Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-15
INT J MOD PHYS A 26 (2011) 5171-5209
Physics
High Energy Physics
High Energy Physics - Theory
35 pages, 14 figures, PACS: String Theory: 11.25.-w; Gauge Theory: 47.20,Ky; Field Theory: 11.27.+d; Intrinsic Geometry: 2.40.
Scientific paper
We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a set of abelian scalar fields. In particular, we show that the nature of marginal and threshold walls of stabilities may be investigated by real geometric methods. Interestingly, we find that the leading order contributions may easily be accomplished by translations of the Fayet parameter. Specifically, we notice that the various possible linear, planar, hyper-planar and the entire moduli space stabilities may easily be reduced to certain polynomials in the Fayet parameter. For a set of finitely many real scalar fields, it may be further inferred that the intrinsic scalar curvature defines the global nature and range of vacuum correlations. Whereas, the underlying moduli space configuration corresponds to a non-interacting basis at the zeros of the scalar curvature, where the scalar fields become un-correlated. The divergences of the scalar curvature provide possible phase structures, viz., wall of stability, phase transition, if any, in the chosen moduli configuration. The present analysis opens up a new avenue towards the stabilizations of gauge and string moduli.
Bellucci Stefano
Tiwari Bhupendra Nath
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