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On Exceptional Instanton Strings | | Michele Del Zotto
; Guglielmo Lockhart
; | | Date: |
1 Sep 2016 | | Abstract: | According to a recent classification of 6d (1,0) theories within F-theory
there are only 5 "pure" 6d gauge theories which have a UV superconformal fixed
point. The corresponding gauge groups are $SU(3),SO(8),F_4,E_6,E_7$, and $E_8$.
These exceptional models have BPS strings which are also instantons for the
corresponding gauge groups. For $G$ simply-laced, we determine the 2d
$mathcal{N}=(0,4)$ worldsheet theories of such BPS instanton strings by a
simple geometric engineering argument. These are given by a twisted $S^2$
compactification of the 4d $mathcal{N}=2$ theories of type $H_2, D_4, E_6,
E_7$ and $E_8$ (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 $T^2 imes S^2$ 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_4 $ instanton. These results unveil a rather surprising relation
with the Schur index of the corresponding 4d $mathcal{N}=2$ models. | | Source: | arXiv, 1609.0310 | | Services: | Forum | Review | PDF | Favorites | |
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