Irrational Monodromies of Vacuum Energy
  We present a theory with axion flux monodromies coupled to gravity, that
reduces to the local vacuum energy sequester below the axion mass scales. If
the axion potentials include a term generated by nonperturbative couplings to
gauge sectors, with a decay constant incommensurate with monodromy periods, the
low energy potential germinates a landscape of irrational axion vacua, with
arbitrarily small cosmological constants. The sensitivity of the values of
cosmological constants to unknown UV physics can be greatly reduced. The
variation of the cosmological constant in each vacuum, from one order in
perturbation theory to the next, can be much smaller than the na\"ive cutoff.
The nonperturbative transitions in the early universe between the vacua
populate this landscape, similar to the case of irrational axion. In such a
landscape of vacua a small cosmological constant can naturally emerge.
