arXiv subjects

Yigal Shamir

Publications and source records attributed to Yigal Shamir.

At least 19 recordsLinked to original sources

arXiv2026

Domain wall fermions

We introduce the formulation of domain wall fermions in the context of lattice QCD. We prove the recovery of exact chiral symmetry in the limit of an infinite fifth direction, and derive the effective four-dimensional operator satisfying the Ginsparg-Wilson relation obtained in this limit. We discuss the residual breaking of chiral symmetry for finite extent of the fifth direction, and how it is affected by spectral features of the Wilson kernel. We also discuss various improvements of domain wall fermions including notably M\"obius fermions. These notes are a chapter contributed to the on-line book ``Lattice QCD at 50 years'' (LQCD@50).

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arXiv2026

Symmetric mass generation and the Nielsen-Ninomiya theorem

The symmetric mass generation (SMG) approach to the construction of lattice chiral gauge theories attempts to use interactions to render mirror fermions massive without symmetry breaking, to obtain the desired chiral massless spectrum (before the gauge field is turned on). If the zeros that often replace the mirror poles of fermion two-point functions in an SMG phase are ``kinematical'' singularities, general constraints can be formulated on the existence of a chiral fermion spectrum which are valid in the presence of (non-gauge) interactions of arbitrary strength, including in any SMG phase. Constructing a one-particle lattice hamiltonian describing the fermion spectrum, we discuss the conditions for the applicability of the Nielsen-Ninomiya theorem to this hamiltonian. If these conditions are satisfied, the massless fermion spectrum must be vector-like.

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arXiv2025

Constraints on the symmetric mass generation paradigm for lattice chiral gauge theories

Within the symmetric mass generation (SMG) approach to the construction of lattice chiral gauge theories, one attempts to use interactions to render mirror fermions massive without symmetry breaking, thus obtaining the desired chiral massless spectrum. If successful, the gauge field can be turned on, and thus a chiral gauge theory can be constructed in the phase in which SMG takes place. In this paper we argue that the zeros that often replace the mirror poles of fermion two-point functions in an SMG phase should be ``kinematical'' singularities. We conjecture that the SMG interactions generate opposite-chirality bound states, which combine with the gapped elementary mirror states to form massive Dirac fermions. The propagator zeros can then be avoided by choosing an appropriate set of interpolating fields that contains both elementary and composite fields. This allows us to apply general constraints on the existence of a chiral fermion spectrum which are valid in the presence of (non-gauge) interactions of arbitrary strength, including in any SMG phase. Using a suitably constructed one-particle lattice hamiltonian describing the fermion spectrum, we formulate a generalized no-go theorem which establishes the conditions for the applicability of the Nielsen-Ninomiya theorem to this hamiltonian. If these conditions are satisfied, the massless fermion spectrum must be vector-like. We add some general observations on the strong coupling limit of SMG models. We also elaborate on the qualitative differences between four-dimensional and two-dimensional theories that limit the lessons that can be drawn from two-dimensional models. Finally, we compile a list of open questions which must be addressed in any SMG model in order to determine whether or not it is subject to the generalized no-go theorem.

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arXiv2025

Power counting of the pion-dilaton effective field theory

Confining QCD-like theories close to the conformal window have a ``walking'' coupling. This is believed to lead to a light singlet scalar meson in the low-energy spectrum, a dilaton, which is the pseudo Nambu--Goldstone boson for the approximate scale symmetry. Extending chiral perturbation theory to include the dilaton requires a new small parameter to control the dilaton mass and its interactions. In our previous work we derived a systematic power counting for the dilaton couplings by matching the effective low-energy theory to the underlying theory using mild assumptions. In this paper we examine two alternative power countings which were proposed in the literature based on a phenomenological picture for the conformal transition. We find that one of these power countings fails, in fact, to generate a systematic expansion; the other coincides with the power counting we derived. We also point out that the so-called $Δ$-potential coincides with the tree-level potential of the former, invalid, power counting.

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arXiv2024

Conserved currents in five-dimensional proposals for lattice chiral gauge theories

We apply the Grabowska-Kaplan framework, originally proposed for lattice chiral gauge theories, to QCD. We show that the resulting theory contains a conserved and gauge invariant singlet axial current, both on the lattice and in the continuum limit. This must give rise to a difference with QCD, with the simplest possibility being a superfluous Nambu-Goldstone boson in the physical spectrum not present in QCD. We find a similar unwanted conserved current in the recent "disk" formalism [Kaplan, Kaplan & Sen], this time limiting ourselves to the continuum formulation. A similar problem is expected when either of these formalisms is used for its original goal of constructing lattice chiral gauge theories. Finally we discuss a conjecture about the possible dynamics that might be associated with the unwanted conserved current, and the fate of 't Hooft vertices.

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arXiv2024

Propagator zeros and lattice chiral gauge theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost.

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arXiv2023

Dilaton chiral perturbation theory at next-to-leading order

We apply dilaton chiral perturbation theory (dChPT) at next-to-leading order to lattice data from the LatKMI collaboration for the eight-flavor SU(3) gauge theory. In previous work, we found that leading-order dChPT does not account for these data, but that a model extension of leading-order dChPT with a varying mass anomalous dimension describes these data well. Here we calculate the next-to-leading order corrections for the pion mass and decay constant. We focus on these quantities, as data for the dilaton mass are of poorer quality. The application of next-to-leading order dChPT is difficult because of the large number of new low-energy constants, and the results of our fits turn out to be inconclusive. They suggest -- yet cannot firmly establish -- that the LatKMI mass range might be outside the scope of dChPT.

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arXiv2023

Infrared fixed point of the SU(3) gauge theory with $N_f = 10$ flavors

We use lattice simulations and the continuous renormalization-group method, based on the gradient flow, to calculate the $β$ function and anomalous dimensions of the SU(3) gauge theory with $N_f=10$ flavors of fermions in the fundamental representation. We employ several improvements to extend the range of available renormalized couplings, including the addition of heavy Pauli-Villars bosons to reduce cutoff effects and the combination of a range of gradient flow transformations. While in the weak coupling regime our result is consistent with those of earlier studies, our techniques allow us to study the system at much stronger couplings than previously possible. We find that the renormalization group $β$ function develops a zero, corresponding to an infrared-stable fixed point, at gradient-flow coupling $g^2=15.0(5)$. We also determine the mass and tensor anomalous dimensions: At the fixed point we find $γ_m\simeq0.6$, suggesting that this system might be deep inside the conformal window.

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arXiv2023

Infrared fixed point and anomalous dimensions in a composite Higgs model

We use lattice simulations and the continuous renormalization-group method, based on the gradient flow, to study a candidate theory of composite Higgs and a partially composite top. The model is an SU(4) gauge theory with four Dirac fermions in each of the fundamental and two-index antisymmetric representations. We find that the theory has an infrared fixed point at $g^2 \simeq 15.5$ in the gradient flow scheme. The mass anomalous dimension of each representation is large at the fixed point. On the other hand, the anomalous dimensions of top-partner operators do not exceed 0.5 at the fixed point. This may not be large enough for a phenomenologically successful model of partial compositeness.

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arXiv2021

Dilaton chiral perturbation theory and applications

We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu-Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

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arXiv2021

$S$ parameter from a prototype composite-Higgs model

We have calculated the low-energy constant $L_{10}$ in a prototype composite Higgs model with dynamical fermions in two different representations of the gauge group. The resulting contribution of the new strong sector to the $S$ parameter is consistent with current bounds on the vacuum misalignment parameter. We end with a brief discussion of future directions.

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arXiv2021

Taming lattice artifacts with Pauli--Villars fields

As fermions are added to a lattice gauge theory, one is driven to stronger bare coupling in order to maintain the same renormalized coupling. Stronger bare couplings are usually associated with larger gauge fluctuations, leading to larger cutoff effects and more expensive simulations. In theories with many light fermions, sometimes the desired physical region cannot be reached before encountering a phase boundary. We show that these undesired effects can be reduced by adding Pauli--Villars fields. We reach significantly larger renormalized couplings while at the same time damping short-distance fluctuations of the gauge field. This may allow for controlled continuum extrapolations from large lattice spacings.

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arXiv2021

Low-energy constant $L_{10}$ in a two-representation lattice theory

We calculate the low-energy constant $L_{10}$ in a two-representation SU(4) lattice gauge theory that is close to a composite-Higgs model. From this we obtain the contribution of the new strong sector to the $S$ parameter. This leads to an upper bound on the vacuum misalignment parameter $ξ$ which is similar to current estimates of this bound. Our result agrees with large-$N_c$ scaling expectations, within large systematic uncertainties.

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arXiv2020

Explorations beyond dilaton chiral perturbation theory in the eight-flavor SU(3) gauge theory

We continue our study of spectroscopy data for the SU(3) gauge theory with eight fundamental fermions, motivated by the effective field theory framework of dilaton chiral perturbation theory (dChPT). At leading order dChPT predicts a constant mass anomalous dimension $γ_m$, consistent with the assumed proximity of an infrared fixed point. For the relatively large fermion masses simulated by the LatKMI collaboration, the influence of the infrared fixed point diminishes, and our fits suggest that $γ_m$ starts running. Since a complete higher-order analysis is not feasible with presently available data, we adopt a more phenomenological approach. We propose a partial extension to higher orders, which incorporates the running of $γ_m$ into the tree-level lagrangian. We find that this extension successfully describes the full fermion-mass range of the LatKMI data, including the pion taste splittings which arise from using staggered fermions in the lattice simulations. We also investigate a more general class of dilaton potentials proposed in the literature, using both the LSD and LatKMI data sets, concluding that these data favor the form predicted by dChPT.

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arXiv2020

Application of dilaton chiral perturbation theory to $N_f=8$, ${\rm SU}(3)$ spectral data

We extend dilaton chiral perturbation theory (dChPT) to include the taste splittings in the Nambu--Goldstone sector observed in lattice simulations of near-conformal theories with staggered fermions. We then apply dChPT to a recent simulation by the LSD collaboration of the SU(3) gauge theory with 8 fermions in the fundamental representation, which is believed to exhibit near-conformal behavior in the infrared, and in which a light singlet scalar state, nearly degenerate with the pions, has been found. We find that the mesonic sector of this theory can be successfully described by dChPT, including, in particular, the mesonic taste splittings found in the simulation. We confirm that current simulations of this theory are in the "large-mass" regime.

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arXiv2019

Fits of $SU(3)$ $N_f=8$ data to dilaton-pion effective field theory

We report on fits of the $SU(3)$ $N_f=8$ LSD spectral data to chiral perturbation theory with a dilatonic meson. These fits confirm that current simulations are in the "large-mass" regime, with approximate hyperscaling as the leading mass dependence. We find that the leading-order effective field theory describes the data well. In particular, the effective field theory allows us to understand the staggered taste splitting, explaining the pattern observed in the LSD data, which looks different from QCD.

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arXiv2019

The $ε$-regime of dilaton chiral perturbation theory

The $ε$-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the $ε$-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the $ε$-regime and the $p$-regime. In the $ε$-regime, moreover, all results agree with the universal predictions to leading order in $ε$.

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arXiv2019

Phase ambiguity of the measure for continuum Majorana fermions

Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative lattice definition, allowing us to discuss the relation between the phase of the lattice pfaffian and the effective $θ$ angle of the theory. We also resolve an apparent paradox regarding the induced $θ$ angle when a theory of $N$ Dirac fermions in a real representation of the gauge group is re-expressed in terms of $2N$ Majorana fermions. We discuss how all this is reflected in chiral perturbation theory.

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