Pure Anti-de Sitter Supergravity and the Conformal Bootstrap

Area of Science:

• Theoretical physics
• Quantum gravity
• String theory

Background:

• Maximal supergravity on anti-de Sitter space (AdS) is holographically dual to conformal field theories (CFTs).
• Exotic CFTs, with only the stress tensor as a light single trace operator, contrast with standard CFTs arising from string theory compactifications.

Purpose of the Study:

• To compute the one-loop correction to graviton scattering in maximal supergravity on AdS.
• To compare these results with conformal bootstrap bounds in the large central charge limit for exotic CFTs.

Main Methods:

• Calculation of one-loop corrections in maximal supergravity on AdS in d+1 dimensions (d=3, 4, 6).
• Utilizing a small Planck length expansion, dual to the large central charge expansion in the corresponding CFT.

Main Results:

• The one-loop correction to the graviton correlator in pure AdS theory saturates the most general nonperturbative conformal bootstrap bounds for d=3, 4, and 6.
• One-loop corrections for CFTs with string and M-theory duals fall within the allowed bootstrap region.

Conclusions:

• The findings support the holographic duality between maximal supergravity on AdS and exotic CFTs.
• The study provides strong evidence for the validity of conformal bootstrap bounds in constraining quantum field theories.