Super Dirac operator on the super fuzzy sphere sf(2|2) in instanton sector using super Ginsparg-Wilson algebra

2021 ◽  
Vol 87 (3) ◽  
pp. 277-290
Author(s):  
M. Lotfizadeh
Keyword(s):  
Dirac Operator ◽  
Fuzzy Sphere

scholarly journals DIFFERENTIAL CALCULUS ON FUZZY SPHERE AND SCALAR FIELD

1998 ◽  
Vol 13 (19) ◽  
pp. 3235-3243 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Scalar Field ◽  
Dirac Operator ◽  
Differential Calculus ◽  
Spectral Triple ◽  
Fuzzy Sphere ◽  
Alternative Possibility ◽  
Operator Ordering

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.

scholarly journals "SCHWINGER MODEL" ON THE FUZZY SPHERE

2010 ◽  
Vol 25 (37) ◽  
pp. 3151-3167 ◽  
Author(s):  
E. HARIKUMAR
Keyword(s):  
Partition Function ◽  
Field Strength ◽  
Dirac Operator ◽  
Path Integral ◽  
Integral Method ◽  
Gauge Fields ◽  
Fuzzy Sphere ◽  
Schwinger Model ◽  
Spinor Fields ◽  
Path Integral Method

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.

scholarly journals The dirac operator on the fuzzy sphere

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

scholarly journals Dirac operator on the q-deformed fuzzy sphere and its spectrum

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

Gauged Dirac operator on the quantum sphere in instanton sector

2020 ◽  
Vol 35 (08) ◽  
pp. 2050048
Author(s):  
M. Lotfizadeh
Keyword(s):  
Dirac Operator ◽  
Fuzzy Sphere ◽  
Limit Case ◽  
Quantum Sphere ◽  
Noncommutative Parameter

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.

GAUGE FIELDS ON THE FUZZY SPHERE

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2431-2438 ◽  
Author(s):  
Peter Prešnajder
Keyword(s):  
Gauge Symmetry ◽  
Dirac Operator ◽  
Spinor Field ◽  
Gauge Fields ◽  
Fuzzy Sphere ◽  
Commutative Case

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.

scholarly journals Extended supersymmetries and the Dirac operator

2005 ◽  
Vol 315 (2) ◽  
pp. 467-487 ◽  
Author(s):  
A. Kirchberg ◽  
J.D. Länge ◽  
A. Wipf
Keyword(s):  
Dirac Operator
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