Infrared asymptotic behavior of the gluon propagator

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

“…The exponent ν has been computed in d-dimensions at O(1/N 2 ) in [16]. To clarify with other work, [9], the exponent η c is related to two other exponents η and η O by…”

“…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 .…”

“…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…”

“…Indeed exploiting the conformal properties of the d-dimensional Wilson-Fisher fixed point the technique has successfully produced the critical exponent η at O(1/N 3 ) in ddimensions, [14], through use of the conformal bootstrap programme. Moreover, this method had developed out of the earlier d-dimensional critical point technique of [15,16] which was based on analysing Schwinger Dyson equations at criticality in large N . In essence the method efficiently reproduces the bubble summation which is the main property of 1/N expansions but more importantly goes beyond the leading order which the conventional bubble sum calculations fail to handle easily.…”