scholarly journals Zero modes of the Dirac operator in three dimensions

1999 ◽  
Vol 60 (12) ◽  
Author(s):  
C. Adam ◽  
B. Muratori ◽  
C. Nash
Keyword(s):  
Dirac Operator ◽  
Three Dimensions ◽  
Zero Modes

scholarly journals Degeneracy of zero modes of the Dirac operator in three dimensions

2000 ◽  
Vol 485 (1-3) ◽  
pp. 314-318 ◽  
Author(s):  
C Adam ◽  
B Muratori ◽  
C Nash
Keyword(s):  
Dirac Operator ◽  
Three Dimensions ◽  
Zero Modes

scholarly journals Chiral condensate and Dirac spectrum of one-and two-flavor QCD at nonzero θ-angle

2018 ◽  
Vol 175 ◽  
pp. 04004 ◽  
Author(s):  
Mario Kieburg ◽  
Jacobus Verbaarschot ◽  
Tilo Wettig
Keyword(s):  
Dirac Operator ◽  
Quark Mass ◽  
Imaginary Axis ◽  
Chiral Condensate ◽  
Dirac Spectrum ◽  
Quark Masses ◽  
Zero Modes

In previous work we showed that the chiral condensate of one-flavor QCD exhibits a Silver Blaze phenomenon when the quark mass crosses m = 0: the chiral condensate remains constant while the quark mass crosses the spectrum of the Dirac operator, which is dense on the imaginary axis. This behavior can be explained in terms of exponentially large cancellations between contributions from the zero modes and from the nonzero modes when the quark mass is negative. In these proceedings we show that a similar Silver Blaze phenomenon takes places for QCD with one flavor and arbitrary θ- angle, and for QCD with two flavors with different quark masses m1 and m2. In the latter case the chiral condensate remains constant when m1 crosses zero at fixed m2 > 0 until the Dashen point m1 = –m2 is reached, where the chiral condensate has a discontinuity. In terms of contributions from the Dirac spectrum the shift of the discontinuity from m1 = 0 to m1 = -m2 also arises from exponentially large cancellations between the zero and nonzero modes when m1m2 < 0. All calculations are performed in the microscopic or ε-domain of QCD. Results for arbitrary θ-angle are discussed as well.

scholarly journals THE SU(2) GLOBAL ANOMALY THROUGH LEVEL CIRCLING

1994 ◽  
Vol 09 (06) ◽  
pp. 501-514 ◽  
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
Gauge Theory ◽  
Dirac Operator ◽  
Gauge Field ◽  
Complex Plane ◽  
Spinor Representation ◽  
Yukawa Couplings ◽  
Zero Modes ◽  
Global Anomaly ◽  
External Gauge

We discuss a novel manifestation of the SU(2) global anomaly in an SU(2) gauge theorywith an odd number of chiral quark doublets and arbitrary Yukawa couplings. We arguethat the massive four-dimensional Euclidean Dirac operator is non-Hermitian with itsspectrum of eigenvalues (λ, −λ) lying in pairs in the complex plane. Consequently theexistence of an odd number of normalizable zero modes of the four-dimensional massiveDirac operator is equivalent to a fermionic level exchange phenomenon, level “circling,”under continuous topologically non-trivial deformations of the external gauge field. Moregenerally global anomalies are a manifestation of fermionic level “circling” in any SP(2n)gauge theory with an odd number of massive fermions in the spinor representation andarbitrary Yukawa couplings.

scholarly journals Zero-modes of the QED Neuberger Dirac operator

2002 ◽  
Vol 106-107 ◽  
pp. 592-597
Author(s):  
Bernd A. Berg ◽  
Urs M. Heller ◽  
Harald Markum ◽  
Rainer Pullirsch ◽  
Wolfgang Sakuler
Keyword(s):  
Dirac Operator ◽  
Zero Modes

FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND ON A SPHERE

2007 ◽  
Vol 22 (21) ◽  
pp. 3643-3653 ◽  
Author(s):  
YU-XIAO LIU ◽  
LI ZHAO ◽  
LI-JIE ZHANG ◽  
YI-SHI DUAN
Keyword(s):  
Riemann Surface ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Topological Structure ◽  
The Self ◽  
Two Dimensional ◽  
Zero Modes ◽  
Self Duality ◽  
Effective Lagrangian ◽  
Topological Term

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra sphere and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a sphere in two simple cases are obtained.

scholarly journals Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Max Geier ◽  
Ion Cosma Fulga ◽  
Alexander Lau
Keyword(s):  
Topological Insulators ◽  
Three Dimensions ◽  
Topological Phases ◽  
Rotation Symmetry ◽  
First Order ◽  
Zero Modes ◽  
Symmetry Classes ◽  
Topological Lattice ◽  
Rotation Symmetric ◽  
Translation Symmetry

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d-2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

scholarly journals TOPOLOGICAL ZERO MODES IN MONTE CARLO SIMULATIONS

1995 ◽  
Vol 06 (01) ◽  
pp. 123-134 ◽  
Author(s):  
H. DILGER
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Dirac Operator ◽  
Zero Mode ◽  
Mode Structure ◽  
Hybrid Monte Carlo ◽  
Schwinger Model ◽  
Zero Modes ◽  
Topological Sector ◽  
Approximate Zero

We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.

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