Abstract
We present exact solutions of four-dimensional Einstein’s equations related to Minkoswki vacuum constructed from Type IIB string theory with non-trivial fluxes. Following [1, 2] we study a non-trivial flux compactification on a fibered product by a four-dimensional torus and a two-dimensional sphere punctured by 5- and 7-branes. By considering only 3-form fluxes and the dilaton, as functions on the internal sphere coordinates, we show that these solutions correspond to a family of supersymmetric solutions constructed by the use of G-theory. Meromorphicity on functions constructed in terms of fluxes and warping factors guarantees that flux and 5-brane contributions to the scalar curvature vanish while fulfilling stringent constraints as tadpole cancelation and Bianchi identities. Different Einstein’s solutions are shown to be related by U-dualities. We present three supersymmetric non-trivial Minkowski vacuum solutions and compute the corresponding soft terms. We also construct a non-supersymmetric solution and study its stability.
Highlights
String flux compactification has been extensively studied in the last decade opening up a strength relation among geometry and the construction of stable four-dimensional vacuum solutions
We present exact solutions of four-dimensional Einstein’s equations related to Minkoswki vacuum constructed from Type IIB string theory with non-trivial fluxes
By considering a specific non-trivial flux configuration composed by only 3-form fluxes and a real dilaton, we have studied conditions to solve four-dimensional Einstein’s equations related to type IIB string compactification on a six-dimensional space given by the fibered product T 4 ×z S2, were the two-dimensional sphere is punctured by the presence of 5- and 7-branes
Summary
String flux compactification has been extensively studied in the last decade opening up a strength relation among geometry and the construction of stable four-dimensional vacuum solutions. We have make an extensive use of the Global Residual Theorem [21] in complex analysis, which states that on a compact space with singular points the total sum of residues related to meromorphic functions vanishes This allows us to prove that by the simple use of “meromorphic fluxes” on the sphere, — meaning that we construct meromorphic functions formed by non-trivial closed string potentials and warping factors — , it is possible to satisfy Bianchi identities, tadpole conditions and Einstein’s equations, circumventing some results followed by the well known no-go theorem [5] as having a constant warping factor in the absence of a five-form flux or the necessity to have orientifold 3-planes to obtain a Minkowski vacuum with no oneform fluxes. In appendix E we show the dimensional reduction of the Dirac-Born-Infeld action of D5-branes into the DBI action of induced D3-branes, required to compute the corresponding soft terms
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
