Consider a random matrix of the form Wn=Mn+Dn, where Mn
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is a Wigner matrix and
Dn
is a real deterministic diagonal matrix (
Dn
is commonly referred to as an external source in the mathematical physics literature). We study the universality of the local eigenvalue statistics of
Wn
for a general class of Wigner matrices
Mn
and diagonal matrices
Dn
. Unlike the setting of many recent results concerning universality, the global semicircle law fails for this model. However, we can still obtain the universal sine kernel formula for the correlation functions. This demonstrates the remarkable phenomenon that local laws are more resilient than global ones. The universality of the correlation functions follows from a four moment theorem, which we prove using a variant of the approach used earlier by Tao and Vu.