Abstract
T-branes are exotic bound states of D-branes, characterized by mutually non-commuting vacuum expectation values for the worldvolume scalars. The M/F-theory geometry lifting D6/D7-brane configurations is blind to the T-brane data. In this paper, we make this data manifest, by probing the geometry with an M2-brane. We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce supersymmetry from N=4 to N=2. Our main tool is 3d mirror symmetry. Through this language, a very concrete framework is developed for understanding T-branes in M-theory. This leads us to uncover a new class of N=2 quiver gauge theories, whose Higgs branches mimic those of membranes at ADE singularities, but whose Coulomb branches differ from their N=4 counterparts.
Highlights
Vanishing area that are interconnected in the form of a Dynkin diagram
We find that the effect of a T-brane is to deform the membrane worldvolume superpotential with monopole operators, which partially break the three-dimensional flavor symmetry, and reduce supersymmetry from N = 4 to N = 2
The point of view that a monopole operator creates a D2-particle state bolsters our claim that off-diagonal strings stretched between D6-branes should uplift in M-theory to M2-branes wrapping vanishing cycles, since such strings appear on the D2 as off-diagonal mass terms that are mirror to monopole operators
Summary
Three-dimensional mirror symmetry without Chern Simons terms (the case of interest in this paper) is reviewed in [8]. The correction comes from the fact that, at the origin of the Coulomb branch, the chiral matter fields become massless, and the naıve Wilsonian effective action develops a singularity It can be derived via heuristic arguments, via a one-loop calculation of the metric of the moduli space, via mirror symmetry, or via a monopole counting argument. This theory has a Coulomb and a Higgs branch (CBB and HBB), which are mutually exclusive. The U(1) vector multiplet described by the monopole operators V± is completed to an N = 4 vector multiplet by pairing it up with an N = 2 chiral multiplet of lowest component Φ This superpotential constrains the meson matrix to be traceless, TrM = 0.
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