Is a classical description of stable non-BPS D-branes possible?

TL;DR

The paper investigates whether a classical supergravity description can capture the geometry of stable non‑BPS D-branes in Type II theories compactified on orbifolds, focusing on a six‑dimensional effective theory derived via S‑duality with the heterotic string on $T^4$. By solving the six‑dimensional field equations with a D0‑brane boundary source, the authors obtain a closed‑form solution whose fields (dilaton, scalars, RR gauge potential, and metric) exhibit a repulson‑like naked singularity for stacks with $N>1$, indicating that a simple ensemble of coincident non‑BPS branes cannot be described classically without pathologies. They show that one‑loop no‑force cancellation can occur at a critical radius, but higher‑order corrections break this property, suggesting that the microscopic no‑force condition does not guarantee a global classical geometry. The paper then develops the most general homogeneous solutions of the bulk equations and discusses possible resolutions, such as varying the internal volume away from the critical value or forming nontrivial bound states, highlighting that restoring a consistent macroscopic description likely requires more elaborate brane configurations or additional bulk fields. Overall, the work exposes limitations of a straightforward classical description for stable non‑BPS D‑branes and motivates exploring bound states and moduli‑driven resolutions to obtain regular geometries.

Abstract

We study the classical geometry produced by a stack of stable (i.e. tachyon free) non-BPS D-branes present in K3 compactifications of type II string theory. This classical representation is derived by solving the equations of motion describing the low-energy dynamics of the supergravity fields which couple to the non-BPS state. Differently from what expected, this configuration displays a singular behaviour: the space-time geometry has a repulson-like singularity. This fact suggests that the simplest setting, namely a set of coinciding non-interacting D-branes, is not acceptable. We finally discuss the possible existence of other acceptable configurations corresponding to more complicated bound states of these non-BPS branes.

Figures (5)

• Figure 1: The leading contribution to the one-point function of a bulk field expressed in a diagrammatic way.
• Figure 2: The bosonic low energy spectrum from three different points of view
• Figure 3: The leading contribution to the one-point function of a bulk field expressed in a diagrammatic way. Diagram (a) yields the leading term in the large distance expansion and is proportional to $Q$, whereas diagram (b) corresponds to the next-to-leading correction proportional to $Q^2$.
• Figure 4: This is the behavior of $G_{00}$ in the region around $x \equiv r/Q^{1/3}=1$. The derivative of $G_{00}$ changes sign around $x_G\sim 0.8$, while the first singularity (the repulson) is at $x_0\sim 0.6$.
• Figure 5: The next to leading order contributions for the dilaton. Diagram (a) represents the two boundary contribution via graviton exchange while diagram (b) corresponds to the gauge field contribution.