Flux tube profile from Holography: finite size and strong coupling corrections

Abstract: We use the holographic correspondence as a tool to infer the classical flux tube profile connecting a static quark-antiquark pair in a $2+1$-dimensional strongly-coupled large $N$ QCD-like theory. Our final prediction extends already known results in the literature in several ways. First, it is an analytical function of both the space-like boundary coordinates; in other words, we keep track of what happens both along and transversely to the inter-quark axis. Then, we take into account the finiteness of the inter-quark distance and the first correction in the strong coupling expansion. To the same order, we also confirm the relation between the mass of the lightest glueball in the spectrum and the intrinsic width of the flux tube profile. We conclude by trying to gain some insights about the quantum fluctuations. Intriguingly, our proposal is in agreement with widespread expectations in the literature. En passant, we also derive a semi-analytical formula that gives the first correction to the scalar glueball masses in the strong coupling expansion.