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Title: Bound on scalar potential slopes in asymptotic field space
Plain: A conjecture says that wherever string theory is weakly coupled, the vacuum energy must slope steeply downhill. Whether this holds, and how steep the slope must be, is unknown.
Precise: The refined de Sitter conjecture (2018) states that in asymptotic, weakly coupled regions of moduli space, $\mid \operatorname{grad} V \mid \ge c V/M_{P}$ or min eigenvalue(grad grad V) <= -c' V/M_P^2 with c, c' of order 1. Determine whether this holds in all asymptotic regions of string moduli spaces and find the optimal value of c in d dimensions.
Settled by: A proof over all asymptotic limits of string compactifications with the sharp constant, or an explicit asymptotic counterexample.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: Candidate sharp values are $c = 2/\sqrt{(d-1)(d-2)}$ from the trans-Planckian censorship conjecture (Bedroya, Vafa 2019) and $c = 2/\sqrt{d-2}$ (Rudelius 2021), tested in many but not all asymptotic limits (2021-2025).
Posed since: 2018