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T-branes and Matrix Models

Iosif Bena, Johan Blåbäck, Raffaele Savelli

TL;DR

This work uncovers a deep link between T-branes in the Hitchin system and longitudinal five-branes in the BFSS matrix model by showing that the Hitchin equations for constant worldvolume fields coincide with the Banks-Seiberg-Shenker equations. Using this connection, the authors construct explicit infinite-N solutions and establish a macroscopic map to Abelian brane configurations, demonstrating that the same T-brane data can be described by intersecting D2-branes or by D4-branes with worldvolume flux, depending on the duality frame. They provide a three-parameter family of solutions with controlled D0, D2, and D4 charges, and show how SUSY is affected by the gamma parameter, linking non-Abelian T-brane physics to Abelian holomorphic embeddings. The results illuminate regimes where worldvolume fields exceed the string scale and open avenues for finite-N corrections and microscopic brane-mapping research.

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.

T-branes and Matrix Models

TL;DR

This work uncovers a deep link between T-branes in the Hitchin system and longitudinal five-branes in the BFSS matrix model by showing that the Hitchin equations for constant worldvolume fields coincide with the Banks-Seiberg-Shenker equations. Using this connection, the authors construct explicit infinite-N solutions and establish a macroscopic map to Abelian brane configurations, demonstrating that the same T-brane data can be described by intersecting D2-branes or by D4-branes with worldvolume flux, depending on the duality frame. They provide a three-parameter family of solutions with controlled D0, D2, and D4 charges, and show how SUSY is affected by the gamma parameter, linking non-Abelian T-brane physics to Abelian holomorphic embeddings. The results illuminate regimes where worldvolume fields exceed the string scale and open avenues for finite-N corrections and microscopic brane-mapping research.

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.

Paper Structure

This paper contains 6 sections, 32 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. From T-branes to Matrix Theory
  3. Finding a solution
  4. The "Abelian" picture
  5. Returning to the original frame
  6. Discussion

Figures (2)

  • Figure 1: The summary of our construction.
  • Figure 2: A projection of Eq. (\ref{['eq:holo']}) onto the equation $y = x \tan \alpha + k$, where the angle $\alpha$ would be derived from the constant $C$, and $k$ from $\kappa$.