Swampland conjectures on quantum gravity theories

5 problems

• Bound on scalar potential slopes in asymptotic field space

  Open

  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.

• Is every infinite-distance limit a decompactification or a weak string

  Partially resolved

  Some parameters of string theory can be pushed infinitely far, and then a tower of particles becomes very light. A conjecture says the light tower is always either extra dimensions opening up or a new weakly interacting string, with no third option.

• Absence of global symmetries in quantum gravity outside anti-de Sitter

  Partially resolved

  It is believed that quantum gravity forbids exact global symmetries, symmetries not tied to a force. This is proven only for spaces with negative vacuum energy and in perturbative string theory.

• Sharp lower bound on the exponent in the distance conjecture

  Open

  When a parameter of string theory is moved through a distance $D$, a tower of particles becomes lighter by a factor $\exp(-\lambda D)$. The conjecture is that $\lambda$ can never be smaller than a fixed number set only by the number of spacetime dimensions.

• Does the weak gravity conjecture hold in all quantum gravity theories

  Partially resolved

  The conjecture says gravity must be the weakest force: some particle must feel electric repulsion stronger than its gravitational attraction. Whether this is a law of all quantum gravity theories is unproven.