arXiv subjects
Publications and source records attributed to Joel Giedt.
We review methods and results for extracting the anomalous dimensions of operators from lattice field theory calculations. The most important application is the anomalous mass dimension in conformal or nearly conformal gauge field theories which might be related to dynamical electroweak symmetry breaking. Some discussion of the underlying theory of renormalization and mixing of operators is also included.
We study the single site lattice gauge theory of SU(N) coupled to one Dirac flavor of fermion in the adjoint representation. We utilize Möbius fermions for this study, and accelerate the calculation with graphics processing units (GPUs). Our Monte Carlo simulations indicate that for sufficiently large inverse 't Hooft coupling b = 1/g^2 N, and for N \leq 10 the distribution of traced Polyakov loops has "fingers" that extend from the origin. However, in the massless case the distribution of eigenvalues of the untraced Polyakov loop becomes uniform at large N, indicating preservation of center symmetry in the thermodynamic limit. By contrast, for a large mass and large b, the distribution is highly nonuniform in the same limit, indicating spontaneous center symmetry breaking. These conclusions are confirmed by comparing to the quenched case, as well as by examining another observable based on the average value of the modulus of the traced Polyakov loop. The result of this investigation is that with massless adjoint fermions center symmetry is stabilized and the Eguchi-Kawai reduction should be successful; this is in agreement with most other studies.
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.
Maximally supersymmetric Yang--Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N), the lattice formulation is naturally described in terms of gauge group U(N). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N) gauge group with the expected apparently conformal behavior at both weak and strong coupling.
A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N=4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice structure, both the symmetries and the geometric interpretation of the fields. In this brief article we provide an explicit example of such a blocking scheme and illustrate its practicality in the context of a small scale Monte Carlo renormalization group calculation. We also discuss the implications of this result, and the possible ways in which to use it in order to obtain further information about the long distance theory.
Motivated by the application of Lüscher's finite volume method to the study of the lightest scalar resonance in the $ππ\to ππ$ isoscalar channel, in this article we describe our studies of multi-pion correlation functions computed using stochastic propagators in quenched lattice QCD, harnessing GPUs for acceleration. We consider two methods for constructing the correlation functions. One "outer product" approach becomes quite expensive at large lattice extent $L$, having an ${\cal O}(L^7)$ scaling. The other "stochastic operator" approach scales as ${\cal O}(N_r^2 L^4)$, where $N_r$ is the number of random sources. It would become more efficient if variance reduction techniques are used and the volume is fairly large. It is also found that correlations between stochastic propagators appearing in the same diagram, when a single set of random source vectors is used, lead to much larger errors than if separate random sources are used for each propagator. The calculations involve states with quantum numbers of the vacuum, so all-to-all propagators must be computed. For this reason, GPUs are ideally suited to accelerating the calculation. For this work we have integrated the Columbia Physics System (CPS) and QUDA GPU inversion library, in the case of clover fermions. Finally, we show that the completely quark disconnected diagram is crucial to the results, and that neglecting it would lead to answers which are far from the true value for the effective mass in this channel. This is unfortunate, because as we also show, this diagram has very large errors, and in fact dominates the error budget.
We study an approach to chiral gauge theories on the lattice that involves decoupling "mirror" fermions from a vector-like theory. We have computed the polarization tensor in the "3-4-5" theory and find a directional discontinuity that appears to be nonzero in the continuum limit. This strongly suggests that the mirror fermions do not decouple.
Recently it has been shown how a topologically twisted version of ${\cal N}=4$ super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The remaining fifteen supersymmetries are broken by terms of ${\cal O}(a)$ where $a$ is the lattice spacing. One would like to know whether these remaining supersymmetries are regained in the continuum limit $a \to 0$ and, if not, how much tuning of the couplings in the lattice action is required. In this paper we derive the form of these additional twisted supersymmetries by combining a set of discrete R-symmetries of the continuum theory with the action of the scalar supersymmetry. We then argue that restoration of rotational symmetry in the continuum limit of the lattice theory likely implies restoration of R-symmetry and hence should lead to an automatic enhancement to the full ${\cal N}=4$ supersymmetry without further fine-tuning.
This White Paper has been prepared as a planning document for the Division of High Energy Physics of the U. S. Department of Energy. Recent progress in lattice-based studies of physics beyond the standard model is summarized, and major current goals of USQCD research in this area are presented. Challenges and opportunities associated with the recently discovered 126 GeV Higgs-like particle are highlighted. Computational resources needed for reaching important goals are described. The document was finalized on February 11, 2013 with references that are not aimed to be complete, or account for an accurate historical record of the field.
An approach to the formulation of chiral gauge theories on the lattice is to start with a vector-like theory, but decouple one chirality (the "mirror" fermions) using strong Yukawa interactions with a chirally coupled "Higgs" field. While this is an attractive idea, its viability needs to be tested with nonperturbative studies. The model that we study here, the so-called "3-4-5" model, is anomaly free and the presence of massless states in the mirror sector is not required by anomaly matching arguments, in contrast to the "1-0" model that was studied previously. We have computed the polarization tensor in this theory and find a directional discontinuity that appears to be nonzero in the limit of an infinite lattice, which is equivalent to the continuum limit at fixed physical volume. We show that a similar behavior occurs for the free massless Ginsparg-Wilson fermion, where the polarization tensor is known to have a directional discontinuity in the continuum limit. We thus find support for the conclusion that in the continuum limit of the 3-4-5 model, there are massless charged modes in the mirror sector so that it does not decouple from the light sector. The value of the discontinuity we obtain allows for two interpretations: either a chiral gauge theory does not emerge and mirror-sector fermions in a chiral anomaly free representation remain massless, or a massless vectorlike mirror fermion appears. We end by discussing some questions for future study.
We provide a scan of the parameter space for neutralino-hadron scattering in the next-to-minimal supersymmetric standard model using an updated value for the strange quark sigma commutator. These results also take into account constraints from WMAP data on the relic density and new constraints from the Large Hadron Collider. We find that the resultant spin-independent cross sections are smaller in magnitude than those found in recent results obtained within the constrained minimal supersymmetric standard model, yet still great enough to feasibly allow for detection in the case of bino-like neutralinos.
We compare observables to the finite size scaling hypothesis in SU(2) lattice gauge theory with two Dirac fermions in the adjoint representation. The fits that we obtain yield an estimate of the anomalous mass dimension that is consistent with four loop perturbation theory: $γ= 0.51 \pm 0.16$, with the error due to systematic uncertainties in the finite size scaling analysis. The result is somewhat larger than one Schrödinger functional study (by 1.3$σ$) but consistent with another.
We present a Monte Carlo Renormalisation Group (MCRG) study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however without this assumption our uncertainty in the running of the coupling leads to a much larger range of allowed values, -0.6 < gamma < 0.6. We discuss the systematic errors affecting the current analysis and possible improvements.
We extract the running coupling based on Creutz ratios in SU(2) lattice gauge theory with two Dirac fermions in the adjoint representation. Depending on how the extrapolation to zero fermion mass is performed, either backward running or an absence of running is observed at strong bare coupling. This behavior is consistent with other findings which indicate that this theory has an infrared fixed point.
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however taking this source of systematic error into account gives a much larger range of allowed values, -0.6 < gamma < 0.6. We also attempt to measure the anomalous mass dimension using the stability matrix method. We discuss the systematic errors affecting the current analysis and possible improvements.
We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U(1)_R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.
We consider N=4 super Yang-Mills theory on a four-dimensional lattice. The lattice formulation under consideration retains one exact supersymmetry at non-zero lattice spacing. We show that this feature combined with gauge invariance and the large point group symmetry of the lattice theory ensures that the only counterterms that appear at any order in perturbation theory correspond to renormalizations of existing terms in the bare lattice action. In particular we find that no mass terms are generated at any finite order of perturbation theory. We calculate these renormalizations by examining the fermion and auxiliary boson self energies at one loop and find that they all exhibit a common logarithmic divergence which can be absorbed by a single wavefunction renormalization. This finding implies that at one loop only a fine tuning of the finite parts is required to regain full supersymmetry in the continuum limit.
We analyze the effects of flavor splitting from staggered fermion lattice simulations of graphene. Both the unimproved action, and the tadpole improved action with a Naik term show significant flavor symmetry breaking in the spectrum of the Dirac operator. We also measure the average plaquette term and describe how it calls for a reinterpretation of previous lattice Monte Carlo simulation results, due to tadpole improvement. From this we infer that the simulations are indicative of a semi-metal phase for suspended graphene.