Abstract
SCFTs in six dimensions are interrelated by networks of RG flows. Compactifying such models on a Riemann surface with flux for the 6d global symmetry, one can obtain a wide variety of theories in four dimensions. These four dimensional models are also related by a network of RG flows. In this paper we study some examples of four dimensional flows relating theories that can be obtained from six dimensions starting with different SCFTs connected by 6d RG flows. We compile a dictionary between different orders of such flows, 6d → 6d → 4d and 6d → 4d → 4d, in the particular case when the six dimensional models are the ones residing on M5 branes probing different A-type singularities. The flows we study are triggered by vacuum expectation values (vevs) to certain operators charged under the six dimensional symmetry. We find that for generic choices of parameters the different orders of flows, 6d → 6d → 4d and 6d → 4d → 4d, involve compactifications on different Riemann surfaces with the difference being in the number of punctures the surface has.
Highlights
Construction as yet another construction of an RG flow leading to a CFT
We compile a dictionary between different orders of such flows, 6d → 6d → 4d and 6d → 4d → 4d, in the particular case when the six dimensional models are the ones residing on M5 branes probing different A-type singularities
The flows we study are triggered by vacuum expectation values to certain operators charged under the six dimensional symmetry
Summary
We start by considering the flow triggered by giving a vev to end to end operators. In 6d a natural choice is to give a vev to one such operator, let us denote it O6d. The resulting picture is the same with the additional NS5-branes mapping to minimal punctures This leads us to conclude that when we give a vev to a 6d SCFT compactified on a torus with flux we expect to flow to a 4d theory associated with a compactification of the 6d SCFT at the end of the flow, but on a torus with additional minimal punctures. It is convenient to consider what we expect of this flow from field theory, where we shall employ the low-energy tensor branch gauge theory In that description, this flow is generated via a vev to the gauge invariant made from the scalar fields in all the bifundamental hypermultiplets, including the ones at the edges, which are gauge-global symmetry bifundamentals.
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