Order $\alpha'$ heterotic domain walls with warped nearly K\"ahler geometry

TL;DR

This paper constructs and analyzes new 1+3-dimensional heterotic supergravity domain wall solutions on warped nearly K"ahler manifolds, incorporating first-order $oldsymbol{rac{oldsymbol{ ext{alpha}}'}{ ext{corrections}}}$ and instanton effects, revealing novel supersymmetric configurations.

Contribution

It provides a unified framework for embedding tanh-kink instantons into half-BPS heterotic solutions with warped nearly K"ahler geometry, including new solutions in unexplored instanton configurations.

Findings

Solutions preserve $rac{1}{2}$-BPS supersymmetry.

Inclusion of first-order $oldsymbol{rac{oldsymbol{ ext{alpha}}'}{ ext{corrections}}}$ affects gauge and Bianchi sectors.

New classes of solutions depending on instanton choices.

Abstract

We consider 1+3-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly K\"ahler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [arXiv:1109.3552]. We include first order $\alpha'$ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on $X_6$ satisfies $W_1^-=0$. The solutions preserve two real supercharges, which corresponds to $\mathcal{N}{=}1/2$ supersymmetry from the four-dimensional point of view. Besides serving as a useful framework for collecting existing solutions, the formulation in terms of dynamic SU(3) structures utilized here allows us to obtain new solutions in as yet unexplored corners of the instanton configuration space. Our approach thus offers a unified description of the embedding of tanh-kink-type instantons into half-BPS solutions of heterotic supergravity where the internal six-dimensional manifold has a warped nearly K\"ahler geometry