Invariant solutions to the Strominger system and the heterotic equations of motion

TL;DR

This paper constructs new invariant solutions to the Strominger system and heterotic equations of motion on specific non-Kähler homogeneous spaces, extending known connections and providing explicit examples with physical relevance.

Contribution

It introduces a 2-parameter family of metric connections for solving the Strominger system, yielding explicit invariant solutions on three distinct non-Kähler spaces, including solutions to heterotic equations of motion.

Findings

Solutions on three different non-Kähler spaces

Explicit solutions with non-flat instanton and positive α'

Invariant solutions to heterotic equations of motion with Bismut connection

Abstract

We construct many new invariant solutions to the Strominger system with respect to a 2-parameter family of metric connections $\nabla^{\varepsilon,\rho}$ in the anomaly cancellation equation. The ansatz $\nabla^{\varepsilon,\rho}$ is a natural extension of the canonical 1-parameter family of Hermitian connections found by Gauduchon, as one recovers the Chern connection $\nabla^{c}$ for $({\varepsilon,\rho})=(0,\frac12)$, and the Bismut connection $\nabla^{+}$ for $({\varepsilon,\rho})=(\frac12,0)$. In particular, explicit invariant solutions to the Strominger system with respect to the Chern connection, with non-flat instanton and positive $\alpha'$ are obtained. Furthermore, we give invariant solutions to the heterotic equations of motion with respect to the Bismut connection. Our solutions live on three different compact non-K\"ahler homogeneous spaces, obtained as the quotient by a lattice of maximal rank of a nilpotent Lie group, the semisimple group SL(2,$\mathbb{C}$) and a solvable Lie group. To our knowledge, these are the only known invariant solutions to the heterotic equations of motion, and we conjecture that there is no other such homogeneous space admitting an invariant solution to the heterotic equations of motion with respect to a connection in the ansatz $\nabla^{\varepsilon,\rho}$.