Noncommutative field theory

The effective potential of quantized scalar field on fuzzy sphere is evaluated to the twoloop level. We see that one-loop potential behaves like that in the commutative sphere and the Coleman-Weinberg mechanism of the radiatively symmetry breaking could be also shown in the fuzzy sphere system. In the two-loop level, we use the heavy-mass approximation and the high-temperature approximation to perform the evaluations. The results show that both of the planar and nonplanar Feynman diagrams have inclinations to restore the symmetry breaking in the tree level. However, the contributions from planar diagrams will dominate over those from nonplanar diagrams by a factor N 2 . Thus, at heavy-mass limit or hightemperature system the quantum field on the fuzzy sphere will behave like those on the commutative sphere. We also see that there is a drastic reduction of the degrees of freedom in the nonplanar diagrams when the particle wavelength is smaller than the noncommutativity scale.

“…The phenomena of the UL/IR mixing [11,12] on the fuzzy sphere are different from those in the noncommutative plane. Especially, it has found by Chu.…”

Section: Introductionmentioning

confidence: 99%

“…The integral of a function F ∈ S 2 N over the fuzzy sphere is given by [7][8][9][10] 12) and the inner product can be defined by…”

Section: Quantized Scalar Field On Fuzzy Sphere: Feynman Rulementioning

confidence: 99%

Effective Potential on Fuzzy Sphere

Huang

2002

“…Obviously, A = Φ −1 ∂ u Φ and B = Φ −1 ∂ x Φ solve the second equation and transform the first one into 5) which is exactly the operator version of (2.8). The standard asymptotic conditions [33] read…”

Section: Dressing Approach and Soliton Configurationsmentioning

confidence: 99%

Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions

Wolf

2002

In this paper we study the noncommutative extension of a modified U (n) sigma model in 2 + 1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U (3) solitons and consider the head-on collision of a U (2) soliton and an antisoliton explicitly, which will result in a 90 o angle scattering. Further we discuss the head-on collision of one U (2) soliton with two antisolitons. This results in a 60 o angle scattering.

“…Field theories on noncommutative spaces have been studied extensively in the past few years (for a lucid review and full list of references, see [1]), even more so, after their appearance in certain limits of String and M-theories [2,3,4]. Noncommutativity of the bosonic space-time coordinates emerges on a D-brane worldvolume, when a constant NS-NS two form field is turned on.…”

Section: Introductionmentioning

confidence: 99%

D=2,N=2, Supersymmetric theories on Non(anti)commutative Superspace

Bhamidipati

Kumar

2004

The classical action of a two dimensional N = 2 supersymmetric theory, characterized by a general Kähler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter C αβ . The theory is explicitly shown to preserve half of the N = 2 supersymmetry, to all orders in (det C) n . The results are further generalized to include arbitrary superpotentials as well.