Mass-deformed $T_N$ as a linear quiver

Abstract

The $T_N$ theory is a non-Lagrangian theory with SU(N) flavor symmetry. We argue that when mass terms are given so that two of SU(N)'s are both broken to SU(N-1) x U(1), it becomes $T_{N-1}$ theory coupled to an SU(N-1) vector multiplet together with N fundamentals. This implies that when two of SU(N)'s are both broken to U(1)${}^{N-1}$, the theory becomes a linear quiver. We perform various checks of this statement, by using the 5d partition function, the structure of the coupling constants, the Higgs branch, and the Seiberg-Witten curve. We also study the case with more general punctures.

36 pages, 5 figures; v2: short discussions on 3d T_N theory appended, typos corrected, and references added