Emergence of quantum-field theory in causal diamonds (in EN)
The experimental successes of quantum-field theory do not justify using it to describe even a finite fraction of the entanglement entropy of a causal diamond with its exterior, in the limit of large diamonds. Susskind and Uglum and Jacobson conjectured that this divergent entropy could be thought of as a renormalization of Newton’s constant in the Bekenstein–Hawking formula, if we applied that formula to arbitrary causal diamonds. Jacobson showed that this leads to a derivation of the null projection of Einstein’s equations as the hydrodynamic equations of the area law for arbitrary diamonds, a derivation which has the added virtue of demonstrating that the cosmological constant is not an energy density. Using a gauge choice adapted to causal diamond boundaries, we revisit arguments of Carlip and Solodukhin that the proper theory of near horizon states is a (cut-off) (1 + 1)-dimensional conformal field theory, with central charge proportional to the transverse area. This leads to a universal formula for fluctuations of the modular Hamiltonian of a diamond, which we argue is compatible with the explanation of the temperature of de Sitter space in terms of an identification between localized energy and the number of constrained q-bits of the holographic degrees of freedom.
- Research Organization:
- Rutgers Univ., Piscataway, NJ (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- SC0010008
- OSTI ID:
- 2580069
- Journal Information:
- International Journal of Modern Physics D, Journal Name: International Journal of Modern Physics D Journal Issue: 14 Vol. 32; ISSN 0218-2718
- Publisher:
- World Scientific
- Country of Publication:
- United States
- Language:
- EN
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