On quantum corrected Kahler potentials in F-theory

Garcia-Etxebarria, Inaki; Savelli, Raffaele; Hayashi, Hirotaka; Shiu, Gary

doi:10.1007/JHEP03(2013)005

Article
Report number	arXiv:1212.4831 ; CERN-PH-TH-2012-359 ; MAD-TH-12-09 ; MPP-2012-185 ; KIAS-P-12085 ; CERN-PH-TH-2012-359
Title	On quantum corrected Kahler potentials in F-theory
Author(s)	Garcia-Etxebarria, Inaki (CERN) ; Hayashi, Hirotaka (Korea Inst. Advanced Study, Seoul) ; Savelli, Raffaele (Munich, Max Planck Inst.) ; Shiu, Gary (Hong Kong U. Sci. Tech. ; Wisconsin U., Madison)
Publication	2013
Imprint	21 Dec 2012
Number of pages	57
Note	Comments: 57 pages, 2 figures 57 pages, 2 figures. v2: Added references, version to appear in JHEP
In:	JHEP 03 (2013) 005
DOI	10.1007/JHEP03(2013)005
Subject category	Particle Physics - Theory
Abstract	We work out the exact in string coupling and perturbatively exact in \alpha' result for the vector multiplet moduli K\"ahler potential in a specific N=2 compactification of F-theory. The well-known correction cubic in {\alpha}' is absent, but there is a rich structure of corrections at all even orders in \alpha'. Moreover, each of these orders independently displays an SL(2,Z) invariant set of corrections in the string coupling. This generalizes earlier findings to the case of a non-trivial elliptic fibration. Our results pave the way for the analysis of quantum corrections in the more complicated N=1 context, and may have interesting implications for the study of moduli stabilization in string theory.
Copyright/License	Preprint: © 2012-2024 CERN (License: CC-BY-3.0)

$Quantum corrections to the prepotential of F-theory on $K3\times K3$. The horizontal axis labels the degree in \a of the correction, and the vertical one the degree in \g. The circles represent the non-vanishing perturbative terms in the prepotential. The solid band on top represents the set of non-perturbative corrections in \g; Notice that there are no such corrections at tree level in \a, as discussed in the text.$ $Atlas of dualities used to compute directly in M-theory the quantum corrections to the vector multiplet moduli space of F-theory on K3$\times$K3. In particular, the c-map is used to get a trivial F-theory fibration (top right corner) from a non trivial one (top left corner). The information of the non-trivial fibration is all encoded in the geometry of $X_3$.$