arXiv subjects

Ray Romero

Publications and source records attributed to Ray Romero.

3 recordsLinked to original sources

arXiv2026

Anomalous behavior of Wilson fermions in the presence of monopoles

Three dimensional compact U(1) gauge theory supports a finite density of monopoles at a fixed lattice gauge coupling. After showing evidence for the expected dependence on the lattice coupling of the density of monopoles, we study the low lying spectrum of a two flavors of two-component Wilson fermions as a function of the bare Wilson mass. The Wilson-Dirac operator that realizes the two flavors are hermitian conjugate of each other to restore parity invariance and the commutativity of the two operators expected in the typical continuum limit is not the case in the presence of monopoles for all values of the lattice gauge coupling. This results in an anomalous behavior where we see clear evidence for the presence of very small eigenvalues for a wide range of a particular sign of the bare Wilson mass. These eigenmodes are typically in one-to-one correspondence with the number of monopoles as defined by the gauge field and the spectrum associated with these modes are separated by a gap from the bulk in the asymptotic regime of the lattice gauge coupling. The eigenvalues come in pairs around zero and the eigenvalues of one sign couple to the monopoles while the modes of the opposite sign couple to the anti-monopole implying flavor symmetry breaking.

hep-lat↗

arXiv2025

Lattice study of two-dimensional SU(2) gauge theories with a single massless Majorana fermion

Massless overlap fermions in the real representation of two dimensional $SU(N_c)$ gauge theories exhibit a mod($2$) index due to the rigidity of its spectrum when viewed as a function of the background gauge field - lattice gauge fields on a periodic torus come under two classes; ones that have one set of chirally paired zero modes and ones that do not. Focusing on $SU(2)$ and a single Majorana fermion in an integer representation, $J$; we present numerical evidence that shows only one of these classes survives the continuum limit and this depends on the boundary conditions of the fermion and the gauge field. As such, two of the four possible partition functions are zero in the continuum limit. By defining modified partition functions which do not include the zero modes of the overlap fermions in the fermion determinant, we are able to define an expectation value for a fermion bilinear as ratios of two mixed partition functions. This observable is referred to as the topological condensate and has a non-zero expectation value on any finite physical torus and also has a non-zero limit as the size of the torus is taken to infinity. We study the spectral density of fermions and the scaling of the lowest eigenvalue with the size of the torus to show the absence of any spontaneous symmetry breaking but the emergence of zero modes in the infinite volume limit where it is prohibited in finite volume. These results remain the same for $J = 1, 2, 3, 4$. These results motivate us to propose an independent plaquette model which reproduces the correct physics in the infinite volume limit using a single partition function.

hep-lat↗

arXiv2024

Massless fermions in uniform flux background on $T^2\times R$: Vacuum quantum numbers from single-particle filled modes using lattice regulator

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.

hep-th↗