We study special cycles on integral models of Shimura varieties
associated with unitary similitude groups of signature (n.1, 1).We construct
an arithmetic theta lift from harmonic Maass forms of weight 2 . n to the
arithmetic Chow group of the integral model of a unitary Shimura variety,
by associating to a harmonic Maass form f a linear combination of Kudla–
Rapoport divisors, equipped with the Green function given by the regularized
theta lift of f . Our main result is an equality of two complex numbers: (1)
the height pairing of the arithmetic theta lift of f against a CM cycle, and (2)
the central derivative of the convolution L-function of a weight n cusp form
(depending on f ) and the theta function of a positive definite hermitian lattice
of rank n − 1. When specialized to the case n = 2, this result can be viewed
as a variant of the Gross–Zagier formula for Shimura curves associated to
unitary groups of signature (1, 1). The proof relies on, among other things, a
new method for computing improper arithmetic intersections.