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
Highlights
Has m solutions if and only if the holonomy group of ∇ is contained in the joint stabilizer subgroup of m spinors, which in turn is related to the G structure of the manifold
The ingredients are a ten-dimensional manifold M, equipped with a Lorentzian metric g, an NS 3-form H, a dilaton φand a gauge connection A∇ˆ, with gauge group SO(32) or E8 × E8. It was shown in [9] that the anomaly cancellation condition of ten-dimensional super Yang-Mills theory coupled to N = 1, D = 10 supergravity can be written as a Bianchi identity on H, dH = α Tr(F ∧ F − R ∧ R), 4 (1.2)
Different connections used in the anomaly cancellation condition (1.2) correspond to different renormalization schemes [12] and there is some discussion about the correct choice of the curvature Rin the literature
Summary
For a background with vanishing fermionic vacuum expectation values to be supersymmetric, the supersymmetry transformations of the corresponding fermionic fields must vanish. Note that (2.14) may be regarded as a generalization of the Hitchin flow equations [27] This a common situation in four-dimensional BPS domain-wall solutions of ten-dimensional supergravity theories [24, 25, 28,29,30]. In order to have a full heterotic supergravity solution, we need to check that the Bianchi identity and the time-like components of the equations of motion are satisfied. This concludes our analysis of the zeroth order case, and we shall turn to the construction of order α solutions
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