Contact term, its holographic description in QCD and dark energy

In this work we study the well-known contact term, which is the key element in resolving the so-called U(1)(A) problem in QCD. We study this term using the dual holographic description. We argue that in the dual picture the contact term is saturated by the D2-branes which can be interpreted as the tunneling events in Minkowski space-time. We quote a number of direct lattice results supporting this identification. We also argue that the contact term receives a Casimir-like correction similar to(Lambda R-QCD)(-1) rather than the naively expected expd(-Lambda R-QCD) when the Minkowski space-time R-3,R-1 is replaced by a large but finite manifold with a size R. Such a behavior is consistent with other quantum field theory (QFT)-based computations when powerlike corrections are due to nontrivial properties of topological sectors of the theory. In holographic description, such a behavior is due to a massless Ramond-Ramond (RR) field living in the bulk of multidimensional space when powerlike corrections is a natural outcome of a massless RR field. In many respects, the phenomenon is similar to the Aharonov-Casher effect when the modular electric field can penetrate into a superconductor where the electric field is exponentially screened. The role of modular operator from the Aharonov-Casher effect is played by a large-gauge transformation operator T in four-dimensional QCD, resulting in the transparency of the system to topologically nontrivial pure gauge configurations. We discuss some profound consequences of our findings. In particular, we speculate that a slow variation of the contact term in expanding universe might be the main source of the observed dark energy.