scholarly journals A lattice implementation of the η-invariant and effective action for chiral fermions on the lattice

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Aoyama Tatsumi ◽  
Yoshio Kikukawa
Keyword(s):  
Domain Wall ◽  
Gauge Field ◽  
Effective Action ◽  
Continuum Limit ◽  
Complex Phase ◽  
Eta Invariant ◽  
Domain Wall Fermion ◽  
Lattice Implementation ◽  
Chern Simons ◽  
Wilson Fermions

Abstract We consider a lattice implementation of the $\eta$-invariant, using the complex phase of the determinant of the simplified domain-wall fermion, which couples to an interpolating 5D gauge field. We clarify the relation to the effective action for chiral Ginsparg–Wilson fermions. The integrability, which holds true for anomaly-free theories in the classical continuum limit, is not assured on a lattice with finite spacing. A lattice expression for the 5D Chern–Simons term is obtained.

COMPOSITE CHERN-SIMONS GAUGE BOSON IN ANYON GAS

1991 ◽  
Vol 05 (01n02) ◽  
pp. 391-401
Author(s):  
NGUYEN VAN HIEU ◽  
NGUYEN HUNG SON
Keyword(s):  
Gauge Field ◽  
Gauge Boson ◽  
Effective Action ◽  
Momentum Dependence ◽  
Composite Boson ◽  
Dispersion Equations ◽  
Vector Gauge ◽  
Chern Simons

It was shown that in a free anyon gas there exists a composite vector gauge field with the effective action containing a Chern-Simons term. The momentum dependence of the energy of the composite boson was found. The mixing between Chern-Simons boson and photon gives rise to the appearance of new quasiparticles -Chern-Simons polaritons. The dispersion equations of Chern-Simons polaritons were derived.

scholarly journals Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD

2018 ◽  
Vol 175 ◽  
pp. 10003 ◽  
Author(s):  
Katsumasa Nakayama ◽  
Shoji Hashimoto ◽  
Hidenori Fukaya
Keyword(s):  
Perturbation Theory ◽  
Domain Wall ◽  
Spectral Density ◽  
Continuum Limit ◽  
Anomalous Dimension ◽  
Perturbative Expansion ◽  
Wide Range ◽  
Domain Wall Fermion ◽  
Discretization Effect ◽  
The Continuum

We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings (a = 0:083; 0:055; 0:044 fm) to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to O(α4s).

CHERN-SIMONS EFFECTIVE ACTION FOR NON-RELATIVISTIC PLANAR ELECTRONS

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2241-2252
Author(s):  
MARIA CRISTINA DIAMANTINI ◽  
ROBERT LINK ◽  
PASQUALE SODANO
Keyword(s):  
Magnetic Fields ◽  
Gauge Field ◽  
Effective Action ◽  
Spin Systems ◽  
Low Energy ◽  
Xy Model ◽  
Wigner Transformation ◽  
Chern Simons ◽  
Hopping Model ◽  
The Continuum

We investigate the low energy second quantized theory of non-relativistic planar electrons in external magnetic fields. We show that a U(1) Chern-Simons term appears in the effective action, for both the continuum and the lattice theories, as a result of a nontrivial phase holonomy. We also show, using the Jordan-Wigner transformation for planar spin systems, that the quantum frustrated XY model is described by an electron hopping model coupled to a U(1) Chern-Simons gauge field.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

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