Weyl Fermions on a Finite Lattice.

The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed in D. B. Kaplan [preceding Letter, Chiral gauge theory at the boundary between topological phases, Phys. Rev. Lett. 132, 141603 (2024).PRLTAO0031-900710.1103/PhysRevLett.132.141603]. In this Letter, we show that similar unpaired Weyl edge states can be seen on a finite lattice. In particular, we consider the discretized Hamiltonian for a Wilson fermion in (2+1) dimensions with a 1+1 dimensional boundary and continuous time. We demonstrate that the low lying boundary spectrum is indeed Weyl-like: it has a linear dispersion relation and definite chirality and circulates in only one direction around the boundary. We comment on how our results are consistent with Nielsen-Ninomiya theorem. This work removes one potential obstacle facing the program outlined in D. B. Kaplan, preceding Letter, for regulating chiral gauge theories.

Chiral Gauge Theory at the Boundary between Topological Phases.

I demonstrate how chiral fermions with an exact gauge symmetry can appear on the d-dimensional boundary of a finite volume (d+1)-dimensional manifold, without any light mirror partners. The condition for the d-dimensional boundary theory to be local is that gauge anomalies cancel and that the volume be large. This can likely be achieved on a lattice and provides a new paradigm for the lattice regularization of chiral gauge theories.

Index Theorems, Generalized Hall Currents, and Topology for Gapless Defect Fermions.

We show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman diagram that computes the index reveals an analog of the quantum Hall current flowing on and off the defect-even in systems without conserved currents or chiral anomalies-and makes explicit the interplay between topology in momentum and coordinate space. We provide several explicit examples.

Fractional Quantum Hall Effect in a Relativistic Field Theory.

We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the fractional quantum Hall effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative U(1)×U(1) gauge theory with integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, bulk anyonic excitations, and exotic phenomena such as a fractional quantum spin Hall effect. We show explicitly how fractionally charged chiral edge states emerge in the IR.

Entanglement Suppression and Emergent Symmetries of Strong Interactions.

Entanglement suppression in the strong-interaction S matrix is shown to be correlated with approximate spin-flavor symmetries that are observed in low-energy baryon interactions, the Wigner SU(4) symmetry for two flavors and an SU(16) symmetry for three flavors. We conjecture that dynamical entanglement suppression is a property of the strong interactions in the infrared, giving rise to these emergent symmetries and providing powerful constraints that predict the nature of nuclear and hypernuclear forces in dense matter.

Nonperturbative Regulator for Chiral Gauge Theories?

We propose a nonperturbative gauge-invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d+1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.

Spacetime as a topological insulator: mechanism for the origin of the fermion generations.

We suggest a mechanism whereby the three generations of quarks and leptons correspond to surface modes in a five-dimensional theory. These modes arise from a nonlinear fermion dispersion relation in the extra dimension, much in the same manner as fermion surface modes in a topological insulator or lattice implementation of domain wall fermions. We also show that the topological properties can persist in a deconstructed version of the model in four dimensions.

Noise, sign problems, and statistics.

We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions.

New field-theoretic method for the virial expansion.

We develop a graphical method for computing the virial expansion coefficients for a nonrelativistic quantum field theory. As an example we compute the third virial coefficient b3 for unitary fermions, a nonperturbative system. By calculating several graphs and performing an extrapolation, we arrive at b3=-0.2930, within 0.7% of a recent computation b3=-0.290 952 95 by Liu, Hu, and Drummond, which involved summing 10,000 energy levels for three unitary fermions in a harmonic trap.

Emergence of symmetry in homooligomeric biological assemblies.

Naturally occurring homooligomeric protein complexes exhibit striking internal symmetry. The evolutionary origins of this symmetry have been the subject of considerable speculation; proposals for the advantages associated with symmetry include greater folding efficiency, reduced aggregation, amenability to allosteric regulation, and greater adaptability. An alternative possibility stems from the idea that to contribute to fitness, and hence be subject to evolutionary optimization, a complex must be significantly populated, which implies that the interaction energy between monomers in the ancestors of modern-day complexes must have been sufficient to at least partially overcome the entropic cost of association. Here, we investigate the effects of this bias toward very-low-energy complexes on the distribution of symmetry in primordial homooligomers modeled as randomly interacting pairs of monomers. We demonstrate quantitatively that a bias toward very-low-energy complexes can result in the emergence of symmetry from random ensembles in which the overall frequency of symmetric complexes is vanishingly small. This result is corroborated by using explicit protein-protein docking calculations to generate ensembles of randomly docked complexes: the fraction of these that are symmetric increases from 0.02% in the overall population to >50% in very low energy subpopulations.

Exotic axion cosmology in theories with phase transitions below the QCD scale.

We show that axion phenomenology may be significantly different than conventionally assumed in theories which exhibit late phase transitions (below the QCD scale). In such theories, one can find multiple pseudoscalars with axionlike couplings to matter, including a string scale axion, whose decay constant far exceeds the conventional cosmological bound. Such theories have several dark matter candidates.

Neutrino oscillations as a probe of dark energy.

We consider a class of theories in which neutrino masses depend significantly on environment, as a result of interactions with the dark sector. Such theories of mass varying neutrinos were recently introduced to explain the origin of the cosmological dark energy density and why its magnitude is apparently coincidental with that of neutrino mass splittings. In this Letter we argue that in such theories neutrinos can exhibit different masses in matter and in vacuum, dramatically affecting neutrino oscillations. As an example of modifications to the standard picture, we consider simple models that may simultaneously account for the LSND anomaly, KamLAND, K2K, and studies of solar and atmospheric neutrinos, while providing motivation to continue to search for neutrino oscillations in short baseline experiments such as BooNE.

Lattice theory for low energy fermions at nonzero chemical potential.

We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the two-body potential and does not suffer from a sign problem. In particular, the theory could be useful in studying the thermodynamic limit of fermion systems for which the scattering length is much larger than the interparticle spacing, with applications to realistic atomic systems and dilute neutron gases.

Charged and superconducting vortices in dense quark matter.

Quark matter at astrophysical densities may contain stable vortices due to the spontaneous breaking of hypercharge symmetry by kaon condensation. We argue that these vortices could be both charged and electrically superconducting. Current carrying loops (vortons) could be long-lived and play a role in the magnetic and transport properties of this matter. We provide a scenario for vorton formation in protoneutron stars.