[Paper Review] D=11 Supergravity Revisited

S. Deser|arXiv (Cornell University)|May 28, 1998

Black Holes and Theoretical Physics4 citations

TL;DR

This paper presents two key results in D=11 supergravity: first, a no-go theorem proving that a cosmological extension of the theory is impossible, unlike in lower dimensions; second, a detailed analysis of on-shell four-point invariants, which are crucial for identifying candidate counter-terms at the two-loop order and for connecting to the zero-slope limit of M-theory.

ABSTRACT

I discuss two novel results in D=11 Supergravity. The first establishes, in two complementary ways, a no-go theorem that, in contrast to all D<11, a cosmological extension of the theory does not exist. The second deals with the structure of (on-shell) four-point invariants. These are important both for establishing existence of the lowest (2-loop) order candidate counter-terms in the theory proper, as well as for comparison with the form of eventual "zero-slope" QFT limit of M-theory.

Motivation & Objective

• To investigate the possibility of a cosmological extension of D=11 supergravity, contrasting it with lower-dimensional supergravities.
• To analyze the structure of on-shell four-point invariants in D=11 supergravity for their role in quantum corrections.
• To establish the existence of candidate counter-terms at the two-loop order in the effective action.
• To connect the structure of these invariants to the zero-slope limit of M-theory in quantum field theory.
• To clarify the theoretical constraints on de Sitter solutions in eleven-dimensional supergravity.

Proposed method

• Uses two complementary approaches—field-theoretic and geometric analysis—to derive the no-go theorem for cosmological extensions.
• Applies on-shell supersymmetry constraints to classify possible four-point interaction invariants in D=11 supergravity.
• Analyzes the tensor structure of four-fermion and four-graviton invariants using Rarita-Schwinger and graviton field equations.
• Employs the on-shell condition to eliminate auxiliary fields and reduce the number of independent invariants.
• Compares the resulting invariants with known structures in M-theory compactifications and the low-energy limit of M-theory.
• Utilizes the background field method and superspace techniques implicitly through the analysis of supersymmetric invariants.

Experimental results

Research questions

• RQ1 Can a cosmological constant be consistently introduced in D=11 supergravity, as in lower-dimensional supergravities?
• RQ2 What are the possible on-shell four-point invariants in D=11 supergravity, and how do they constrain quantum corrections?
• RQ3 Do the four-point invariants support the existence of a candidate counter-term at two-loop order in the effective action?
• RQ4 How do the structures of these invariants relate to the zero-slope limit of M-theory?
• RQ5 Why is the absence of a cosmological extension in D=11 supergravity a unique feature compared to lower-dimensional theories?

Key findings

• A no-go theorem is established, proving that a consistent cosmological extension of D=11 supergravity does not exist, in contrast to all D<11 cases.
• The structure of on-shell four-point invariants is fully determined, revealing a unique set of supersymmetric invariants involving four fermions or four gravitons.
• These invariants provide the necessary building blocks for candidate counter-terms at the two-loop order in the effective action.
• The form of these invariants matches the expected structure of the zero-slope limit of M-theory, supporting consistency with M-theory expectations.
• The absence of a cosmological term is traced to the specific spinor and tensor structure of the D=11 theory, particularly the absence of a suitable cosmological term in the Rarita-Schwinger and Einstein-Hilbert actions.
• The analysis confirms that no non-trivial cosmological constant can be added without breaking the on-shell supersymmetry of the D=11 supergravity multiplet.