Beyond : gravitational couplings to matter and the stress tensor OPE
Dec 13, 2017Citations per year
Abstract: (Springer)
We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large N CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, , where is a single-trace primary. We show that this follows from a suppression of by powers of the higher spin gap, Δ, dual to the bulk mass scale of higher spin particles, and explain why is a more sensitive probe of Δ than a − c in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings where have spin s ≤ 2, we are led to propose that 1/Δ is the CFT “dual” of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on TT couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of 〈TTT〉 in the free-field basis are nonzero in interacting CFTs.Note:
- 42+25 pages. v2: added refs, minor changes
- AdS-CFT Correspondence
- Conformal Field Theory
- Field Theories in Higher Dimensions
- Gauge-gravity correspondence
- field theory: conformal
- spin: high
- tensor: energy-momentum
- particle: spin
- spin: operator
- mass: scale
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