Distance and de Sitter conjectures on the Swampland
Hirosi Ooguri (Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Japan, Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, USA); Eran Palti (Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munchen, Germany); Gary Shiu (Department of Physics, University of Wisconsin-Madison, Madison, USA); Cumrun Vafa (Jefferson Physical Laboratory, Harvard University, Cambridge, USA)
Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Bousso's covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine–Seiberg problem.
