2018/11/30 by Brice Bastian, Stefan Hohenegger · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.99.066013
published as Phys. Rev. D 99, 066013 (2019) · 58 pages, v2: minor corrections
arxiv created 2019/11/17 · arxiv updated 2019/11/19
Recent studies (arXiv:1610.07916, arXiv:1711.07921, arXiv:1807.00186) of six-dimensional supersymmetric gauge theories that are engineered by a class of toric Calabi-Yau threefolds XN,M, have uncovered a vast web of dualities. In this paper we analyse consequences of these dualities from the perspective of the partition functions ZN,M (or the free energy FN,M) of these theories. Focusing on the case M=1, we find that the latter is invariant under the group \mathbbG(N)× SN: here SN corresponds to the Weyl group of the largest gauge group that can be engineered from XN,1 and \mathbbG(N) is a dihedral group, which acts in an intrinsically non-perturbative fashion and which is of infinite order for N≥ 4. We give an explicit representation of \mathbbG(N) as a matrix group that is freely generated by two elements which act naturally on a specific basis of the Kähler moduli space of XN,1. While we show the invariance of ZN,1 under \mathbbG(N)× SN in full generality, we provide explicit checks by series expansions of FN,1 for a large number of examples. We also comment on the relation of \mathbbG(N) to the modular group that arises due to the geometry of XN,1 as a double elliptic fibration, as well as T-duality of Little String Theories that are constructed from XN,1.