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We derive a noncommutative U(1) and U(n) gauge theory on the fuzzy sphere from a three dimensional matrix model by expanding the model around a classical solution of the fuzzy sphere. Chern-Simons term is added in the matrix model to make…

High Energy Physics - Theory · Physics 2009-11-07 S. Iso , Y. Kimura , K. Tanaka , K. Wakatsuki

We define and solve the $\text{U(1)}$ Chern-Simons-Maxwell theory on spacetime lattice, with an emphasis on the chirality of the theory. Realizing Chern-Simons theory on lattice has been a problem of interest for decades, and over the years…

High Energy Physics - Theory · Physics 2025-08-18 Ze-An Xu , Jing-Yuan Chen

We revisit the lattice formulation of the Abelian Chern-Simons model defined on an infinite Euclidean lattice. We point out that any gauge invariant, local and parity odd Abelian quadratic form exhibits, in addition to the zero eigenvalue…

High Energy Physics - Theory · Physics 2009-10-31 F. Berruto , M. C. Diamantini , P. Sodano

In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a…

Strongly Correlated Electrons · Physics 2018-02-23 N. Menezes , C. Morais Smith , Giandomenico Palumbo

For $n \geq 2$, consider $\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a…

Analysis of PDEs · Mathematics 2024-11-22 Songbo Hou , Xiaoqing Kong

The Majorana lattice gauge theory purely composed of Majorana fermions on square lattice is studied throughly. The ground state is obtained exactly and exhibits the coexistence of symmetry breaking and topological order. The $Z_2$ symmetry…

Strongly Correlated Electrons · Physics 2023-01-18 Jian-Jian Miao

Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to…

High Energy Physics - Lattice · Physics 2009-10-22 S. Aoki , H. Hirose

A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Alexei Kitaev

We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a…

High Energy Physics - Lattice · Physics 2014-11-17 J. Nishimura , M. A. Vazquez-Mozo

In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This…

High Energy Physics - Lattice · Physics 2011-09-28 Wolfgang Bietenholz

We introduce a Hamiltonian lattice model for the $(1+1)$-dimensional $\text{SU}(N_c)$ gauge theory coupled to one adjoint Majorana fermion of mass $m$. The discretization of the continuum theory uses staggered Majorana fermions. We analyze…

High Energy Physics - Theory · Physics 2024-05-02 Ross Dempsey , Igor R. Klebanov , Silviu S. Pufu , Benjamin T. Søgaard

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model…

Strongly Correlated Electrons · Physics 2022-06-20 Umberto Borla , Bhilahari Jeevanesan , Frank Pollmann , Sergej Moroz

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction…

High Energy Physics - Lattice · Physics 2018-03-14 Daniel G. Figueroa , Mikhail Shaposhnikov

We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…

Strongly Correlated Electrons · Physics 2009-11-13 Su-Peng Kou , Michael Levin , Xiao-Gang Wen

Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^3$ in terms of a holonomy on the Chern-Simons bundle and the…

Differential Geometry · Mathematics 2025-06-26 Lynn Heller , Sebastian Heller , Martin Traizet

We explore a $Z_2$ Hamiltonian lattice gauge theory in one spatial dimension with a coupling $h$, without imposing any Gauss' law constraint. We show that in our model $h=0$ is a free deconfined quantum critical point containing massless…

Strongly Correlated Electrons · Physics 2020-06-02 Jernej Frank , Emilie Huffman , Shailesh Chandrasekharan

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for…

High Energy Physics - Theory · Physics 2015-06-15 Benjamin Béri , David Tong , Kenny Wong

We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…

High Energy Physics - Theory · Physics 2019-06-26 Roland Bittleston , David Skinner

Chern-Simons gauge theory is formulated on three dimensional $Z_2$ orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum…

High Energy Physics - Theory · Physics 2009-12-15 Petr Horava

We formulate $U(1)$ $bda$ Chern-Simons theory, which is also called BF theory, on a lattice, adapting a method proposed by Kantor and Susskind for the groups $\mathbb{R}$ and $\mathbb{Z}_N$. Our method applies to any finite or infinite…

High Energy Physics - Theory · Physics 2022-07-20 Tom Banks , Bingnan Zhang