N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds

Abstract: We explore further our recent generalization of the $\mathcal{N}=4$ superconformal Chern-Simons theories of Gaiotto and Witten. We find and construct explicitly theories of enhanced $\mathcal{N}=5$ or 6 supersymmetry, especially $\mathcal{N}=5$, $Sp(2M)\times O(N)$ and $\mathcal{N}=6$, $Sp(2M)\times O(2)$ theories. The $U(M)\times U(N)$ theory coincides with the $\mathcal{N}=6$ theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We argue that the $\mathcal{N}=5$ theory with $Sp(2N)\times O(2N)$ gauge group can be understood as an orientifolding of the ABJM model with $U(2N)\times U(2N)$ gauge group. We briefly discuss the Type IIB brane construction of the $\mathcal{N}=5$ theory and the geometry of the M-theory orbifold.

• The paper introduces enhanced supersymmetry models by extending N=4 to N=5 and N=6 Chern-Simons theories for M2-brane applications.
• It applies orientifolding and algebraic deformation techniques to refine gauge group configurations, aligning results with theoretical predictions.
• The research advances understanding of superconformal field theories and establishes frameworks that support further exploration in string theory.

An Overview of Enhanced Superconformal Chern-Simons Theories and M2-Branes

In this paper, the authors extend existing frameworks in the domain of superconformal field theories. They explore the enhancement of supersymmetry in N=4 superconformal Chern-Simons-matter theories, proposing new models including N=5, Sp(2M) × O(N), and N=6, Sp(2M) × O(2) theories. Notably, these models are presented as refinements of existing work in this field, closely examining the properties of gauge groups and their relationships with M2-branes.

Key Constructs and Models

The research introduces a series of superconformal Chern-Simons theories with enhanced supersymmetry. The authors focus on:

• N=5 Theories: Specifically, theories with Sp(2M) × O(N) gauge groups. The authors explore an orientifolding of the ABJM model to understand the Sp(2N) × O(2N) gauge group configuration.
• N=6 Theories: These include models with U(M) × U(N) and Sp(2M) × O(2) gauge groups. Particularly, they illustrate that the U(M) × U(N) theory coincides with the N=6 ABJM model known for its applications to M2-branes.

Theoretical Implications and Numerical Results

The paper draws on prior work, particularly referencing the ABJM model that connects with M-theory geometry. The theories extend classical configurations through technical constructs such as orientifolding, providing mechanisms for enhancing supersymmetry beyond the N=4 baseline. Through explicit calculations, the authors demonstrate that their constructed models align with theoretical predictions, thereby contributing to the foundational understanding of superconformal field theories.

The research further highlights the Algebraic consistency of these models. Enhanced supersymmetry conditions are substantiated via algebraic identities and deformation theory, ensuring the maintenance of dual properties such as those hypothesized in the context of M-theory duals.

Practical Implications

The implications of this work are significant, particularly in the field of theoretical physics and string theory. By establishing predictions related to M2-brane configurations, the findings have potential applications in constructing viable string theory models. The adherence to known dualities, particularly in relation to Type IIB string theory and M-theory, opens pathways for deeper exploration.

Future Directions

Future research might pivot towards broader classifications of these theories, dissecting potential N=7 and N=8 configurations and their geometric dualities. Further studies could also focus on non-supersymmetric generalizations and their contribution to the AdS/CFT correspondence. Additionally, exploring the conformity of these models with integrability and partition functions would provide more holistic insights into the underlying geometry of these physical models.

In conclusion, the paper augments current understandings in the domain of superconformal Chern-Simons theories, offering models with enhanced supersymmetry. Through rigorous mathematical formulations and potential implications in higher string theories, it sets the stage for continuous exploration within the landscape of theoretical physics.