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The quantum numbers of monopoles in $R^3$in the presence of massless fermions have been analyzed using a uniform flux background in $S^2\times R$coupled to fermions. An analogous study in $T^2\times R$is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on $T^2$with a total flux of $Q$in the continuum. The degenerate ground states are classified based on their transformation properties under $\frac{\pi }{2}$rotations of $T^2$that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society2025 

We numerically address the issue of which monopole operators are relevant under renormalization group flow in three-dimensional parity-invariant noncompact QED with four flavors of massless two-component Dirac fermion. Using lattice simulation and finite-size scaling analysis of the free energy to introduce monopole-antimonopole pairs in N = 4 and N = 12 flavor noncompact QED3, we estimate the infrared scaling dimensions of monopole operators that introduce 2π and 4π fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-N expectations for N =12 QED3. Applying the same procedure in N = 4 QED3, we estimate the scaling dimension of 4π flux monopole operator to be 3.7(3), which allows the possibility of the operator being irrelevant. This finding offers support to the scenario in which higher-flux monopoles are irrelevant deformations to the Dirac spin liquid phase that could be realized on certain non-bipartite lattices by forbidding 2π - flux monopoles. 

Two-dimensional QCD with Nc colors and Nf flavors of massless fermions in the fundamental representation is expected to exhibit conformal behavior in the infrared governed by a u(Nf) Wess–Zumino–Witten model with level Nc. Using numerical analysis within the lattice formalism with exactly massless overlap fermions, we show the emergence of such behavior in the infrared limit. Both the continuum extrapolated low-lying eigenvalues of the massless Dirac operator and the propagator of scalar mesons exhibit a flow from the ultraviolet to the infrared. We find that the amplitude of the conserved current correlator remains invariant under the flow, while the amplitude of the scalar correlator approaches Nf-independent values in the infrared. 

The spectra of two-dimensional su(2) gauge theories coupled to a single massless Majorana fermion in integer representations, J, are numerically investigated using the discrete light-cone Hamiltonian. One of our aims is to explore the possible presence of massless states for J > 2 in spite of the absence of a continuous symmetry. After comparing to existing results for J = 1 (adjoint fermions), we present results for J = 2, 3, 4. As expected, for J = 2 there are no massless states but in contrast to the J = 1 theory, the lightest state is a boson. We find exact massless modes in the bosonic and fermionic sector for all values of total momentum for J = 3 and J = 4 and, in each sector, the number of massless modes grows with the value of the total momentum. In addition to the spectrum, we present results on the particle number and momentum fraction distributions and argue for a separation of bulk states from edge states. 

Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-k Chern–Simons action, “half-CS” term and the mixed Chern–Simons (BF) coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, we demonstrate numerically how the lattice formalism beautifully reproduces the continuum expectations, such as the flow of action under large gauge transformations.