E. Onofri

On the positivity of the effective action in a theory of random surfaces

AbstractIt is shown that the functional

A note on coherent state representations of Lie groups

S[\eta ] = \frac{1}{{24\pi }}\int {\left( {\frac{1}{2}\left| {\nabla \eta } \right|^2 + 2\eta } \right)d\mu _0 }

A differential equation for a four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

, defined onC∞ functions on the two-dimensional sphere, satisfies the inequalityS[η]≧0 if η is subject to the constraint

Planar Limit for SU(

\int {(e^\eta - 1)d\mu _0 = 0}

) Symmetric Quantum Dynamical Systems

. The minimumS[η]=0 is attained at the solutions of the Euler-Lagrange equations. The proof is based on a sharper version of Moser-Trudingers inequality (due to Aubin) which holds under the additional constraint