Classification of the vacua of the dimensionally reduced low-energy limit of the heterotic string over nearly-Kähler manifolds

We examine the vacua of the scalar potential of the effective 4-d action, obtained after the dimensional reduction of the 10-d N=1$\mathcal {N}=1$ heterotic supergravity coupled to an N=1$\mathcal {N}=1$ Yang-Mills sector. The (Coset Space) dimensional reduction takes place over the three 6-d nearly-Kähler manifolds, namely the homogeneous 6-d non-symmetric coset spaces, G2/◂⋅▸S⁢U⁡(3)$G_2/SU(3)$, ◂+▸◂+▸S⁢p4/◂⋅▸S⁢U⁡(2)×U⁡(1)$Sp_4/SU(2)\times U(1)$ and ◂+▸◂+▸◂⋅▸S⁢U⁡(3)/U⁡(1)×U⁡(1)$SU(3)/U(1)\times U(1)$. The current work consists a complete catalogue of the kinds of vacua of theories obtained after the reduction of the heterotic string over the 6-d non-symmetric coset spaces and, moreover, a contribution to the dialogue of the possibility to result with non-AdS vacua in the framework of string theories.