Horowitz-Polchinski Solutions at Large $k$

TL;DR

The paper addresses Horowitz-Polchinski backgrounds beyond weak coupling by formulating a large $k$ effective field theory for the radion and winding tachyon, and solving the resulting radial system under HP boundary conditions. It shows that HP-like solutions exist only for $6<d<d_c$ with $d_c\approx7$ (and a critical line in $\phi_\infty$), while at large $d$ EBH-like configurations emerge with a smooth radial cutoff, hinting at a phase structure between HP-like and EBH-like phases. A geometric interpretation is provided by mapping $\phi$ and $\chi$ to deformations of an $S^3$ with $H$-flux via non-Abelian Thirring perturbations, clarifying how symmetry breaking controls the solution space. Overall, the work yields a controlled framework to study HP dynamics beyond weak coupling and elucidates connections to Euclidean black holes and NS5-brane physics in a consistent large-$k$ regime.

Abstract

In arXiv:2509.02905 [hep-th], we introduced an approximation that allows one to study Horowitz-Polchinski backgrounds beyond the weak coupling regime. In this paper we describe the resulting solutions, and discuss a few related issues.

Figures (6)

• Figure 1: The profiles of $\chi=-\sqrt2\phi$, $\Phi$ and $g_{rr}$ for $d=6.5$.
• Figure 2: Dependence on $d$ of the solution with $\chi=-\sqrt{2}\phi$.
• Figure 3: The profiles of $\chi$, $\Phi$ and $g_{rr}$ for $d=6.99$.
• Figure 4: The dependence of $\chi(0)$ and $\Phi(0)$ on $\phi_\infty$ for $d=6.5$.
• Figure 5: For $d=6.5$, the geometry of the three-sphere and value of the dilaton develop a singularity at $r=0$, at $\phi_\infty\approx 0.0033$.