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T-branes as branes within branes

Andres Collinucci, Raffaele Savelli

TL;DR

This work reframes perturbative IIB D7-brane physics with T-branes in the tachyon condensation language, using the derived category of coherent sheaves to compute gauge groups and spectra. It shows that diagonalizable tachyon data yield straightforward unbroken gauge groups, while non-diagonalizable cases create bound states with lower-dimensional branes and unconventional matter localization, captured by Ext$^1$ calculations and Jordan-block classifications. The authors incorporate stability via $\Pi$-stability and illustrate the framework with explicit one-modulus compactifications, demonstrating constant and point-like matter T-branes and their stability conditions. They also outline a path toward an F-theory lift through coherent sheaves on CY fourfolds, aiming to extend these insights to non-perturbative configurations and SL$(2,\mathbb{Z})$-covariant setups.

Abstract

Bound states of 7-branes known as 'T-branes' have properties that defy usual geometric intuition. For instance, the gauge group of n coincident branes may not be U(n). More surprisingly, matter may show up at unexpected loci, such as points. By analyzing T-branes of perturbative type IIB string theory in the tachyon condensation picture we gain the following insights: In a large class of models, the tachyon can be diagonalized even though the worldvolume Higgs cannot. In those cases, we see the structure of these bound states more manifestly, thereby drastically simplifying analysis of gauge groups and spectra. Whenever the tachyon is not diagonalizable, matter localizes at unexpected loci, and we find that there is a lower-dimensional brane bound to the 7-brane.

T-branes as branes within branes

TL;DR

This work reframes perturbative IIB D7-brane physics with T-branes in the tachyon condensation language, using the derived category of coherent sheaves to compute gauge groups and spectra. It shows that diagonalizable tachyon data yield straightforward unbroken gauge groups, while non-diagonalizable cases create bound states with lower-dimensional branes and unconventional matter localization, captured by Ext calculations and Jordan-block classifications. The authors incorporate stability via -stability and illustrate the framework with explicit one-modulus compactifications, demonstrating constant and point-like matter T-branes and their stability conditions. They also outline a path toward an F-theory lift through coherent sheaves on CY fourfolds, aiming to extend these insights to non-perturbative configurations and SL-covariant setups.

Abstract

Bound states of 7-branes known as 'T-branes' have properties that defy usual geometric intuition. For instance, the gauge group of n coincident branes may not be U(n). More surprisingly, matter may show up at unexpected loci, such as points. By analyzing T-branes of perturbative type IIB string theory in the tachyon condensation picture we gain the following insights: In a large class of models, the tachyon can be diagonalized even though the worldvolume Higgs cannot. In those cases, we see the structure of these bound states more manifestly, thereby drastically simplifying analysis of gauge groups and spectra. Whenever the tachyon is not diagonalizable, matter localizes at unexpected loci, and we find that there is a lower-dimensional brane bound to the 7-brane.

Paper Structure

This paper contains 11 sections, 45 equations, 1 figure.

Table of Contents

  1. Introduction
  2. D7-branes as D9/anti-D9 tachyon condensates
  3. T-branes as coherent sheaves
  4. Gauge group breaking via nilpotent Higgsing
  5. Stability in compactifications
  6. Review of $\Pi$-stability for D-particles
  7. $\Pi$-stability for $O7/D7$ systems
  8. Examples of T-branes in a one-modulus compactification
  9. Case 1: Constant T-brane
  10. Case 2: Point-like matter
  11. Discussion

Figures (1)

  • Figure 1: Figure (a) depicts a system where the tachyon field is realized by strings going from the anti-D9's to the D9's. Figure (b) depicts a more general situation with strings going back and forth between D9 and anti-D9. The data is unfolded into a complex.