In particular, properties of supersymmetry relate SSB to the ground-state energy, which can be probed using hybrid quantum--classical algorithms such as the variational quantum eigensolver (VQE). In this work we present VQE analyses for supersymmetric quantum mechanics with various superpotentials. A key new feature is an adaptive ansatz construction algorithm that reduces the number of variational parameters within our ans\"atze. This lowers the resource burden on both the classical optimizer and the noisy quantum processor, thereby improving the feasibility of these calculations in the NISQ era. Additionally, we present preliminary VQE results obtained from real IBM quantum devices, highlighting accuracy, resource constraints, and computational cost, both with and without the application of error mitigation techniques.

quant-ph↗

arXiv2025

Quantum Variational Methods for Supersymmetric Quantum Mechanics

We employ quantum variational methods to investigate a single-site interacting fermion-boson system -- an example of a minimal supersymmetric model that can exhibit spontaneous supersymmetry breaking. Our study addresses the challenges inherent in calculating mixed fermion-boson systems and explores the potential of quantum computing to advance their analysis. By using adaptive variational techniques, we identify optimal ans\"atze that scale efficiently, allowing for reliable identification of spontaneous supersymmetry breaking. This work lays a foundation for future quantum computing investigations of more complex and physically rich fermion-boson quantum field theories in higher dimensions.

quant-ph↗

arXiv2025

Maximally supersymmetric Yang--Mills in three dimensions

We present the latest results from our ongoing lattice field theory investigations of maximally supersymmetric Yang--Mills theory in three space-time dimensions, focusing on its non-perturbative phase diagram. Exploiting a lattice formulation that preserves a subset of the supersymmetry algebra at non-zero lattice spacing, we study the 'spatial deconfinement' phase transition that holography relates to the transition between localized and homogeneous black branes in the dual quantum gravity. Fixing $N_L^2 \times 8$ lattice volumes and N=8 colors in the SU(N) gauge group, we consider four aspect ratios $\alpha = N_L / N_T \leq 4$ corresponding to $N_L = 16$, $20$, $24$ and $32$. The transition temperatures we determine are in good agreement with the low-temperature, large-N holographic expectation $T_c \propto \alpha^3$.

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arXiv2024

Hyper Stealth Dark Matter and Long-Lived Particles

A new dark matter candidate is proposed that arises as the lightest baryon from a confining $SU(N)$ gauge theory which equilibrates with the Standard Model only through electroweak interactions. Surprisingly, this candidate can be as light as a few GeV. The lower bound arises from the intersection of two competing requirements: i) the equilibration sector of the model must be sufficiently heavy, at least several TeV, to avoid bounds from colliders, and ii) the lightest dark meson (that may be the dark $\eta'$, $\sigma$, or the lightest glueball) has suppressed interactions with the SM, and must decay before BBN. The low energy dark sector consists of one flavor that is electrically neutral and an almost electroweak singlet. The dark matter candidate is the lightest baryon consisting of $N$ of these light flavors leading to a highly suppressed elastic scattering rate with the SM. The equilibration sector consists of vector-like dark quarks that transform under the electroweak group, ensuring that the dark sector can reach thermal equilibrium with the SM in the early Universe. The lightest dark meson lifetimes vary between $10^{-3} \lesssim c \tau \lesssim 10^7$~meters, providing an outstanding target for LHC production and experimental detection. We delineate the interplay between the lifetime of the light mesons, the suppressed direct detection cross section of the lightest baryon, and the scale of equilibration sector that can be probed at the LHC.

hep-ph↗

arXiv2024

Finite-temperature phase diagram of the BMN matrix model on the lattice

We investigate the thermal phase structure of the Berenstein--Maldacena--Nastase (BMN) matrix model using non-perturbative lattice Monte Carlo calculations. Our main analyses span three orders of magnitude in the coupling, involving systems with sizes up to $N_{\tau} = 24$ lattice sites and SU($N$) gauge groups with $8 \leq N \leq 16$. In addition, we carry out extended checks of discretization artifacts for $N_{\tau} \leq 128$ and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-$N$ dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.

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arXiv2024

Towards quantum simulation of lower-dimensional supersymmetric lattice models

Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle physics and fostering connections to theories of quantum gravity. However, lattice studies exploring the non-perturbative features of these models, such as spontaneous supersymmetry breaking and real-time evolution encounter significant challenges, particularly due to the infamous sign problem. The sign problem obstructs simulations on classical computers, especially when dealing with high-dimensional lattice systems. While one potential solution is to adopt the Hamiltonian formalism, this approach necessitates an exponential increase in classical resources with the number of lattice sites and degrees of freedom, rendering it impractical for large systems. In contrast, quantum hardware offers a promising alternative, as it requires in principle a polynomial amount of resources, making the study of these models more accessible. In this context, we explore the encoding of lower-dimensional supersymmetric quantum mechanics onto qubits. We also highlight our ongoing efforts to implement and check the model supersymmetry breaking on an IBM gate-based quantum simulator with and without shot noise, addressing the technical challenges we face and the potential implications of our findings for advancing our understanding of supersymmetry.

hep-lat↗

arXiv2024

Exploring lattice supersymmetry with variational quantum deflation

Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. Focusing on lower-dimensional lattice systems with more modest resource requirements, in particular the N=1 Wess--Zumino model in 1+1 dimensions, we are exploring ways quantum computing could be used to study spontaneous supersymmetry breaking. A particularly promising recent development is to apply the variational quantum deflation algorithm, which generalizes the variational quantum eigensolver so as to resolve multiple low-energy states.

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arXiv2023

Stealth dark matter spectrum using LapH and Irreps

We present non-perturbative lattice calculations of the low-lying meson and baryon spectrum of the SU(4) gauge theory with fundamental fermion constituents. This theory is one instance of stealth dark matter, a class of strongly coupled theories, where the lowest mass stable baryon is the dark matter candidate. This work constitutes the first milestone in the program to study stealth dark matter self-interactions. Here, we focus on reducing excited state contamination in the single baryon channel by applying the Laplacian Heaviside method, as well as projecting our baryon operators onto the irreducible representations of the octahedral group. We compare our resulting spectrum to previous work involving Gaussian smeared non-projected operators and find good agreement with reduced statistical uncertainties. We also present the spectrum of the low-lying odd-parity baryons for the first time.

hep-lat↗

arXiv2023

Nonperturbative phase diagram of two-dimensional ${\cal N} = (2, 2)$ super-Yang--Mills

We consider two-dimensional ${\cal N} = (2, 2)$ Yang--Mills theory with gauge group SU($N$) in Euclidean signature compactified on a torus with thermal fermion boundary conditions imposed on one cycle. We perform non-perturbative lattice analyses of this theory for large $12 \leq N \leq 20$. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional ${\cal N} = (8, 8)$ Yang--Mills theory, which has a well-defined gravity dual. We perform lattice field theory calculations to determine the phase diagram, observing a spatial deconfinement transition similar to the maximally supersymmetric case. However, the transition does not continue to low temperature, implying the absence of a topology-changing transition between black hole geometries in any holographic dual for this four-supercharge theory.

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arXiv2023

First-order bulk transitions in large-$N$ lattice Yang--Mills theories using the density of states

We use the Logarithmic Linear Relaxation (LLR) density of states algorithm to study the bulk phase transitions of pure-gauge SU($N$) lattice Yang--Mills theories with $4 \leq N \leq 8$. This approach avoids super-critical slowing down at such transitions, which poses a problem for traditional importance sampling Monte-Carlo methods. We analyse the effect of different updating strategies within the LLR algorithm, different reconstruction techniques of the density of states and different lattice volumes. By comparing our results for the weakly first-order SU(5) bulk phase transition against those for the stronger transitions with $N \geq 6$, we demonstrate the advantages of the LLR method for analyses of strong transitions with large latent heat.

hep-lat↗

arXiv2023

Deconfinement Phase Transition in Bosonic BMN Model at General Coupling

We present our analysis of the deconfinement phase transition in the bosonic BMN matrix model. The model is investigated using a non-perturbative lattice framework. We used the Polyakov loop as the order parameter to monitor the phase transition, and the results were verified using the separatrix ratio. The calculations are performed using a large number of colors and a broad range of temperatures for all couplings. Our results indicate a first-order phase transition in this theory for all the coupling values that connect the perturbative and non-perturbative regimes of the theory.

hep-lat↗

arXiv2023

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.

hep-lat↗

arXiv2023

Lattice Studies of 3D Maximally Supersymmetric Yang--Mills

We present ongoing investigations of maximally supersymmetric Yang--Mills ($Q = 16$ SYM) theory in three space-time dimensions. At low temperatures and large $N$ this theory is related to black branes in higher-dimensional quantum gravity. Building on previous work that focused on the homogeneous `D2' phase of the theory, we are now exploring phase transitions between this D2 phase and the localized `D0' phase.

hep-lat↗

arXiv2023

Advances in using density of states for large-N Yang--Mills

We present work in progress using the Logarithmic Linear Relaxation (LLR) density of states algorithm to analyse first-order phase transitions in pure-gauge SU(N) Yang--Mills theories, focusing on N = 4 and 6. By using the LLR algorithm we aim to avoid super-critical slowing down at such transitions. Motivation for this study comes from composite dark matter models, which may feature a first-order confinement transition in the early Universe that would produce a background of gravitational waves. Improving our understanding of these phase transitions will help probe these models using observations from future gravitational-wave observatories. In addition to the confinement transition, we also analyze bulk phase transitions of the lattice theories, which feature much larger latent heat.

hep-lat↗

arXiv2023

Quantum Computing for the Wess-Zumino Model

Future quantum computers will enable novel sign-problem-free studies of dynamical phenomena in non-perturbative quantum field theories, including real-time evolution and spontaneous supersymmetry breaking. We are investigating applications of quantum computing to low-dimensional supersymmetric lattice systems that can serve as testbeds for existing and near-future quantum devices. Here we present initial results for the $\mathcal{N} = 1$ Wess--Zumino model in 1+1 dimensions, building on our prior analyses of 0+1-dimensional supersymmetric quantum mechanics. In addition to exploring supersymmetry breaking using the variational quantum eigensolver, we consider the prospects for real-time evolution.

hep-lat↗

arXiv2022

Progress applying density of states for gravitational waves

Many models of composite dark matter feature a first-order confinement transition in the early Universe, which would produce a stochastic background of gravitational waves that will be searched for by future gravitational-wave observatories. We present work in progress using lattice field theory to predict the properties of such first-order transitions. Targeting SU(N) Yang--Mills theories, this work employs the Logarithmic Linear Relaxation (LLR) density of states algorithm to avoid super-critical slowing down at the transition.

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