  We analyze four-dimensional quantum field theories with continuous 2-group
global symmetries. At the level of their charges such symmetries are identical
to a product of continuous flavor or spacetime symmetries with a 1-form global
symmetry $U(1)^{(1)}_B$, which arises from a conserved 2-form current
$J_B^{(2)}$. Rather, 2-group symmetries are characterized by deformed current
algebras, with quantized structure constants, which allow two flavor currents
or stress tensors to fuse into $J_B^{(2)}$. This leads to unconventional Ward
identities, which constrain the allowed patterns of spontaneous 2-group
symmetry breaking and other aspects of the renormalization group flow. If
$J_B^{(2)}$ is coupled to a 2-form background gauge field $B^{(2)}$, the
2-group current algebra modifies the behavior of $B^{(2)}$ under background
gauge transformations. Its transformation rule takes the same form as in the
Green-Schwarz mechanism, but only involves the background gauge or gravity
fields that couple to the other 2-group currents. This makes it possible to
partially cancel reducible 't Hooft anomalies using Green-Schwarz counterterms
for the 2-group background gauge fields. The parts that cannot be cancelled are
reinterpreted as mixed, global anomalies involving $U(1)_B^{(1)}$ and receive
contributions from topological, as well as massless, degrees of freedom.
Theories with 2-group symmetry are constructed by gauging an abelian flavor
symmetry with suitable mixed 't Hooft anomalies, which leads to many simple and
explicit examples. Some of them have dynamical string excitations that carry
$U(1)_B^{(1)}$ charge, and 2-group symmetry determines certain 't Hooft
anomalies on the world sheets of these strings. Finally, we point out that
holographic theories with 2-group global symmetries have a bulk description in
terms of dynamical gauge fields that participate in a conventional
Green-Schwarz mechanism.
