Infinitely many \( \mathcal{N}=1 \) dualities from \(m + 1-m=1\)

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Abstract: We discuss two infinite classes of 4d supersymmetric theories,

T_{N}^{(m)}

and

{c a l U}_{N}^{(m)}

, labelled by an arbitrary non-negative integer,

m

. The

T_{N}^{(m)}

theory arises from the 6d,

A_{N - 1}

type

c a l N = (2, 0)

theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree

(m + 1, - m)

; the

m = 0

case is the

c a l N = 2

supersymmetric

T_{N}

theory. The novelty is the negative-degree line bundle. The

{c a l U}_{N}^{(m)}

theories likewise arise from the 6d

c a l N = (2, 0)

theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed)

T_{N}^{(m)}

theories. The

T_{N}^{(m)}

and

{c a l U}_{N}^{(m)}

theories can be represented, in various duality frames, as quiver gauge theories, built from

T_{N}

components via gauging and nilpotent Higgsing. We analyze the RG flow of the

{c a l U}_{N}^{(m)}

theories, and find that, for all integer

m > 0

, they end up at the same IR SCFT as

S U (N)

SQCD with

2 N

flavors and quartic superpotential. The

{c a l U}_{N}^{(m)}

theories can thus be regarded as an infinite set of UV completions, dual to SQCD with

N_{f} = 2 N_{c}

. The

{c a l U}_{N}^{(m)}

duals have different duality frame quiver representations, with

2 m + 1

gauge nodes.

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