On quantum corrected Kähler potentials in F-theory

Abstract

Abstract:We work out the exact in g s and perturbatively exact in α result for the vector multiplet moduli Kähler potential in a specific N = 2 compactification of F-theory. The well-known α 3 correction is absent, but there is a rich structure of corrections at all even orders in α . Moreover, each of these orders independently displays an SL(2, Z) invariant set of corrections in the string coupling constant. 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.

Onα′corrections inN=1F-theory compactifications

“…It is worth noting that the non-triviality of the elliptic fibration causes the appearance of an α ′ correction already at order two, a phenomenon also observed in [19] for a different correction in F-theory compactifications on K3×K3.…”

“…The 4d higher curvature correction is matched with a higher curvature modification of the Dirac-Born-Infeld actions of D7-branes and O7-planes derived in [17]. Different α ′ corrections to F-theory effective actions and their weak coupling interpretations have been found in [18,19]. A class of α ′2 corrections in the heterotic string has been discussed recently in [20].…”

“…Since these have no components along the fiber, all corrections in (3) go to zero and the α ′ corrections in (12) are absent in the resulting N = 2 theory. Another N = 2 corner of F-theory vacua is reached by taking Y 4 = K3× K3, a configuration studied in [19] with a focus on α ′ corrections. In this case c 3 (Y 4 ) = 0 and the volume correction (13) vanishes identically.…”

F-term stabilization of odd axions in LARGE volume scenario

“…This α 3 -correction breaks the no-scale structure, 4 and the ansatz (17) results in the following form of F-term effective scalar potential 4 In the meantime, there have been proposals for string-loop corrections [56,57] as well as 'new' α -corrections [58][59][60] (see also [61] for a related progress in N = 2 F-theory compactifications). However, an 'extended' no-scale structure has been observed making the LARGE volume scenarios more robust.…”

Explicit de Sitter flux vacua for global string models with chiral matter

“…25 Because of the 'extended no-scale structure' [74,75], these corrections are negligible since they scale as V −10/3 whereas V α ′ behaves as V −3 . The last contribution V soft reads: 18) where the soft scalar mass for the matter field φ living in the bulk scales as the gravitino mass m 3/2 = e K/2 |W | ≃ |W 0 |/V suppressed by a factor of order ln(M P /m 3/2 ) [76,77] (c is 25 For recent activity on stringy perturbative corrections see [69][70][71][72][73].…”