Worldvolume uncertainty relations for D-branes

Abstract

By quantizing an open string ending on a D-brane in a nontrivial supergravity background, we argue that there is a new kind of uncertainty relation on a D-brane worldvolume. Furthermore, we fix the form of the uncertainty relations and their dependence on the string coupling constant by requiring them to be consistent with various string theory and M theory dualities. In this way we find a web of uncertainties of spacetime for all kinds of brane probes, including fundamental strings, D-branes of all dimensions as well as M theory membranes and fivebranes.

Dual Brane Pairs, Chains and the Bekenstein–hawking Entropy

“…Evidence for such a smallest volume unit on a brane's worldvolume comes from the 'worldvolume uncertainty relation' for D-branes [13] as we will now explain (cf. also the discussion in [15]).…”

“…Furthermore, it was shown in [13] that a non-trivial expectation value for F can also arise from integrating out quantum fluctuations around a classical background, even when a background flux F is absent. The proper framework to describe this result is string field theory, where one describes the D-brane through a normalized wave-function Ψ(X) with X the brane's target space coordinates.…”

“…The tensions of the dual branes satisfy (l P l is the D=11 Planck-length) (13) and G 4 can be expressed in terms of the D=11 Newton's constant as…”

“…In [13] the expectation value |F ij | has been calculated for the D1-brane case by using for the action S in eq. (26) the supergravity action which is a valid approximation at small string coupling.…”

Noncommutativity parameter as a field on the string worldsheet

“…The noncommutativity parameter also can be non-constant [3,4,5]. One can achieve to this, by introducing a nontrivial B-field [4] or more general, a curved background metric g µν with nontrivial B-field [5].…”