Anomaly polynomial of general 6d SCFTs (1408.5572v2)

Abstract: We describe a method to determine the anomaly polynomials of general 6d $\mathcal{N}=(2,0)$ and $\mathcal{N}=(1,0)$ SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. We demonstrate our method in many concrete examples, including $\mathcal{N}=(2,0)$ theories of arbitrary type and the theories on M5 branes on ALE singularities, reproducing the $N^3$ behavior. We check the results against the anomaly polynomials computed M-theoretically via the anomaly inflow.

• The paper presents a field-theoretical method employing anomaly matching on tensor branches to compute anomaly polynomials of 6d SCFTs.
• It reproduces the characteristic N^3 growth and matches anomalies obtained via M-theoretic inflow in both (2,0) and (1,0) settings.
• The approach extends anomaly analyses to previously unexplored SCFT types, offering robust insights into the geometric and supersymmetric dynamics.

Anomaly Polynomial of General 6d SCFTs

The paper "Anomaly Polynomial of General 6d SCFTs" by Kantaro Ohmori et al. presents a comprehensive method for determining the anomaly polynomials of general six-dimensional superconformal field theories (SCFTs) with $\mathcal{N}=(2,0)$ or $\mathcal{N}=(1,0)$ supersymmetry. The authors focus on exploiting the anomaly matching conditions on the tensor branches of these theories, utilizing an almost purely field-theoretical approach. This method is applicable to all known 6d SCFTs.

The broader context of this research lies in the understanding of the rich dynamics of higher-dimensional field theories. The (2,0) theories play a central role in organizing many aspects of lower-dimensional supersymmetric dynamics, and the (1,0) theories hold similar potential but remain partially unexplored. The paper, therefore, emphasizes the importance of understanding these 6d theories themselves, particularly through their anomalies, which serve as an infrared-stable property that remains invariant across duality frames.

Key Contributions

1. Anomaly Matching on Tensor Branches: The essence of the paper's methodology lies in matching the anomalies on the tensor branch of 6d SCFTs. This involves computing the contributions from individual multiplets in a manner consistent with effective theories in lower-dimensional settings.
2. Application Across Known Theories: The authors apply their method to a variety of concrete examples, including $\mathcal{N}=(2,0)$ theories of arbitrary type and theories on M5-branes placed on ALE singularities. Through this, they successfully reproduce the characteristic $N^3$ growth in the number of degrees of freedom, a prominent feature of these theories.
3. Consistency with M-Theoretical Anomalies: The anomaly polynomials derived through field-theoretical methods are corroborated by previous computations using M-theoretic approaches, notably via anomaly inflow. This consistency serves as a robust check on the validity of their field-theoretical approach.

Strong Numerical Results and Implications

The method provides strong numerical results in the form of anomaly coefficients for various 6d SCFTs, showcasing their modularity and uniform applicability to different configurations.

• $N^3$ Behavior: The reproduced $N^3$ behavior in the anomalies serves as a compelling verification of theoretical predictions from string theory and M-theory perspectives, reflecting the geometric nature of these 6d theories.
• Extension Beyond Known Types: This method successfully extends the analysis to 6d $\mathcal{N}=(2,0)$ types E and D, where direct string-theoretical computations were previously lacking.
• Implications for F-theory: The paper highlights connections to F-theory classifications, implicating their methods for anomaly computations as instrumental in verifying geometric classifications arising in F-theory constructs.

Future Directions

The framework introduced here surfaces several avenues for further exploration:

• Broader Classes of Symmetries: Extending this framework to include additional symmetries and scenarios not conventionally captured by string-theoretical constructions.
• Applications in Lower Dimensions: Understanding the implications of these anomaly polynomials when these 6d SCFTs are reduced to lower dimensions, thus contributing to the paper of dualities and symmetry enhancements in varied backgrounds.
• Global Anomalies and Non-Perturbative Aspects: The paper indicates the potential for exploring global anomaly aspects beyond perturbative computations, thus enriching the understanding of the topological and geometric influences in higher-dimensional field theories.

In summary, this paper provides a crucial advancement in the understanding of 6d SCFTs through detailed computational methods and consistency checks. Its implications span theoretical physics, from enhancing mathematical frameworks to improving the understanding of supersymmetric field theories' dynamics across dimensions.