Daniel S. Park

F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds

A bstractThe Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study CalabiYau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations — which relate the Néron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold — serve as an important tool in our analysis.

Anomaly equations and intersection theory

A bstractSix-dimensional supergravity theories with

Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry

\mathcal{N}

6D SCFTs and Gravity

= (1, 0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional

6D supergravity without tensor multiplets

\mathcal{N}

On the Defect Group of a 6D SCFT

= (1, 0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients — in particular, those of the abelian gauge groups — that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.

The Seiberg-Witten Kähler potential as a two-sphere partition function

A bstractWe study six-dimensional

The Cremmer-Scherk mechanism in F-theory compactifications on K3 manifolds

\mathcal{N}

Tall sections from non-minimal transformations

= (1, 0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups — including abelian factors — and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.

Quantization of anomaly coefficients in 6D \( \mathcal{N}=\left(1,\;0\right) \) supergravity

A bstractWe study how to couple a 6D superconformal field theory (SCFT) to gravity. In F-theory, the models in question are obtained working on the supersymmetric background ℝ