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We propose 4-point S-matrices for three-dimensional F-theory. We will use the twistor formalism to facilitate constructing the amplitude. We write the amplitude in a way such that the F-symmetry (U-duality symmetry) is manifest. The amplitude can be schematically written as $A_{4} = w^{4}/stu$, where $w$ is an analog of the linearized Weyl tensor in F-theory, and $w^{4}$ is a shorthand for the sum of various contractions that can happen between the Weyl tensors. The gauge invariance is actually non-trivial since $w$ is in general not gauge invariant. With the help of the twistor formalism, one can verify that this formula is indeed gauge invariant. The amplitude also reduces to the ordinary 4-graviton amplitude under the reduction to M-theory (which is just 4D supergravity).
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We construct a general class of new time dependent solutions of non-linear sigma models coupled to gravity. These solutions describe configurations of expanding or contracting codimension two solitons which are not subject to a constraint on the total tension. The two dimensional metric on the space transverse to the defects is determined by the Liouville equation. This space can be compact or non-compact, and of any topology. We show that this construction can be applied naturally in type IIB string theory to find backgrounds describing a number of 7-branes larger than 24.
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We consider the construction of a topological version of F-theory on a particular $Spin(7)$ 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions using Hitchins gradient flow method. A symmetry of the eight-dimensional theory which follows from modular transformations of the torus induces duality transformations of the variables of the topological A- and B-models. We also consider target space form actions in the presence of background fluxes in six dimensions.
We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of $gamma$-deformed $mathcal N=4$ SYM. We show that the single-trace partial amplitude is protected from quantum corrections whereas the double-trace partial amplitude is a nontrivial infrared finite function of the ratio of Mandelstam invariants. Applying the Lehmann--Symanzik--Zimmerman reduction procedure to the known expression of a four-point correlation function in the fishnet theory, we derive a new representation for this function that is valid for arbitrary coupling. We use this representation to find the asymptotic behavior of the double-trace amplitude in the high-energy limit and to compute the corresponding exact Regge trajectories. We verify that at weak coupling the expressions obtained are in agreement with an explicit five-loop calculation.
The Tate forms for elliptically fibered Calabi-Yau manifolds are reconsidered in order to determine their general validity. We point out that there were some implicit assumptions made in the original derivation of these Tate forms from the Tate algorithm. By a careful analysis of the Tate algorithm itself, we deduce that the Tate forms (without any futher divisiblity assumptions) do not hold in some instances and have to be replaced by a new type of ansatz. Furthermore, we give examples in which the existence of a Tate form can be globally obstructed, i.e., the change of coordinates does not extend globally to sections of the entire base of the elliptic fibration. These results have implications both for model-building and for the exploration of the landscape of F-theory vacua.
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