Abstract
We study the interplay between the 〈Aμ2〉 condensate and instantons in non-Abelian gauge theory. Therefore we use the formalism of Local Composite Operators, with which the vacuum expectation value of this condensate can be analytically computed. We first use the dilute gas approximation and partially solve the infrared problem of instanton physics. In order to find quantitative results, however, we turn to an instanton liquid model, where we find how the different contributions to the condensate add up.
Highlights
IntroductionA μ in pure Yang–Mills theory has been proposed in [1,2], and it has been investigated in different ways since [3,4,5,6,7,8,9,10,11,12,13,14]
First there is the resilience of the infrared divergence. One could say this is due to the strength of the LCO formalism—the gluon mass is left free in order to determine it by the gap equation, which allows the possibility for the mass to be zero, which again allows instantons to proliferate and to so destabilize the action
A first conclusion arrived at in this Letter is that we have not been able to solve the infrared problem plaguing instanton physics by adding an effective gluon mass coming from the dimension two condensate
Summary
A μ in pure Yang–Mills theory has been proposed in [1,2], and it has been investigated in different ways since [3,4,5,6,7,8,9,10,11,12,13,14]. A term quadratic in the source must be added, which in turn spoils the energy interpretation of the effective action. One way around this is to perform the Legendre inversion, but this is rather cumbersome, especially with a general, space–time dependent source. The precise renormalization details of the procedure proposed in [3] were given in [4] Instantons play an important role in the QCD vacuum and have a large influence in many infrared properties (see [16] for a review) As such it is an interesting question what their connection with the dimension two condensate is.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
