Dirac Operator on Fuzzy Sphere with U(1) Dirac Monopole Background

2004 ◽  
Vol 42 (2) ◽  
pp. 247-250
Author(s):  
Xiong Chuan-Hua ◽  
Yue Rui-Hong
2020 ◽  
Vol 35 (15) ◽  
pp. 2050118 ◽  
Author(s):  
Derar Altarawneh ◽  
Manfried Faber ◽  
Roman Höllwieser

We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. We find some evidence for fractional topological charge during cooling the spherical center vortex on a [Formula: see text] lattice. We identify the object with topological charge [Formula: see text] as a Dirac monopole with a gauge field fading away at large distances. Therefore, even for periodic boundary conditions, it does not need an anti-monopole.


1998 ◽  
Vol 13 (19) ◽  
pp. 3235-3243 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.


2010 ◽  
Vol 25 (37) ◽  
pp. 3151-3167 ◽  
Author(s):  
E. HARIKUMAR

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.


1995 ◽  
Vol 33 (2) ◽  
pp. 171-181 ◽  
Author(s):  
H. Grosse ◽  
P. Prešnajder
Keyword(s):  

2006 ◽  
Vol 2006 (09) ◽  
pp. 037-037 ◽  
Author(s):  
E Harikumar ◽  
Amilcar R Queiroz ◽  
Paulo Teotonio-Sobrinho
Keyword(s):  

2020 ◽  
Vol 35 (08) ◽  
pp. 2050048
Author(s):  
M. Lotfizadeh

In this paper, we construct the [Formula: see text]-deformed fuzzy Dirac and chirality operators on quantum fuzzy Podles sphere [Formula: see text]. Using the [Formula: see text]-deformed fuzzy Ginsparg–Wilson algebra, we study the [Formula: see text]-deformed gauged fuzzy Dirac and chirality operators in instanton sector. We will show the correct fuzzy sphere limit in the limit case [Formula: see text] and the correct commutative limit in the limit case when [Formula: see text] and noncommutative parameter [Formula: see text] tends to infinity.


2003 ◽  
Vol 18 (33n35) ◽  
pp. 2431-2438 ◽  
Author(s):  
Peter Prešnajder

The free spinor field on a fuzzy sphere is described within Watamura approach to Dirac operator. Except of the highest mode, its spectrum is the same but truncated as in the commutative case. We present a simple gauge extension of the model with usual polynomial interaction. The gauge symmetry is exact, and the chiral properties of the field modes are standard except the highest mode.


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