Abstract
We study a systematic derivation of four dimensional $\mathcal{N}=1$ supersymmetric effective theory from ten dimensional non-Abelian Dirac-Born-Infeld action compactified on a six dimensional torus with magnetic fluxes on the D-branes. We find a new type of matter K\"{a}hler metric while gauge kinetic function and superpotential are consistent with previous studies. For the ten dimensional action, we use a symmetrized trace prescription and focus on the bosonic part up to $\mathcal{O}(F^4)$. In the presence of the supersymmetry, four dimensional chiral fermions can be obtained via index theorem. The new matter K\"{a}hler metric is independent of flavor but depends on the fluxes, 4D dilaton, K\"{a}hler moduli and complex structure moduli, and will be always positive definite if an induced Ramond-Ramond charge of the D-branes on which matters are living are positive. We read the superpotential from an F-term scalar quartic interaction derived from the ten dimensional action and the contribution of the new matter K\"{a}hler metric to the scalar potential which we derive turns out to be consistent with the supergravity formulation.
Highlights
Superstring theory is an attractive candidate for a unified theory consistent with quantum gravity
We study a systematic derivation of four-dimensional N 1⁄4 1 supersymmetric effective theory from a ten-dimensional non-Abelian Dirac-Born-Infeld action compactified on a six-dimensional torus with magnetic fluxes on the D-branes
We find a new type of matter Kähler metric, while gauge kinetic function and superpotential are consistent with previous studies
Summary
Superstring theory is an attractive candidate for a unified theory consistent with quantum gravity. The chiral nature of matter fields is realized by introducing magnetic fluxes on the world volume of D-branes in the compact extra dimensions [1,2,3,4]. It is less known to compute explicitly 4D effective theories via compactification on a magnetized torus This naturally motivates us to study dimensional reduction of the non-Abelian DBI action for including higher order corrections. It turns out that there exists a new flux contribution to the matter Kähler potential, while gauge kinetic functions and holomorphic Yukawa couplings in the superpotential are consistent with previous works. Such a new flux correction to the Kähler metric has been often neglected, a flux contribution to gauge coupling is frequently discussed for the coupling unification. In Appendixes A and B, we give the details of the calculations
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.