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arXiv · 1504.07895

String gravitational equations with Hermitian structure

F. Naderi·A. Rezaei-Aghdam·F. Darabi
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Abstract

We consider a string model at one-loop related to a $\sigma$-model whose antisymmetric tensor field is constructed as complex structure on the background manifold, specially on a manifold $R\times N$ where $N$ is a complex manifold. As an example, we consider a homogeneous anisotropic $(1+4)$-dimensional $\sigma$-model where space part of the background is a $4$-dimensional complex manifold. By solving the related one-loop $\beta$-functions we obtain a static solution so that by reduction of this solution to $(1+3)$-dimension we obtain a static solution of Einstein equation where the matter sector is effectively interpreted as an inhomogeneous, anisotropic and barotropic matter satisfying all the energy conditions. Finally, the $T$-dual background of the solution is investigated and it is shown that the duality transformation and reduction processes commute with each other.

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F. Naderi, A. Rezaei-Aghdam, F. Darabi. 2015-04-29. String gravitational equations with Hermitian structure. https://doi.org/10.1142/s0217751x16500135

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