Abstract
Heterotic supergravity with (1 + 3)-dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds 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 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 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 corrections to the heterotic supergravity. Such a formalism is applied for general and/or warped almost-Kähler 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 [] in order to construct and study generic off-diagonal nonholonomic deformations of the Kerr metric, encoding contributions from heterotic supergravity.
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