Effective Field Theory, Black Holes, and the Cosmological Constant

Effective Field Theory, Black Holes, and the Cosmological Constant

31 Mar 1999 | Andrew G. Cohen, David B. Kaplan, and Ann E. Nelson
The authors explore the implications of black hole thermodynamics and the Bekenstein bound on the validity of effective field theories (EFTs). They propose a relationship between the ultraviolet (UV) and infrared (IR) cutoffs in EFTs, suggesting that an EFT should be a good description of nature if these cutoffs satisfy a specific constraint. This constraint, \( L^3 \Lambda^4 \lesssim L M_P^2 \), is more restrictive than the Bekenstein bound and excludes states within their Schwarzschild radius. The authors argue that this constraint does not conflict with experimental successes of quantum field theory but explains why conventional EFT estimates of the cosmological constant fail. The paper discusses the cosmological constant problem, suggesting that the discrepancy between the observed cosmological constant and the quantum contribution can be resolved without fine-tuning. By imposing the proposed IR constraint, the quantum contribution to the vacuum energy density is consistent with current bounds, eliminating the need for fine-tuning. The authors also explore the impact of these constraints on precision experiments, such as the electron's $(g-2)$, and show that the minimal correction to $(g-2)$ is larger than the contribution from the top quark. Finally, the authors consider the implications for gauge coupling unification and the renormalization group flow of vacuum energy, concluding that the fine-tuning problem associated with the cosmological constant is not as severe as previously thought. They emphasize that the experimental success of quantum field theory is maintained as long as the UV and IR cutoffs satisfy the proposed constraint.The authors explore the implications of black hole thermodynamics and the Bekenstein bound on the validity of effective field theories (EFTs). They propose a relationship between the ultraviolet (UV) and infrared (IR) cutoffs in EFTs, suggesting that an EFT should be a good description of nature if these cutoffs satisfy a specific constraint. This constraint, \( L^3 \Lambda^4 \lesssim L M_P^2 \), is more restrictive than the Bekenstein bound and excludes states within their Schwarzschild radius. The authors argue that this constraint does not conflict with experimental successes of quantum field theory but explains why conventional EFT estimates of the cosmological constant fail. The paper discusses the cosmological constant problem, suggesting that the discrepancy between the observed cosmological constant and the quantum contribution can be resolved without fine-tuning. By imposing the proposed IR constraint, the quantum contribution to the vacuum energy density is consistent with current bounds, eliminating the need for fine-tuning. The authors also explore the impact of these constraints on precision experiments, such as the electron's $(g-2)$, and show that the minimal correction to $(g-2)$ is larger than the contribution from the top quark. Finally, the authors consider the implications for gauge coupling unification and the renormalization group flow of vacuum energy, concluding that the fine-tuning problem associated with the cosmological constant is not as severe as previously thought. They emphasize that the experimental success of quantum field theory is maintained as long as the UV and IR cutoffs satisfy the proposed constraint.
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