Fuzzy Instantons

Abstract

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l 2 . For small values of the dimension n 2 of the matrix algebra the integer resembles the result of a quantization condition but as n → ∞ the ratio l/n can tend to an arbitrary real number between zero and one.

Spin and Statistics on the Groenewold–moyal Plane: Pauli-Forbidden Levels and Transitions

“…Chaichian et al [1] and Aschieri et al [2] have proved that the Poincaré group acts as automorphisms on A θ (R d+1 ) if the coproduct is deformed. (See also the prior work of Majid [3], Oeckl [4] and Grosse et al [5]). In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of [2].…”

Finite gauge theory on fuzzy CP2

“…The other equations of (10) are redundand except at the south sphere. In particular, note that fixing a value for x 8 determines a 3-sphere S 3 ⊂ R 4 t = x 4 , x 5 , x 6 , x 7 .…”

Spherically symmetric monopoles in noncommutative space

“…In this representation, r is a continuous commutative variable. Notice that the algebra (3) and (4) for fixed r describes a fuzzy sphere [14 -25], so essentially what we are doing is foliating the threedimensional noncommutative space with concentric fuzzy spheres (a similar construction was done in [19,22]). …”