Fundamental Superstrings as Holograms

TL;DR

This work proposes and develops an exact holographic description of the near-horizon region of small black strings by treating the worldsheet of a macroscopic fundamental string as the boundary hologram. Using an $AdS_3$-based framework, the authors construct bulk worldsheet CFTs with $SL(2,\mathbb{R})_{k=2}$ (and its heterotic counterpart) coupled to internal manifolds like $T^5$, and derive the boundary Virasoro algebras, R-symmetries, and supersymmetries from bulk currents. Their central charges, determined by bulk Chern-Simons terms, reproduce the Wald entropy via a Cardy-like formula, providing a nonperturbative check of the holographic correspondence for both Type II and heterotic small black strings. The analysis clarifies how global and local symmetries emerge on the boundary, highlights gauge-choice effects (compact and internal light-cone gauges) on conformal realizations, and outlines extensions to other compactifications such as $K3\times S^1$, with numerous open problems remaining in correlators, bulk string-field theory, and higher-spin extensions.

Abstract

The worldsheet of a macroscopic fundamental superstring in the Green-Schwarz light-cone gauge is viewed as a possible boundary hologram of the near horizon region of a small black string. For toroidally compactified strings, the hologram has global symmetries of AdS_3 \times S^{d-1} \times T^{8-d}, (d =3,..,8), only some of which extend to local conformal symmetries. We construct the bulk string theory in detail for the particular case of d=3. The symmetries of the hologram are correctly reproduced from this exact worldsheet description in the bulk. Moreover, the central charge of the boundary Virasoro algebra obtained from the bulk agrees with the Wald entropy of the associated small black holes. This construction provides an exact CFT description of the near horizon region of small black holes both in Type-II and heterotic string theory arising from multiply wound fundamental superstrings.