arXiv subjects

David Schaich

Publications and source records attributed to David Schaich.

At least 55 records · Page 3Linked to original sources

arXiv2018

$SO(4)$ invariant Higgs-Yukawa model with reduced staggered fermions

We explore the phase structure of a four dimensional $SO(4)$ invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of $SO(4)$. The model is a generalization of a four fermion system with the same symmetries that has received recent attention because of its unusual phase structure comprising massless and massive symmetric phases separated by a very narrow phase in which a small bilinear condensate breaking $SO(4)$ symmetry is present. The generalization described in this paper simply consists of the addition of a scalar kinetic term. We find a region of the enlarged phase diagram which shows no sign of a fermion condensate or symmetry breaking but in which there is nevertheless evidence of a diverging correlation length. Our results in this region are consistent with the presence of a single continuous phase transition separating the massless and massive symmetric phases observed in the earlier work.

hep-lat↗

arXiv2018

S-duality in lattice super Yang-Mills

We present a progress report on studying S-duality in lattice N=4 super Yang-Mills. This is being done through a computation of 1/2-BPS states on the Coulomb branch, especially the 't Hooft--Polyakov monopole and the W boson. Key to these calculations is the use of twisted and C-periodic boundary conditions. In addition we describe a variational method to disentangle operators with definite scaling dimension, particularly the Konishi and supergravity operators.

hep-lat↗

arXiv2018

Testing holography using lattice super-Yang--Mills on a 2-torus

We consider maximally supersymmetric SU(N) Yang--Mills theory in Euclidean signature compactified on a flat two-dimensional torus with anti-periodic (`thermal') fermion boundary conditions imposed on one cycle. At large N, holography predicts that this theory describes certain black hole solutions in Type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N=16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory--Laflamme transition.

hep-th↗

arXiv2018

Nonperturbative beta function of twelve-flavor SU(3) gauge theory

We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $\tilde g_c^2(L)$ we determine the continuum-extrapolated discrete beta function up to $g_c^2 \approx 8.2$. We observe an IR fixed point at $g_{\star}^2 = 7.3\left(_{-2}^{+8}\right)$ in the $c = \sqrt{8t} / L = 0.25$ scheme, and $g_{\star}^2 = 7.3\left(_{-3}^{+6}\right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the $(a / L) \to 0$ extrapolations, the interpolation of $\tilde g_c^2(L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller $c \lesssim 0.2$ with smaller $L \leq 12$, leading to an IR fixed point at $g_{\star}^2 = 5.9(1.9)$ in the c=0.2 scheme, which resolves to $g_{\star}^2 = 6.9\left(_{-1}^{+6}\right)$ upon considering only $L \geq 16$. At the IR fixed point we measure the leading irrelevant critical exponent to be $γ_g^{\star} = 0.26(2)$, comparable to perturbative estimates.

hep-lat↗

arXiv2017

Phases of a strongly coupled four-fermion theory

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant four-fermion interaction. As in previous studies of four-fermion and Higgs--Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.

hep-lat↗

arXiv2017

Testing the holographic principle using lattice simulations

The lattice studies of maximally supersymmetric Yang-Mills (MSYM) theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory--Laflamme) between them.

hep-lat↗

arXiv2017

Novel phases in strongly coupled four-fermion theories

We study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an $SU(4)$-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs--Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.

hep-lat↗

arXiv2016

Latest results from lattice N=4 supersymmetric Yang--Mills

We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.

hep-lat↗

arXiv2016

Strongly interacting dynamics and the search for new physics at the LHC

We present results for the spectrum of a strongly interacting SU(3) gauge theory with $N_f = 8$ light fermions in the fundamental representation. Carrying out non-perturbative lattice calculations at the lightest masses and largest volumes considered to date, we confirm the existence of a remarkably light singlet scalar particle. We explore the rich resonance spectrum of the 8-flavor theory in the context of the search for new physics beyond the standard model at the Large Hadron Collider (LHC). Connecting our results to models of dynamical electroweak symmetry breaking, we estimate the vector resonance mass to be about 2 TeV with a width of roughly 450 GeV, and predict additional resonances with masses below ~3 TeV.

hep-lat↗

arXiv2015

Aspects of lattice N=4 supersymmetric Yang--Mills

Non-perturbative investigations of $\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.

hep-lat↗

arXiv2015

Maximally supersymmetric Yang-Mills on the lattice

We summarize recent progress in lattice studies of four-dimensional N=4 supersymmetric Yang--Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.

hep-th↗

arXiv2015

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.

hep-lat↗

arXiv2015

Nonperturbative beta function of eight-flavor SU(3) gauge theory

We present a new lattice study of the discrete beta function for SU(3) gauge theory with Nf=8 massless flavors of fermions in the fundamental representation. Using the gradient flow running coupling, and comparing two different nHYP-smeared staggered lattice actions, we calculate the 8-flavor step-scaling function at significantly stronger couplings than were previously accessible. Our continuum-extrapolated results for the discrete beta function show no sign of an IR fixed point up to couplings of g^2~14. At the same time, we find that the gradient flow coupling runs much more slowly than predicted by two-loop perturbation theory, reinforcing previous indications that the 8-flavor system possesses nontrivial strongly coupled IR dynamics with relevance to BSM phenomenology.

hep-lat↗

arXiv2015

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.

hep-lat↗

arXiv2015

Stealth Dark Matter: Dark scalar baryons through the Higgs portal

We present a new model of "Stealth Dark Matter": a composite baryonic scalar of an $SU(N_D)$ strongly-coupled theory with even $N_D \geq 4$. All mass scales are technically natural, and dark matter stability is automatic without imposing an additional discrete or global symmetry. Constituent fermions transform in vector-like representations of the electroweak group that permit both electroweak-breaking and electroweak-preserving mass terms. This gives a tunable coupling of stealth dark matter to the Higgs boson independent of the dark matter mass itself. We specialize to $SU(4)$, and investigate the constraints on the model from dark meson decay, electroweak precision measurements, basic collider limits, and spin-independent direct detection scattering through Higgs exchange. We exploit our earlier lattice simulations that determined the composite spectrum as well as the effective Higgs coupling of stealth dark matter in order to place bounds from direct detection, excluding constituent fermions with dominantly electroweak-breaking masses. A lower bound on the dark baryon mass $m_B \gtrsim 300$ GeV is obtained from the indirect requirement that the lightest dark meson not be observable at LEP II. We briefly survey some intriguing properties of stealth dark matter that are worthy of future study, including: collider studies of dark meson production and decay; indirect detection signals from annihilation; relic abundance estimates for both symmetric and asymmetric mechanisms; and direct detection through electromagnetic polarizability, a detailed study of which will appear in a companion paper.

hep-ph↗

arXiv2015

Direct Detection of Stealth Dark Matter through Electromagnetic Polarizability

We calculate the spin-independent scattering cross section for direct detection that results from the electromagnetic polarizability of a composite scalar baryon dark matter candidate -- "Stealth Dark Matter", that is based on a dark SU(4) confining gauge theory. In the nonrelativistic limit, electromagnetic polarizability proceeds through a dimension-7 interaction leading to a very small scattering cross section for dark matter with weak scale masses. This represents a lower bound on the scattering cross section for composite dark matter theories with electromagnetically charged constituents. We carry out lattice calculations of the polarizability for the lightest baryons in SU(3) and SU(4) gauge theories using the background field method on quenched configurations. We find the polarizabilities of SU(3) and SU(4) to be comparable (within about 50%) normalized to the baryon mass, which is suggestive for extensions to larger SU(N) groups. The resulting scattering cross sections with a xenon target are shown to be potentially detectable in the dark matter mass range of about 200-700 GeV, where the lower bound is from the existing LUX constraint while the upper bound is the coherent neutrino background. Significant uncertainties in the cross section remain due to the more complicated interaction of the polarizablity operator with nuclear structure, however the steep dependence on the dark matter mass, $1/m_B^6$, suggests the observable dark matter mass range is not appreciably modified. We briefly highlight collider searches for the mesons in the theory as well as the indirect astrophysical effects that may also provide excellent probes of stealth dark matter.

hep-ph↗

arXiv2014

Results from lattice simulations of N=4 supersymmetric Yang--Mills

We report recent results and developments from our ongoing lattice studies of $\mathcal N = 4$ supersymmetric Yang--Mills theory. These include a proof that only a single fine-tuning needs to be performed, so long as the moduli space is not lifted by nonperturbative effects. We extend our investigations of supersymmetry restoration in the continuum limit by initiating Monte Carlo renormalization group studies. We present additional numerical evidence that the lattice theory does not suffer from a sign problem. Finally we study the static potential, which we find to be Coulombic at both weak and strong coupling. We compare the static potential Coulomb coefficients to perturbation theory, including initial results for N=3 colors in addition to N=2.

hep-lat↗

arXiv2014

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.

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