Heterotic Black Holes in Duality-Invariant Formalism

TL;DR

The paper develops a duality-invariant framework for two-dimensional heterotic strings with a charged black hole, using a double field theory-inspired action that exhibits $O(1,2; \mathbb{R})$ symmetry (and $O(1,1+r; \mathbb{R})$ with $r$ abelian fields). It derives the two-derivative charged BH and its T-dual geometry, analyzes gauge-dependence in the duality map, and demonstrates that the higher-derivative corrections can be classified by a single eigenvalue $\rho$ of $\mathcal{D}\mathcal{S}$, yielding a non-perturbative function $F(\rho)$ with a single coefficient per even derivative order. The authors then implement a Gasperini-Codina $f$-parametrization to obtain an exact, non-perturbative charged BH solution that remains well-defined beyond the two-derivative limit, and extend this construction to the general abelian case with $\,O(1,1+r; \mathbb{R})$ symmetry. The work clarifies how duality operates on metric and gauge fields, exposes features and limitations of dual geometries (including naked singularities in the dual frame), and lays groundwork for further exploration of higher-derivative heterotic backgrounds, including gauged-WZW connections and quantum corrections.

Abstract

We consider the effective theory of heterotic strings in two spacetime dimensions, in a double field theory-inspired formalism, manifestly consistent with $T$-duality in string theory. Restricting the gauge group to a single $\mathrm{U}(1)$, we study the charged black hole solution and perform a precise analysis of the properties of the dual geometry with the $\mathrm{O}(1,2; \mathbb{R})$-valued generalized metric. We comment on some aspects related to singularities and gauge dependence. We show that the classification program for higher derivative corrections can also be applied to the heterotic case. We further elucidate how a previously proposed solution to the equations of motion, parametrized in a manner fully non-perturbative in $α'$, can be extended to the scenario with $r$ abelian fields and the corresponding $\mathrm{O}(1,1+r; \mathbb{R})$ symmetry. We discuss some novel features of the solution for charged black holes.

Figures (1)

• Figure 1: The behavior of the metric component $-g_{tt}$ in the original and dual geometries. In both cases, $n(x) = m(x)^{-1}$. The mass and charge parameters are chosen to be $\mu =2$ and $Q = 3$.