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There and back again: A T-brane's tale

Iosif Bena, Johan Blåbäck, Ruben Minasian, Raffaele Savelli

TL;DR

This paper shows that T-branes with large non-Abelian vevs admit an Abelian description: a single curved Dp-brane whose worldvolume geometry encodes the original flux and non-commutative data. By traversing a chain of dualities, the authors map the non-Abelian D7 configuration to a Nahm-dynamics D6 system, then to a funnel-shaped D8-brane with flux, and finally back to a curved D7-brane wrapping a holomorphic curve in C^2, specifically $ZW=N/2$ in the maximal-partition case. The results identify a regime where the Abelian description is valid (large curvature control and large $N$), and they generalize to partitions $\{n_i\}$ with corresponding holomorphic curves $ZW=n_i/2$; the work suggests a deep link between non-Abelian T-brane data and curved Abelian worldvolume geometries, with potential implications for string phenomenology and brane recombination. Overall, the paper provides a concrete, calculable bridge between non-Abelian T-brane physics and an Abelian, curvature-encoded description that remains valid beyond the traditional large-VEV regime.

Abstract

T-branes are supersymmetric configurations described by multiple Dp-branes with worldvolume flux and non-commuting vacuum expectation values for two of the worldvolume scalars. When these values are much larger than the string scale this description breaks down. We show that in this regime the correct description of T-branes is in terms of a single Dp-brane, whose worldvolume curvature encodes the T-brane data. We present the tale of the journey to reach this picture, which takes us through T-dualities and rugby-ball-shaped brane configurations that no eye has gazed upon before.

There and back again: A T-brane's tale

TL;DR

This paper shows that T-branes with large non-Abelian vevs admit an Abelian description: a single curved Dp-brane whose worldvolume geometry encodes the original flux and non-commutative data. By traversing a chain of dualities, the authors map the non-Abelian D7 configuration to a Nahm-dynamics D6 system, then to a funnel-shaped D8-brane with flux, and finally back to a curved D7-brane wrapping a holomorphic curve in C^2, specifically in the maximal-partition case. The results identify a regime where the Abelian description is valid (large curvature control and large ), and they generalize to partitions with corresponding holomorphic curves ; the work suggests a deep link between non-Abelian T-brane data and curved Abelian worldvolume geometries, with potential implications for string phenomenology and brane recombination. Overall, the paper provides a concrete, calculable bridge between non-Abelian T-brane physics and an Abelian, curvature-encoded description that remains valid beyond the traditional large-VEV regime.

Abstract

T-branes are supersymmetric configurations described by multiple Dp-branes with worldvolume flux and non-commuting vacuum expectation values for two of the worldvolume scalars. When these values are much larger than the string scale this description breaks down. We show that in this regime the correct description of T-branes is in terms of a single Dp-brane, whose worldvolume curvature encodes the T-brane data. We present the tale of the journey to reach this picture, which takes us through T-dualities and rugby-ball-shaped brane configurations that no eye has gazed upon before.

Paper Structure

This paper contains 7 sections, 43 equations, 4 figures.

Table of Contents

  1. Introduction
  2. T-branes
  3. The D6 picture
  4. The D8 picture
  5. … and back again
  6. Discussion
  7. Funnel shapes for the D8-branes

Figures (4)

  • Figure 1: Summary of our construction.
  • Figure 2: Sketch of the D8 shape. The length of the line at $\sigma = \infty$, along $X^3$, is $CN$.
  • Figure 3: Sketch of the D8 shape after zooming into a small neighborhood of the equator.
  • Figure 4: Three-dimensional profile of the D7-brane after T-duality, in which $|Z|$ and $|W|$ are plotted and rotated on the diagonal. The size of the minimal circle is proportional to $N$.