On Brane Systems with O+ Planes: Deriving Magnetic Quivers for 5D and 6D Superconformal Field Theories

Core Concepts

This paper presents a method for deriving magnetic quivers for 5D and 6D superconformal field theories (SCFTs) realized on brane systems with O+ planes, revealing a modified stable intersection rule for branes intersecting on the orientifold.

Abstract

Bibliographic Information:

Akhond, M., Arias-Tamargo, G., Carta, F., Grimminger, J. F., & Hanany, A. (2024). On brane systems with O+ planes – 5d and 6d SCFTs. arXiv.org, arXiv:2411.02491v1.

Research Objective:

This paper aims to determine the magnetic quivers of 5D and 6D SCFTs realized on brane systems containing O7+ planes, focusing on how the presence of the orientifold modifies the established rules for deriving these quivers.

Methodology:

The authors utilize a combination of brane dynamics, tropical geometry, and quiver subtraction techniques. They begin with known magnetic quivers for 6D SCFTs and analyze their behavior under twisted circle compactification to 5D. By tracking mass deformations in both the brane web and magnetic quiver descriptions, they deduce the modified stable intersection rule for branes intersecting on the O7+ plane.

Key Findings:

• The presence of an O7+ plane modifies the stable intersection number used to determine the links in the magnetic quiver.
• The modified stable intersection rule is not SL(2,Z) invariant in its initial form, necessitating a generalization to ensure invariance under global SL(2,Z) transformations.
• The orientation of the O7+ monodromy cut plays a crucial role in determining the correct intersection number.
• The derived magnetic quivers allow for the computation of Higgs branch properties, including Hasse diagrams and Hilbert series, which in turn enable the identification of the global symmetry groups of the SCFTs.

Main Conclusions:

The paper provides a systematic method for deriving magnetic quivers for a class of 5D and 6D SCFTs realized on brane systems with O7+ planes. This method, based on a modified stable intersection rule, allows for a deeper understanding of the Higgs branches of these theories and their global symmetries.

Significance:

This research contributes significantly to the study of 5D and 6D SCFTs by providing new tools for analyzing their properties. The derived magnetic quivers and the insights gained from them can be used to further explore the landscape of these theories and their connections to other areas of theoretical physics.

Limitations and Future Research:

The paper primarily focuses on specific families of SCFTs with SO and SU gauge groups. Further research could explore the applicability of these methods to a wider range of theories and brane configurations. Additionally, a more rigorous derivation of the FI quiver subtraction rules for non-simply laced quivers would strengthen the proposed method.

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Key Insights Distilled From

On brane systems with O${}^+$ planes -- 5d and 6d SCFTs

by Mohammad Akh... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02491.pdf

Deeper Inquiries

How do the methods presented in this paper relate to other approaches for studying the Higgs branches of 5D and 6D SCFTs, such as geometric engineering or algebraic techniques?

This paper leverages the power of magnetic quivers, derived from brane webs, to study the Higgs branches of 5D and 6D SCFTs. This approach provides a direct connection between the brane dynamics and the field theory description, allowing for a concrete visualization of the Higgs branch moduli space.
Let's compare this with other prominent methods:

Geometric Engineering: This approach realizes the SCFTs as worldvolume theories on branes probing singularities in string/M-theory. The Higgs branch is then studied through the resolution of these singularities. While powerful, this method can be computationally intensive, especially for intricate singularities. The magnetic quiver approach, when applicable, offers a more streamlined route to the Higgs branch description.

Algebraic Techniques: These methods, often employing tools like superconformal algebra and representation theory, provide a more abstract characterization of the Higgs branch. They are particularly useful for deriving general properties and constraints. However, they might not always yield a concrete description of the moduli space, unlike the magnetic quiver approach, which explicitly encodes the structure of the Higgs branch.
In essence, the methods presented in the paper serve as a valuable complement to these existing techniques. They provide a more intuitive and, in many cases, computationally simpler way to study the Higgs branches of SCFTs, especially those admitting brane web realizations.

Could the modified stable intersection rule be a manifestation of some deeper geometric structure associated with the presence of orientifold planes in string theory?

The modified stable intersection rule, a central result of this paper, strongly suggests a deeper geometric underpinning tied to the presence of orientifold planes, specifically O7+ planes, in string theory.
Here's why this modification is intriguing:

SL(2,Z) Invariance: The standard stable intersection number is inherently SL(2,Z) invariant, reflecting the duality symmetries of Type IIB string theory. However, the O7+ plane breaks this symmetry. The modified rule, by incorporating the O7+ monodromy and charges, restores this invariance, hinting at a consistent geometric interpretation within the framework of string theory.

Orientifold Projection: Orientifold planes act as mirrors, introducing an identification in spacetime and projecting the string spectrum. This projection, in the context of intersecting branes, could be responsible for the additional contribution to the intersection number. The specific form of the modification, involving the NS charges, might hold clues to the precise nature of this projection on the brane configurations.
Further research is certainly warranted to unravel the precise geometric structure underlying this modified rule. It could potentially involve:

Exploring the connection to F-theory: F-theory provides a geometrized description of Type IIB string theory with varying axio-dilaton. Since O7+ planes are associated with specific monodromies of the axio-dilaton, an F-theory perspective might offer valuable insights into the modified intersection number.

Investigating the role of D-brane charges: The dependence of the modification on D-brane charges suggests a potential connection to the worldvolume gauge theory on the D-branes. Understanding how the orientifold projection affects the D-brane charges and their interactions could shed light on the geometric origin of the modified rule.
Unveiling this deeper geometric structure would not only solidify the results of the paper but also potentially lead to a more profound understanding of orientifolds and their implications for string theory.

What are the implications of the global symmetry enhancements observed in these SCFTs for their potential applications in particle physics or cosmology?

The global symmetry enhancements observed in these 5D and 6D SCFTs, as revealed through their Higgs branches, carry significant implications for their potential applications in particle physics and cosmology.
Here's why these enhancements are noteworthy:

Constraints on Low-Energy Physics: Global symmetries in a high-energy theory can impose powerful constraints on the structure of the low-energy effective theory, even after the symmetry is spontaneously broken. The enhanced global symmetries in these SCFTs could potentially lead to novel selection rules and relations among couplings in the low-energy theory, potentially offering new avenues for model building.

New Physics at High Scales: The appearance of these enhanced symmetries might signal the presence of new degrees of freedom or interactions becoming relevant at the energy scale of the SCFT. This could have profound implications for our understanding of physics beyond the Standard Model, potentially offering clues to the unification of forces or the nature of dark matter.
Let's consider some specific potential applications:

Particle Physics: The enhanced global symmetries could be used to construct new models of grand unification, where the Standard Model gauge group is embedded into a larger symmetry group. The specific representations under the enhanced symmetry could guide the choice of particle content and interactions in these models.

Cosmology: The SCFTs with enhanced global symmetries could play a role in inflationary scenarios, where the inflaton field could be identified with a scalar field charged under the global symmetry. The breaking of this symmetry during inflation could lead to the generation of density perturbations that seed the formation of large-scale structures in the universe.
However, it's important to acknowledge the challenges:

Understanding the Breaking Mechanism: To fully exploit these enhanced symmetries, a detailed understanding of how they are spontaneously broken to the symmetries of the Standard Model is crucial. This breaking mechanism would dictate the low-energy spectrum and interactions.

Connecting to Observable Scales: Bridging the gap between the high energy scales of these SCFTs and the observable scales of particle physics and cosmology remains a significant challenge.
Despite these challenges, the observed global symmetry enhancements provide tantalizing hints of the rich structure and potential of these SCFTs. Further exploration of their properties and implications could lead to exciting new discoveries in our quest to understand the fundamental laws of nature.