Brane Baldness vs. Superselection Sectors

TL;DR

This paper investigates when localized intersecting brane solutions fail to exist and how removal of transverse separation induces delocalization (baldness) in the gravity description. It develops a generalized AdS/CFT framework for two-charge brane systems, showing that delocalization corresponds to large fluctuations of moduli in the intersection field theory and to the absence of superselection sectors in low-dimensional (0+1 and 1+1) theories, in line with Coleman–Mermin–Wagner constraints. The authors establish quantitative agreement between the gravity analysis and the dual gauge theory, including explicit scaling relations for delocalization lengths and the matching of instanton-moduli fluctuations to the gravity rate. They extend the analysis to asymptotically flat, orthogonal branes and discuss exceptions where holography is subtle, such as smeared D4/D6 configurations and NS-NS objects, providing a unified view that connects black hole hair intuitions with brane-field theory dynamics. Overall, the work offers a predictive framework for hair-like behavior in brane systems and highlights the deep links between classical gravity and quantum moduli dynamics in low-dimensional intersections.

Abstract

The search for intersecting brane solutions in supergravity is a large and profitable industry. Recently, attention has focused on finding localized forms of known `delocalized' solutions. However, in some cases, a localized version of the delocalized solution simply does not exist. Instead, localized separated branes necessarily delocalize as the separation is removed. This phenomenon is related to black hole no-hair theorems, i.e. `baldness.' We continue the discussion of this effect and describe how it can be understood, in the case of Dirichlet branes, in terms of the corresponding intersection field theory. When it occurs, it is associated with the quantum mixing of phases and lack of superselection sectors in low dimensional field theories. We find surprisingly wide agreement between the field theory and supergravity both with respect to which examples delocalize and with respect to the rate at which this occurs.