Abstract
We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group. The general elliptic fiber is the Calabi-Yau onefold in dP_2. We classify its resolved elliptic fibrations over a general base B. The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1)xU(1) and SU(5)xU(1)xU(1) constructions. We determine for the first time certain matter curves and surfaces using techniques involving prime ideals. The vertical cohomology ring of these fourfolds is calculated for both cases and general formulas for the Euler numbers are derived. Explicit calculations are presented for a specific base B=P^3. We determine the general G_4-flux that belongs to H^{(2,2)}_V of the resolved Calabi-Yau fourfolds. As a by-product, we derive for the first time all conditions on G_4-flux in general F-theory compactifications with a non-holomorphic zero section. These conditions have to be formulated after a circle reduction in terms of Chern-Simons terms on the 3D Coulomb branch and invoke M-theory/F-theory duality. New Chern-Simons terms are generated by Kaluza-Klein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield non-vanishing results precisely for fourfolds with a non-holomorphic zero section. Taking into account the new Chern-Simons terms, all 4D matter chiralities are determined via 3D M-theory/F-theory duality. We independently check these chiralities using the subset of matter surfaces we determined. The presented techniques are general and do not rely on toric data.
Highlights
Introduction and summary of resultsFour-dimensional F-theory compactifications provide a broad domain of the string theory landscape with the potential to derive promising particle physics consequences of string theory
The origin of non-Abelian gauge symmetries in four-dimensional F-theory compactifications is well understood since the origins of F-theory [13,14,15], and it is due to the full classification of codimension one singularities of elliptically fibered Calabi-Yau fourfolds with a section in the Weierstrass or Tate model [16,17,18]
In this paper we have advanced the program on F-theory compactifications on elliptic Calabi-Yau manifolds with rank two Mordell-Weil group to four-dimensional chiral compactifications
Summary
Four-dimensional F-theory compactifications provide a broad domain of the string theory landscape with the potential to derive promising particle physics consequences of string theory. The origin of non-Abelian gauge symmetries in four-dimensional F-theory compactifications is well understood since the origins of F-theory [13,14,15], and it is due to the full classification of codimension one singularities of elliptically fibered Calabi-Yau fourfolds with a section in the Weierstrass or Tate model [16,17,18]. It is the purpose of this paper to develop explicit techniques for the calculation of the matter spectrum and their chiralities for four-dimensional F-theory compactifications with two U(1)-factors This involves F-theory compactifications on elliptically fibered Calabi-Yau fourfolds with rank two Mordell-Weil groups.
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