Four-Dimensional SCFTs from M5-Branes (1203.0303v1)

Abstract: We engineer a large new set of four-dimensional N=1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS_5 M-theory backgrounds which describe these fixed points at large N, and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in arXiv:1112:5487.

• The paper introduces innovative AdS5 supergravity solutions that generate 4D SCFTs from M5-branes wrapped on complex curves.
• The paper computes central charges via the M5-brane anomaly polynomial, confirming theoretical consistency in the large N limit.
• The paper demonstrates holographic RG flows and generalized quiver constructions that bridge 6D M5-brane dynamics with 4D field theories.

Four-Dimensional SCFTs from M5-Branes: An Analysis

This essay examines the construction of novel four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) derived from M5-branes wrapped on complex curves. The paper detailed within the paper presents new supergravity solutions in $AdS_5$ M-theory backgrounds that describe these SCFTs in the large $N$ limit and construct their corresponding dual four-dimensional CFTs for specific configurations. Additionally, the methodology incorporates the calculation of central charges using the M5-brane anomaly polynomial, solidifying the existence of these SCFTs both theoretically and holographically.

Key Contributions and Methodology

The paper initially introduces the context through the exploration of the intricate properties of M5-branes within the framework of string/M-theory, particularly emphasizing the scenarios when these branes are wrapped on compact holomorphic curves. The strategy employed facilitates the derivation of low-energy four-dimensional theories from the six-dimensional dynamics inherent to M5-branes. This involves varying degrees of preserved supersymmetry contingent on the choice of wrapping and compactification.

1. Supergravity Solutions and Dual CFTs: The paper provides a suite of new supergravity solutions in $AdS_5$ space, detailed to match specified large $N$ field theory duals. These solutions account for different configurations of M5-branes wrapped on Riemann surfaces or complex curves, effectively producing a broad array of $\mathcal{N}=1$ SCFTs.
2. Central Charge Calculations via Anomaly Polynomials: Verification of these solutions as viable SCFTs involves calculating their central charges derived from the anomaly polynomial for the M5-branes, ensuring these are integrable and consistent with expected $SU(N)$ gauge-theoretic duals. This is conducted under assumptions related to the absence of accidental symmetries.
3. Holographic RG Flows: Numerical solutions are presented detailing flows from the UV to IR, corresponding to the RG flows in the boundary CFTs, supporting the dynamic realization of these theories. Such studies confirm the emergence of described fixed points, further evidenced by complementary holographic analyses.
4. Generalized Quiver Constructions: The paper describes methodologies to construct these SCFTs through novel quiver gauge theories employing $T_N$ building blocks. These generalized quivers extend the known range of SCFTs and underpin the theory's connections to $N=2$ structures, while permitting symmetry breaking to $N=1$ cases.

Numerical Results and Implications

Numerically, the construction yields the central charges aligning with theoretical expectations under large $N$ limits, with results carefully detailing dependences on the degrees of line bundles involved in the compactifications. The findings allow novel insights into the counting of marginal operators and underscore discrepancies due to intricate chiral ring relations, suggesting areas for further exploration.

Future Research Directions

The paper delineates a new class of M5-brane theories enhancing the comprehension of SCFT landscapes. Foreseen research pathways include understanding punctured surfaces' impacts, additional embeddings, and potential duality webs within these frameworks. Moreover, the implications for broader non-Lagrangian field theories in lower dimensions are projected to spur further research, possibly extending toward theories compactified on associative cycles in $G_2$ manifolds.

In conclusion, the delineation of these new SCFTs, both theoretically and holographically, offers an enriched palette of field theories in four dimensions, serving both as a robust framework for special supersymmetry scenarios and a groundwork for developing complex interconnected gauge theories in the landscape of string and M-theory. The paper showcases both the elegance and potential intricacies inherent in leveraging M5-brane dynamics to inform four-dimensional gauge theory formulations.