Abstract
We find that the equations describing T-branes with constant worldvolume fields are identical to the equations found by Banks, Seiberg and Shenker twenty years ago to describe longitudinal five-branes in the BFSS matrix model. Besides giving new ways to construct T-brane solutions, this connection also helps elucidate the physics of T-branes in the regime of parameters where their worldvolume fields are larger than the string scale. We construct explicit solutions to the Banks-Seiberg-Shenker equations and show that the corresponding T-branes admit an alternative description as Abelian branes at angles.
Highlights
Hitchin system describing T-branes come from reductions of ten-dimensional super-YangMills theory to lower dimensions: the BFSS matrix model is the reduction of this theory to a particular one-dimensional matrix quantum mechanics, while the Hitchin system arises from an intermediate two-dimensional compactification of the self-duality equations of the super-Yang-Mills theory [25]
One can use the extensive technology developed in the good old matrix-model days to construct, rather straightforwardly, several solutions of Tbranes with constant fields. To obtain such T-branes one has to consider infinite matrices, and we construct a map between these T-branes and their Abelian counterparts following a path similar to that of [19]: the system of equations we obtain in the T-brane frame is mapped to a dual system via two T-dualities along the worldvolume of the T-brane
We focused on solutions preserving eight supercharges and we restricted to T-branes characterized by constant profiles of the worldvolume scalars, which forced us to consider stacks made of an infinite number of D-branes
Summary
T-branes preserving eight supercharges are non-trivial solutions of the so-called Hitchin system:. T-brane configurations are characterized by a non-trivial commutator [Φ, Φ†] and, because of the cyclicity of the trace, have a traceless worldvolume flux. As noted in [20], this system of equations admits no non-trivial solutions in terms of finite matrices, and to proceed we will use infinite matrices. As explained at the beginning of this section, we will consider T-branes for which the N212 = N234 = 0 because of the necessity of the tracelessness of equation (2.1b) for finite matrices. We will impose this condition in order not to introduce new features unrelated to T-branes.
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