TheCP N?1 model: Calculation of anomalous dimensions and the mixing matrices in the order 1/N

Crossover exponent inO(N)φ4theory atGracey1 2002Phys. Rev. E201120View full textAdd to dashboardCite

“…Diagrams where T ab is inside a closed φ a loop vanish when one computes the group theory factor of the graph. Therefore, at leading order, O(1/N ), there is only one Feynman diagram to calculate and applying the method of [19], we find…”

“…Its elimination produces the usual φ 4 interaction. The method of [15,16,19] elegantly exploits the properties of the d-dimensional Wilson-Fisher fixed point in that, for example, the (massless) propagators of the fields of (4) have simple power law behaviour. In momentum space, representing the propagator by the same letter as the field, the leading asymptotic scaling forms in the critical region are…”

“…Previously the exponent had been calculated at O(1/N ) in d-dimensions in [17,18]. To achieve this we follow the extension of the large N fixed point Schwinger Dyson approach of [15,16], to the computation of the anomalous dimensions of composite operators, [19].…”

“…We have chosen to express the relation for φ c in this way since in a gauge theory the combination η c would be independent of a covariant gauge parameter although the analogous η and η O would each depend on the choice of gauge. In the large N critical point method of [19] the exponent η O is extracted by inserting the operator T ab in a two point Green's function and extracting the residue of the simple pole with respect to the large N regularization in a well defined fashion according to [15,16]. The residues of the simple pole of each Feynman diagram are then combined to obtain η O .…”

On the finiteness of the SUSY nonlinear sigma model in three dimensions

“…Three-dimensional nonlinear sigma models are perturbatively non-renormalizable, but they are argued to be renormalizable in the 1/N expansion [2,3,4,5]. The O(N) and CP N −1 sigma models were studied to next-to-leading order in 1/N and their β-functions were determined to this order [5,6].…”