Four-point correlator of vector currents and electric current susceptibility in holographic QCD

Anomalous QCD contribution to the Debye screening in an external field via holography

“…The bulk-to-boundary propagators v 0 and v i are solutions to these equations without the interaction terms, subject to boundary conditions (9),(8), (10). (A more detailed study of the perturbation theory in question may be found in [19].) Two branches of the solution to the spatial equation are v i = 1 (see Eq.…”

“…(involving N f quark flavors) vertices from the non-Abelian part of the Yang-Mills action do not contribute to the correlator under consideration (see [19]). We can depict the J 0 J 0 and J 3 J 3 correlation functions that determine the electric and the magnetic screening masses as a sum of diagrams ( Fig.…”

“…1) that include the aforementioned vertex from the Chern-Simons term (while the correlators J 1 J 1 = J 2 J 2 are discussed further below). From the action (16) we read out the vertex functional [19]:…”

“…Note however, that these quantities vanish only in the leading order of large N c expansion. To find the 1 Nc corrections to this result, one should consider the diagrams with dilaton and graviton exchange in the bulk, which can produce nonzero input to Π 11 and Π 22 (see [19]). The consistent treatment of 1 Nc corrections involves taking account of higher orders of string perturbation theory, which is out of the scope of this paper.…”

“…As it was pointed out in the previous Subsection (III B), the contribution of the Chern-Simons action to the equations of motion is reduced to a mixing between the axial and the vector fields, see Eq. (19). The relevant part of the whole action involving the V 0 and A 3 fields assumes the form:…”