My question is about what we know, in dimension $4$, about the loss of compactness of Yang-Mills connections with $L^2$-bounded curvature. My background is more analytical than geometrical and it is hard for me to go through the modern literature on the subject, I apologize in advance if the miss references.

More precisely, I consider $P$ a $SU(2)$-bundle over $M$ a compact $4$-manifold and a sequence of Yang-Mills connection $\nabla_n$ such that $\Vert F_{\nabla_n}\Vert_2\leq M<+\infty$.  

From Uhlenbeck's work we know that, if the sequence is not compact, it must concentrate at a finite number of points.

From Taubes's work, we know that such examples exists. In fact there is some condition to the existence work of Taubes. First he proves the existence of self-dual connections (which is obviously stronger than just Yang-Mills).

In his 82 paper, he proves that if the intersection form is definite he can glue an instanton everywhere on $M$.

In his 84 paper, he proves that if $-c_2 \geq \max (4/3 b_-,1)$ if $b_-\not=2$ or $-c_2 \geq 4$ if $b_-=2$ then there is  a self-dual connection. Here $c_2$ is the second chern class of $P$ and $b_-=1/2(rank(Q)-sign(Q))$ where $Q$ is the intersection form.

The connections are obtained by perturbing some connections which concentrate $k$ instantons, but in the 84 case he needs to solves an obstruction. Which he did by some topological arguments. In particular we do not know where are the point of concentrations.

My first question is for self-dual connection : do we expect that a sequence connections should concentrate to particular point (or configuration of points) of the based manifold (with respect to the metric)? Is there some refinement of Uhlenbeck work in this direction when $Q$ is not definite? 

My second question is for Yang-Mills connection: Taubes hypothesis are optimal for certain configurations of $b_-$ and $c_2$. Can we expect to lower them if we relax the self-dual condition to Yang Mills?

Any recent reference on the (analytic) development of the blow-up analysis of Yang-Mills in dimension $4$ will be welcome.

Thx in advance.