Fractional M2-branes (0807.4924v3)

Abstract: We consider two generalizations of the N=6 superconformal Chern-Simons-matter theories with gauge group U(N)xU(N). The first generalization is to N=6 superconformal U(M)xU(N) theories, and the second to N=5 superconformal O(2M)xUSp(2N) and O(2M+1)xUSp(2N) theories. These theories are conjectured to describe M2-branes probing C^4/Z_k in the unitary case, and C^4/\hat{D}_k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M-N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.

• The paper extends N=6 superconformal field theories by formulating U(M)xU(N) and O(M)xUSp(2N) models that introduce fractional M2-branes characterized by the rank difference |M-N|.
• The authors employ discrete torsion and orientifolding techniques to establish novel AdS/CFT dualities linking field theory configurations with supergravity backgrounds.
• The study elucidates gauge group equivalences and parity transformations that offer promising avenues for exploring integrable models and quantum supersymmetric vacua.

Overview of "Fractional M2-branes"

The paper "Fractional M2-branes" by Ofer Aharony, Oren Bergman, and Daniel Louis Jafferis investigates advanced topics in string theory and M-theory by expanding on three-dimensional superconformal field theories, particularly related to M2-branes. The paper focuses on two primary generalizations of N=6 superconformal Chern-Simons-matter theories and examines their implications within string theory dualities.

M2-branes, which are fundamental components in M-theory, are explored from the perspective of their fractional counterparts in certain singularity configurations. The authors propose that these generalizations provide alternative frameworks for understanding the dynamics of M2-branes on various orbifold backgrounds.

Key Generalizations

1. U(M) x U(N) Theories:
   • The investigation extends the N=6 superconformal U(N) x U(N) theories into U(M) x U(N) configurations. The symmetry breaking of this formulation introduces fractional M2-branes characterized by the absolute difference in rank, |M-N|.
   • Classical and quantum aspects of these generalized models are evaluated, emphasizing unitary superconformal field theory conditions for |M-N| ≤ |k|, where k denotes the level of the Chern-Simons term.
2. O(M) x USp(2N) Theories:
   • The second generalization involves theories introduced via orientifolding techniques, leading to O(M) x USp(2N) configurations. These theories are posited to describe M2-branes at a C^4/D_k singularity.

Theoretical Implications and Dualities

AdS/CFT Correspondence

The paper makes significant contributions to the AdS/CFT duality framework by presenting new supergravity backgrounds sourced from fractional M2-branes. The U(M) x U(N) theories are conjectured to be dual to M-theory on AdS_4 x S^7/Z_k with additional discrete torsion, providing novel examples of extended superconformal symmetries in these dualities.

String and M-Theory Realizations

The quantum mechanical constraints of these models imply profound insights into string theory phenomena, such as torsion flux, orbifold discrete torsion, and orientifold effects, thereby creating novel string theory backgrounds. The transition to type IIA string theory is discussed, detailing its relevance under specific parameter regimes, and showing how fractional M2-branes manifest as D4-branes in these backgrounds.

Specific Claims and Results

The paper discusses intricate relationships between field theory models and their gravitational counterparts:

• Discrete Torsion: Activation of discrete torsion in M-theory affects both the field theories' moduli spaces and their dual supergravity backgrounds.
• Gauge Group Equivalence: Dualities indicate that various gauge group configurations exhibit equivalent physical behaviors, supported by level-rank duality arguments.
• Parity Transformations: The analogous parity transformations in type IIA highlight unifying characteristics across varying configurations.

Speculations and Future Directions

The findings present rich fields for future inquiry:

• Investigating these branes' properties in the 't Hooft limit may yield integrable models akin to those discovered in previous string theory research.
• Analysis of these models in non-parity invariant configurations holds potential applications in condensed matter physics.
• Potential exploration into the existence and properties of supersymmetric vacua at the quantum level inspires further theoretical development.

This paper offers a comprehensive venture into generalized superconformal Chern-Simons-matter theories, accentuating the capabilities of fractional M2-branes to probe the intricate interplay between high-dimensional supergravity theories and low-dimensional field theories. The discussions and results provide significant hypothesizing about future developments in the understanding and application of these theoretical constructs in the field of high-energy physics.