All AdS_7 solutions of type II supergravity (1309.2949v2)

Abstract: In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. In this paper, we find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3.

• The paper classifies AdS7×M3 solutions in type IIA supergravity with non-zero Romans mass using a pure spinor formalism that avoids conventional Ansätze.
• It demonstrates that no analogous AdS7 solutions exist in type IIB, highlighting the unique role of the Romans mass in type IIA.
• The study incorporates numerical solutions with D8-brane sources, yielding regular metrics that reflect the R-symmetry of the dual conformal field theory.

Overview of AdS$_7$ Solutions in Type II Supergravity

The paper presents a classification of AdS$_7\times M_3$ solutions in type II supergravity. It specifically addresses the existence of these solutions within type IIA supergravity with a non-zero Romans mass and excludes solutions in type IIB. The methodology involves using a pure spinor formalism reminiscent of generalized complex geometry. This approach circumvents the necessity of making an Ansatz by providing a unique determination of the metric and fluxes, up to solving ordinary differential equations (ODEs).

Key Findings

1. Existence in Type IIA with Romans Mass:
   • The paper reveals that AdS$_7\times S^4$ and its orbifolds are the sole supersymmetric AdS$_7$ solutions in M-theory. However, in type IIA supergravity with a non-zero Romans mass, new supersymmetric solutions exist.
   • The research utilizes a framework akin to generalized complex geometry and pure spinor methods to derive these solutions without resorting to any specific Ansatz.
2. Inapplicability to Type IIB:
   • This paper determines that no new AdS$_7\times M_3$ solutions exist under type IIB supergravity contexts, emphasizing the uniqueness of the findings exclusive to type IIA with non-zero Romans mass.
3. Metric Construction and R-Symmetry:
   • The metric on $M_3$ is conceptually defined as an $S^2$ fibration over an interval, aligning with the Sp(1) R-symmetry of the dual conformal field theory (CFT). This symmetry facilitates a deeper understanding of the solution structure in relation to theoretical physics perspectives on holography.
4. Numerical Solutions with D8-Branes:
   • By integrating D8-brane sources, the paper establishes numerical solutions where $M_3$ is topologically analogous to an $S^3$. The presence of D8-branes introduces novel considerations in the solution dynamics, especially regarding the balance between electric and gravitational forces.

Implications and Future Directions

• Theoretical Significance: The identification of these new solutions advances the understanding of six-dimensional superconformal field theories and their gravitational duals, enriching the landscape of possible physical interactions and symmetries in higher dimensions.
• Use in Holography: These solutions contribute significantly to the toolkit available for exploring holographic principles, potentially leading to new interpretations of duality and symmetry breaking in lower-dimensional quantum field theories.
• Application of Pure Spinor Methods: The methodology showcases the potential of pure spinor formalism and generalized complex geometry in deriving significant results without conventional Assumptions, hinting at broader applications across various contexts in theoretical physics.
• Numerical Analysis and Regularity: The rigorous numerical analysis exemplified by the paper demonstrates the practical considerations required when balancing flux quantization and supersymmetry. This precursor for larger numerical methods provides insight into how singularities are handled and resolved in supergravity solutions.

These findings point to a rich field of exploration for AdS solutions with expansive implications both theoretically and in prospects of new mathematical methods in high-energy physics. Future research could further explore the possibility of other analogous solutions in different contexts or dimensions, potentially expanding the understanding of string theory and M-theory landscapes.