D-brane width

TL;DR

This paper proposes that Dp-branes in string theory have non-zero 9-volume due to minimal volume principles from loop quantum gravity, challenging the traditional view of their p-volume only.

Contribution

It introduces the novel idea that Dp-branes possess non-zero widths in perpendicular directions, implying they have non-zero 9-volume, supported by an action equivalence and induction argument.

Findings

D-branes have non-zero widths in perpendicular directions.

Width is approximately 2 pi sqrt(alpha') when fields are zero.

First-order corrections modify the width with non-zero fields.

Abstract

Loop quantum gravity predicts that there are non-zero minimal area, and non-zero minimal volume in (3+1) dimensions. Given this, one can easily guess that one will have a non-zero minimal 9-volume in (9+1) dimensions. Therefore, in this paper, we argue that not only D9-brane but also Dp-brane for p less than 9 has a 9-volume. This idea is new, as the present view states that such a Dp-brane has p-volume but no 9 volume. To demonstrate this, first, we equate D8-brane action with D9-brane action and show that 9th direction which is perpendicular to D8-brane has non-zero width. We repeat this step for different ps; we equate Dp-brane action with Dp-1 brane action. By this iteration and induction we conclude that Dp-brane has non-zero widths for each of (9-p) directions perpendicular to the Dp-brane, and therefore, non-zero volume. When antisymmetric tensor and field strength are zero, this width is calculated to be 2 pi sqrt(alpha') for all (9-p) directions. For non-vanishing antisymmetric tensor and field strength, the width receives small corrections. In this paper, we only calculate up to the first order correction.