Higher d Eisenstein series and a duality-invariant distance measure

A bstract The Petersson inner product is a natural inner product on the space of modular invariant functions. We derive a formula, written as a convergent sum over elementary functions, for the inner product E s ( G , B ) of the real analytic Eisenstein series Eₛ(τ ,τ ̄) and a general point in Narain moduli space. We also discuss the utility of the Petersson inner product as a distance measure on the space of 2d CFTs, and apply our procedure to evaluate this distance in various examples.