Abstract
In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge numbers h1,1 and h4,1. The former gives rise to the largest geometric gauge group in the currently known 2d (0,2) supergravity landscape, which is {E}_8^{482;632;421}times {F}_4^{3;224;195;728}times {G}_2^{11;927;989;964}times mathrm{SU}{(2)}^{25;625;222;180} . Besides that, we systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation. Moreover, we also initiate the study of singular bases in 2d F-theory. We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly.
Highlights
For theories with eight supercharges, such as 6d (1, 0) supergravity, the currently known maximal number of tensor multiplet, T = 193, and the maximal rank of the gauge group, rG = 296, are both given by F-theory on the elliptic Calabi-Yau threefold X3 with maximal h1,1 [3,4,5,6]
We systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation
We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly
Summary
We introduce the basics of globally consistent compactification of F-theory to 1+1 dimensions on compact elliptic Calabi-Yau fivefolds, including the geometric tools and the gravitational anomaly computation of the low energy effective theory.
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