Order α′ heterotic domain walls with warped nearly Kähler geometry

Abstract

Abstract:We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold X 6 in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order α 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 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 Kähler geometry.

On heterotic vacua with fermionic expectation values

“…For zero condensate, this system has been analyzed to a great degree in the literature before, see e.g. [12,15,[28][29][30][31][32][33]. Here we will see how it can also admit solutions with non trivial condensate.…”

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

“…Higher-dimensional instanton equations generalise the self-dual YangMills equations in four dimensions, and were first constructed in [62][63][64]. The instanton condition can be reformulated as a G 2 invariant constraint [36,37,[65][66][67][68][69][70][71][72][73], and explicit solutions to the instanton condition on certain G 2 manifolds are also known [74,75]. Here, we show that the G 2 instanton condition is implied by a supersymmetry constraint in string compactifications, and that it, in turn, implies the Yang-Mills equations as an equation of motion of the theory.…”

The Infinitesimal Moduli Space of Heterotic G 2 Systems

“…One can define a canonical differential complexΛ * (Y ) as a sub complex of the de Rham complex [32], and the associated cohomologiesȞ * (Y ) have similarities with the Dolbeault complex of complex geometry. Heterotic vacua on seven dimensional non-compact manifolds with an integrable G 2 structure lead to fourdimensional domain wall solution that are of interest in physics [33][34][35][36][37][38][39][40][41][42][43][44][45][46], and whose moduli determine the massless sector of the four-dimensional theory. Furthermore, families of SU (3) structure manifolds can be studied through an embedding in integrable G 2 geometry.…”

“…We find in particular, a G 2 analogue of Atiyah's deformation space for holomorphic systems [52]. We restrict ourselves in the current paper to scenarios where the internal geometry Y is compact, though we are confident that the analysis can also be applied in non-compact scenarios such as the domain wall solutions [33][34][35][36][37][38][39][40][41][42][43][44][45][46], provided suitable boundary conditions are imposed.…”