Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2410.19984

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

Nikhil Karthik·Rajamani Narayanan·Ray Romero
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 $\fracπ{2}$ 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.

Explore related subjects

hep-thhep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Nikhil Karthik, Rajamani Narayanan, Ray Romero. 2024-12-19. Massless fermions in uniform flux background on $T^2\times R$: Vacuum quantum numbers from single-particle filled modes using lattice regulator. https://arxiv.org/abs/2410.19984

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Introduction to Generalized Symmetries

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in $(1+1)$-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to $(3+1)$-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.

hep-th↗
arXiv2026

Planar loop integrands from cuts in $D$ dimensions

We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal Möbius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes. As an application we write down closed-formulas for loop integrands in pure Yang--Mills theory, where the required cuts are generated by gluing $D$-dimensional tree amplitudes and summing over internal gluon states. We also use the two-loop five-point case as a validation, comparing with known integrand data and after integration-by-parts reduction, with known integrated helicity amplitudes. The same framework also produces compact cut-organized data for larger examples, including the two-loop six-point and three-loop four-point cases. We also describe the corresponding simplification in maximally supersymmetric Yang--Mills theory, where the absence of bubble and triangle subgraphs reduces the relevant cut poset substantially.

hep-th↗
arXiv2026

Free Field Realization of $\mathcal{W}$-Algebra Associated with Exceptional Lie Algebras

We study the free field realization of the $\mathcal{W}$-algebra associated with the exceptional Lie algebras $E_6$, $E_7$, $E_8$, and $F_4$. We develop a recursive construction in which a $\mathcal{W}$-algebra of rank $r$ is obtained from a $\mathcal{W}$-algebra of rank $r-1$ together with a free boson. The $\mathcal{W}$-currents are constructed from the zero commutation relation with the screening charges. The $\mathcal{W}E_6/\mathcal{W}E_7$ algebra is constructed from the $\mathcal{W}D_5/\mathcal{W}D_6$ algebra and is shown to be the same as that realized from the $\mathcal{W}A_5/\mathcal{W}E_6$ algebra, up to a change of the free field basis. The spin-$8$ generator of the $\mathcal{W}E_8$ algebra is built from the $\mathcal{W}D_7$ algebra. The recursive construction of the $\mathcal{W}BC_r$ algebras is also studied. We then realize the $\mathcal{W}F_4$ algebra based on the $\mathcal{W}BC_3$ algebra. Furthermore, the $\mathcal{W}$-charges of the generators of the $\mathcal{W}E_{6,7}$, $\mathcal{W}BC_{2,3}$, and $\mathcal{W}F_4$ algebras are calculated and expressed in terms of the Casimir invariants.

hep-th↗