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T-branes, Anomalies and Moduli Spaces in 6D SCFTs

Noppadol Mekareeya, Tom Rudelius, Alessandro Tomasiello

TL;DR

<3-5 sentence high-level summary>We investigate 6D SCFTs arising from M5-branes at ADE singularities and their Higgsing into T-brane configurations, revealing universal relations between Higgs moduli space dimensions and nilpotent orbit data. By deriving general formulas for the anomaly coefficients (δ, γ, β, α) and expressing them in terms of nilpotent-orbit data, we connect RG flows to orbit hierarchies and Slodowy-slice intersections, thereby providing a robust framework for tracking changes in the conformal data. We prove the a-theorem for a broad class of Higgs-branch flows, including SU(k), SO(2k), and E_k families, and extend the analysis to formal Type IIA constructions that access spinor representations in SO(2k) theories. The results unify geometric, algebraic, and field-theoretic aspects of T-branes in F-theory and IIA, with implications for conformal matter, Kraft–Procesi transitions, and the landscape of 6D SCFTs.

Abstract

The worldvolume theory of M5-branes on an ADE singularity $\mathbb{R}^5/Γ_G$ can be Higgsed in various ways, corresponding to the possible nilpotent orbits of $G$. In the F-theory dual picture, this corresponds to activating T-brane data along two stacks of 7-branes and yields a tensor branch realization for a large class of 6D SCFTs. In this paper, we show that the moduli spaces and anomalies of these T-brane theories are related in a simple, universal way to data of the nilpotent orbits. This often works in surprising ways and gives a nontrivial confirmation of the conjectured properties of T-branes in F-theory. We use this result to formally engineer a class of theories where the IIA picture naïvely breaks down. We also give a proof of the $a$-theorem for all RG flows within this class of T-brane theories.

T-branes, Anomalies and Moduli Spaces in 6D SCFTs

TL;DR

<3-5 sentence high-level summary>We investigate 6D SCFTs arising from M5-branes at ADE singularities and their Higgsing into T-brane configurations, revealing universal relations between Higgs moduli space dimensions and nilpotent orbit data. By deriving general formulas for the anomaly coefficients (δ, γ, β, α) and expressing them in terms of nilpotent-orbit data, we connect RG flows to orbit hierarchies and Slodowy-slice intersections, thereby providing a robust framework for tracking changes in the conformal data. We prove the a-theorem for a broad class of Higgs-branch flows, including SU(k), SO(2k), and E_k families, and extend the analysis to formal Type IIA constructions that access spinor representations in SO(2k) theories. The results unify geometric, algebraic, and field-theoretic aspects of T-branes in F-theory and IIA, with implications for conformal matter, Kraft–Procesi transitions, and the landscape of 6D SCFTs.

Abstract

The worldvolume theory of M5-branes on an ADE singularity can be Higgsed in various ways, corresponding to the possible nilpotent orbits of . In the F-theory dual picture, this corresponds to activating T-brane data along two stacks of 7-branes and yields a tensor branch realization for a large class of 6D SCFTs. In this paper, we show that the moduli spaces and anomalies of these T-brane theories are related in a simple, universal way to data of the nilpotent orbits. This often works in surprising ways and gives a nontrivial confirmation of the conjectured properties of T-branes in F-theory. We use this result to formally engineer a class of theories where the IIA picture naïvely breaks down. We also give a proof of the -theorem for all RG flows within this class of T-brane theories.

Paper Structure

This paper contains 40 sections, 86 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Six-dimensional SCFTs and T-branes
  3. Overview
  4. The $G=SU(k)$ theories
  5. NS5 movement.
  6. The nilpotent part.
  7. Anomalies
  8. Universal formulae for anomaly coefficients
  9. The coefficient $\delta$
  10. The relation with the dimension of the orbit.
  11. Example 1.
  12. Example 2.
  13. Example 3.
  14. Example 4.
  15. Example 5.
  16. ...and 25 more sections

Figures (1)

  • Figure 1: Two equivalent brane diagrams engineering the theory in \ref{['quivex']}. The nodes represent NS5-branes (spanning directions 0--5), the horizontal lines D6-branes (spanning 0--6), the vertical lines D8-branes (transverse to direction 6).