Abstract
We propose 5d descriptions of 6d mathcal{N}=left(1, 0right) superconformal field theories arising from Type IIA brane configurations with an O8−-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two O7−- planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two O7−-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the SL(2, ℤ) duality of Type IIB string theory, leading to completely different group structure. These lead to a very rich class of dualities between 5d gauge theories whose UV completion is the same 6d superconformal field theory. We also explore Higgsing of the 6d theories and their 5d counterparts. Decoupling the same flavors from the dual 5d theories gives rise to another dual 5d theories whose UV completion is the same 5d superconformal field theory. Finally we propose the 6d description of 5d theories which is obtained by a generalization of 5d TN theories with additional flavors, which turns out not to be in the class of Type IIA brane construction generically.
Highlights
6d N = (1, 0) superconformal field theories (SCFTs) possess many interesting as well as mysterious features
The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories
Given a 6d SCFT, we first move to a tensor branch where scalars in tensor multiplets acquire a vacuum expectation value (VEV), and perform a circle compactification with gauge or flavor Wilson lines along the S1
Summary
While the quantum resolution of both O7− planes leads to the 5d SU(N + 2) gauge theory with 2N + 8 flavors, one may resolve only one of the two O7− planes which arise from T-duality of the O8− plane in Type IIA brane picture of 6d Sp(N ) theory. In this process of reducing the 6d theory to 5d, the Wilson line is introduced such that all the D5-branes are located above the unresolved O7− plane, to retain an Sp gauge group. One can resolve the O7− plane with a pair of [1, 1] and [1, −1] 7-branes as chosen earlier, and one can resolve it with a pair of [2, 1] and [0, 1] 7-branes
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