Brane baldness versus superselection sectors

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. March, 19991

Polarization of the D0 ground state in quantum mechanics and supergravity

“…It is worth taking a moment to contrast the polarization effects studied here with those studied in [19] which were argued to be dual to certain effects in the D4-brane field theory. While both works considered a change in the characteristic size of the D0-brane supergravity solution induced by the D4-brane, the details are rather different.…”

“…Indeed, it is known that the D0-brane contribution to the supergravity solution is greatly distorted in the limit of zero separation [19]. However, pursuing such an analysis in D0-brane quantum mechanics would require an understanding of the full non-abelian dynamics as a truncation to O(λ 3 ) or any other finite order would no longer be sufficient.…”

“…It is conceptually simplest to discuss the full D0/D4 solution and then take a suitable decoupling limit. Such full solutions are known exactly, but only as an infinite sum over Fourier modes [19]. As a result, we find it more profitable here to follow a perturbative method as suggested by the quantum mechanical calculation above.…”

“…Thus, the leading contribution is of second order inS 1 and we have 19) where the T represents time ordering. Again the factor T (T rΦ 2 )(S 1 ) 2 0 is explicitly independent of g, λ, H 4 , and f .…”

“…One might try to measure the size of the D0-brane configuration by studying properties of the Fourier transform (as in [18,19]) or by identifying where the potential becomes of order one. However, it is clear that we wish to follow Polchinski [9] and use the measure that successfully reproduces the size of the unperturbed D0-brane bound state.…”