Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-02-18
J. Geom. and Phys. 61(2011) 1854-1867
Physics
High Energy Physics
High Energy Physics - Theory
25pages, 40 figures
Scientific paper
10.1016/j.geomphys.2011.04.009
Renormalisation group flows of the bosonic nonlinear \sigma-model are governed, perturbatively, at different orders of \alpha', by the perturbatively evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the flow equations at various orders in \alpha' can be thought of as \em approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the abovementioned RG flow equations as viable {\em geometric} flows in their own right and without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions . In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S^2, H^2, unwarped S^2 x H^2 and simple warped products. We analyze and solve the higher order RG flow equations within the appropriate perturbative domains and find the \em corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error which arises when higher orders are ignored. We also investigate the higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of the higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes, correspond to constant curvature Anti-de Sitter (AdS) spacetime, modulo an overall flow--parameter dependent scale factor. The functional form of this scale factor (which we obtain) changes on the inclusion of successive higher order terms in the flow.
Das Sanjit
Kar Sayan
Prabhu Kartik
No associations
LandOfFree
On higher order geometric and renormalisation group flows does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On higher order geometric and renormalisation group flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On higher order geometric and renormalisation group flows will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-405101