T-branes through 3d mirror symmetry

TL;DR

This work provides a 3d mirror-symmetric framework to uncover T-brane data in M-theory by probing stacks of D6-branes with D2-branes; T-brane vevs map to monopole-operator deformations, reducing supersymmetry from N=4 to N=2 and partially breaking flavor symmetry. The authors introduce local 3d mirror symmetry, enabling a node-by-node analysis that yields reduced quiver descriptions while preserving the Higgs branch ADE singularity, and they extend the construction from the A-series to D and E series. They propose a universal M-theory uplift of T-branes via monopole deformations and demonstrate how the Coulomb branch is altered in the dual theory, including the interesting phenomenon of singularity “frozen” behavior. The results offer a concrete, calculable bridge between T-brane data, M-theory geometry, and 3d $ ext{N}=2$ quiver dynamics, with potential extensions to non-Abelian mirrors and Hilbert-series techniques.

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.

Figures (10)

• Figure 1: Example of the mirror of $\mathcal{N}=2$ SQED with $N=3$ flavors
• Figure 2: Example of the mirror of $\mathcal{N}=4$ SQED with $N=3$ flavors
• Figure 3: When $g_s$ is turned on, a D2 ending on a D4 becomes a smooth funnel shape.
• Figure 4: Example of the A$_{3}$-theory with a minimal T-brane. The effect of the T-brane on the quiver is to remove the corresponding node and substitute the arrow ending and starting from that node with new arrows that connect the adiacent nodes (by abuse of notation the new quarks are also denoted as $q_3,\tilde{q}^3$).
• Figure 5: D$_N$ quiver.