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According to a recent classification of 6d (1 , 0) theories within F-theory there are only six 'pure' 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are SU(3) , SO(8) , F , E , E , and E . These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For G simply-laced, we determine the 2d $$ \mathcal{N}=\left(0,4\right) $$ worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted S compactification of the 4d $$ \mathcal{N}=2 $$ theories of type H , D , E , E and E (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding T × S partition functions and the Hilbert series for moduli spaces of G instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one F instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d $$ \mathcal{N}=2 $$ models. [ABSTRACT FROM AUTHOR]

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity. [ABSTRACT FROM AUTHOR]

Recently, at least 50 million of novel examples of compact G holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry for compactifications of Type II superstrings in this context. We focus on G manifolds obtained from building blocks constructed from dual pairs of tops, which are the closest to toric CY hypersurfaces, and formulate the analogue of the Batyrev mirror map for this class of G holonomy manifolds, thus obtaining several millions of novel dual superstring backgrounds. In particular, this leads us to conjecture a plethora of novel exact dualities among the corresponding 2d $$ \mathcal{N} $$ = 1 sigma models. [ABSTRACT FROM AUTHOR]