Heterotic Supergravity with Internal Almost-K\"ahler Spaces, Instantons for $SO(32)$, or $E_8 \times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures

TL;DR

This paper develops geometric methods to construct exact solutions in heterotic supergravity with internal almost-K"ahler spaces, instantons, and black hole deformations, incorporating first-order $oldsymbol{\alpha'}$ corrections and nonholonomic structures.

Contribution

It introduces a unified approach for embedding nonholonomically deformed instantons into heterotic supergravity solutions with $oldsymbol{rac{1}{2}}$ supersymmetry, including domain walls and black holes with quasiperiodic internal structures.

Findings

Constructed new exact solutions with $oldsymbol{rac{1}{2}}$ supersymmetry.

Generated black hole and domain wall configurations with internal quasiperiodic structures.

Extended the geometric framework to include first-order $oldsymbol{\alpha'}$ corrections.

Abstract

Heterotic supergravity with (1+3)--dimensional domain wall configurations and (warped) internal, six dimensional, almost-K\"ahler manifolds $\ ^6\mathbf{X}$ are studied. Considering ten dimensional spacetimes with nonholonomic distributions and conventional double fibrations, 2+2+...=2+2+3+3, and associated $SU(3)$ structures on internal space, we generalize for real, internal, almost symplectic gravitational structures the constructions with gravitational and gauge instantons of tanh-kink type. They include the first $\alpha ^{\prime}$ corrections to the heterotic supergravity action, parameterized in a form to imply nonholonomic deformations of the Yang-Mills sector and corresponding Bianchi identities. We show how it is possible to construct a variety of solutions depending on the type of nonholonomic distributions and deformations of 'prime' instanton configurations characterized by two real supercharges. This corresponds to $\mathcal{N}=1/2$ supersymmetric, nonholonomic manifolds from the four dimensional point of view. Our method provides a unified description of embedding nonholonomically deformed tanh-kink-type instantons into half-BPS solutions of heterotic supergravity. This allows us to elaborate new geometric methods of constructing exact solutions of motion equations, with first order $\alpha ^{\prime}$ corrections to the heterotic supergravity. Such a formalism is applied for general and/or warped almost-K\"ahler configurations, which allows us to generate nontrivial (1+3)-d domain walls and black hole deformations determined by quasiperiodic internal space structures. This formalism is utilized in our associated publication [EPJC 77 (2017) 17, arXiv: 1608.01980] in order to construct and study generic off-diagonal nonholonomic deformations of the Kerr metric, encoding contributions from heterotic supergravity.