6d Conformal Matter (1407.6359v3)

Abstract: A single M5-brane probing G, an ADE-type singularity, leads to a system which has G x G global symmetry and can be viewed as "bifundamental" (G,G) matter. For the A_N series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1,0) superconformal system in six dimensions. Similarly, an ADE singularity intersecting the Horava-Witten wall leads to a superconformal matter system with E_8 x G global symmetry. Using the F-theory realization of these theories, we elucidate the Coulomb/tensor branch of (G,G') conformal matter. This leads to the notion of fractionalization of an M5-brane on an ADE singularity as well as fractionalization of the intersection point of the ADE singularity with the Horava-Witten wall. Partial Higgsing of these theories leads to new 6d SCFTs in the infrared, which we also characterize. This generalizes the class of (1,0) theories which can be perturbatively realized by suspended branes in IIA string theory. By reducing on a circle, we arrive at novel duals for 5d affine quiver theories. Introducing many M5-branes leads to large N gravity duals.

• The paper introduces M5-brane fractionalization to reveal novel 6d SCFTs emerging from ADE-type singularities.
• It employs F-theory methods and Higgsing to bridge 6d conformal matter to 5d affine quiver theories and large N gravity duals.
• The research advances understanding of non-Lagrangian quantum field theories and paves the way for exploring string-dualities in lower dimensions.

Overview of "6d Conformal Matter"

The paper "6d Conformal Matter" by Michele Del Zotto, Jonathan J. Heckman, Alessandro Tomasiello, and Cumrun Vafa provides a detailed exposition of 6-dimensional (6d) superconformal field theories (SCFTs) within the framework of string theory. This research focuses on M5-branes probing ADE-type singularities and extends to encompass interactions with the Hořava-Witten wall. Through the lens of F-theory, the paper illuminates the complex machinery of conformal matter and specifies the tensor branches of these SCFTs, revealing the intricate relationship between M-theory setups and 6d conformal field theories.

M5-branes and ADE Singularities

The central premise of the paper is the paper of M5-branes interacting with ADE-type singularities, which yield $G\times G$ global symmetry and can be interpreted as "bifundamental" $(G, G)$ matter. For the $A_N$ series, this bifundamental matter is well-understood; however, for other ADE cases, it leads to strongly interacting $(1,0)$ superconformal systems that resist a Lagrangian description. The interaction of an ADE singularity with the Hořava-Witten wall results in a superconformal matter system possessing $E_8\times G$ global symmetry.

Fractionalization and Tensor Branch

In analyzing the Coulomb/tensor branch of $(G,G')$ conformal matter, the paper introduces the concept of M5-brane fractionalization. This concept describes how an M5-brane behaves when interacting with an ADE singularity or at the intersection point with the Hořava-Witten wall. The authors highlight intriguing dynamics wherein M5-branes fractionate into components that partake in additional gauge symmetries with tensionless strings.

By partially Higgsing these constructions, the authors demonstrate novel 6d SCFTs in the infrared limit. These generalize the class of $(1,0)$ theories originally derived from suspended branes in IIA string theory. Furthermore, by compactifying the analysis on a circle, the exploration extends to new dual descriptions of 5d affine quiver theories, revealing large $N$ gravity duals when many M5-branes are incorporated.

Practical and Theoretical Implications

This work holds substantial theoretical implications by advancing the classification of 6d SCFTs without relying on a weakly coupled UV Lagrangian, thus contributing to the broader understanding of quantum field theories without conventional Lagrangian descriptions. Practically, these insights bridge connections to possible applications in condensed matter systems where similar physics involving tensionless strings may occur.

Future Directions

The extensions of this research into non-simply laced symmetries present a clear trajectory for future work. Additionally, understanding these theories' lower-dimensional reductions sheds light on string-dualities and could advance the application of such theoretical constructs in more concrete settings.

In sum, the paper provides a crucial advancement in understanding the geometry of string theory’s extra dimensions and the resulting low-energy theories, significantly enriching the theoretical framework for 6d SCFTs and laying the groundwork for exploring novel dualities and theoretical constructs.