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N = 1 SCFTs from Brane Monodromy

Jonathan J. Heckman, Yuji Tachikawa, Cumrun Vafa, Brian Wecht

TL;DR

The paper identifies a broad new class of strongly coupled $N=1$ SCFTs arising from D3-brane probes of tilted seven-branes in F-theory, where monodromy in the seven-brane sector yields field-dependent mass deformations that generically flow to interacting IR fixed points. A central methodological advance is the use of $a$-maximization to determine the IR R-symmetry and central charges, revealing that the holomorphic data is not fully fixed by the Casimirs of the deformation, and that the IR structure can be affected by nilpotent versus monodromic mass terms. The authors analyze concrete examples including deformations of the $D_4$ theory and a spectrum of $E_n$ theories, in both finite and large $N$ limits, and study maximal and discrete monodromies, observing consistent flows to new IR SCFTs with calculable central charges and operator dimensions. They also discuss stabilization mechanisms for the D3-brane position and how the CFT sector can couple to the visible sector in F-theory GUT contexts, outlining potential phenomenological implications and directions for holographic and dual descriptions.

Abstract

We present evidence for a new class of strongly coupled N = 1 superconformal field theories (SCFTs) motivated by F-theory GUT constructions. These SCFTs arise from D3-brane probes of tilted seven-branes which undergo monodromy. In the probe theory, this tilting corresponds to an N = 1 deformation of an N = 2 SCFT by a matrix of field-dependent masses with non-trivial branch cuts in the eigenvalues. Though these eigenvalues characterize the geometry, we find that they do not uniquely specify the holomorphic data of the physical theory. We also comment on some phenomenological aspects of how these theories can couple to the visible sector. Our construction can be applied to many N = 2 SCFTs, resulting in a large new class of N = 1 SCFTs.

N = 1 SCFTs from Brane Monodromy

TL;DR

The paper identifies a broad new class of strongly coupled SCFTs arising from D3-brane probes of tilted seven-branes in F-theory, where monodromy in the seven-brane sector yields field-dependent mass deformations that generically flow to interacting IR fixed points. A central methodological advance is the use of -maximization to determine the IR R-symmetry and central charges, revealing that the holomorphic data is not fully fixed by the Casimirs of the deformation, and that the IR structure can be affected by nilpotent versus monodromic mass terms. The authors analyze concrete examples including deformations of the theory and a spectrum of theories, in both finite and large limits, and study maximal and discrete monodromies, observing consistent flows to new IR SCFTs with calculable central charges and operator dimensions. They also discuss stabilization mechanisms for the D3-brane position and how the CFT sector can couple to the visible sector in F-theory GUT contexts, outlining potential phenomenological implications and directions for holographic and dual descriptions.

Abstract

We present evidence for a new class of strongly coupled N = 1 superconformal field theories (SCFTs) motivated by F-theory GUT constructions. These SCFTs arise from D3-brane probes of tilted seven-branes which undergo monodromy. In the probe theory, this tilting corresponds to an N = 1 deformation of an N = 2 SCFT by a matrix of field-dependent masses with non-trivial branch cuts in the eigenvalues. Though these eigenvalues characterize the geometry, we find that they do not uniquely specify the holomorphic data of the physical theory. We also comment on some phenomenological aspects of how these theories can couple to the visible sector. Our construction can be applied to many N = 2 SCFTs, resulting in a large new class of N = 1 SCFTs.

Paper Structure

This paper contains 26 sections, 94 equations, 1 figure, 7 tables.

Table of Contents

  1. Introduction
  2. Geometric preliminaries
  3. Probing a $D_{4}$ Singularity
  4. Mass Deformations and the $\mathcal{N}=1$ Curve
  5. $a$-Maximization and Nilpotent Mass Deformations
  6. Large $N$ Limit
  7. $\mathcal{N}=1$ Deformations: Generalities
  8. The $\mathcal{N} = 1$ Curve and Relative Scaling Dimensions
  9. Characteristic Polynomials in the Infrared
  10. Central Charges and $a$-Maximization
  11. Nilpotent Mass Case
  12. Monodromic Case
  13. Probing an $E_n$ Singularity
  14. Nilpotent Mass Deformations
  15. Large $N$ Limit
  16. ...and 11 more sections

Figures (1)

  • Figure 1: Depiction of the various theories obtained by performing a single $n \times n$ nilpotent Jordan block deformation of the $E_{8}$$\mathcal{N}=2$ SCFT. Also indicated is the associated non-abelian flavor symmetry of each $\mathcal{N} = 1$ theory. As summarized in table \ref{['table1']}, increasing the size of the block leads to a further flow, and a decrease in the central charge $a_\text{IR}$. In the $n=3$ theory the non-abelian flavor symmetry is $E_{6}$, but it is nevertheless possible to deform the theory to the $\mathcal{N}=2$$E_{7}$ SCFT. Similarly, the $n=4$ theory with non-abelian flavor symmetry $SO(10)$ can be deformed to the $\mathcal{N}=2$$E_{6}$ SCFT.