  We search for stochastic gravitational wave background emitted from cosmic
strings using the Parkes Pulsar Timing Array data over 15 years. While we find
that the common power-law excess revealed by several pulsar timing array
experiments might be accounted for by the gravitational wave background from
cosmic strings, the lack of the characteristic Hellings-Downs correlation
cannot establish its physical origin yet. The constraints on the cosmic string
model parameters are thus derived with conservative assumption that the common
power-law excess is due to unknown background. Two representative cosmic string
models with different loop distribution functions are considered. We obtain
constraints on the dimensionless string tension parameter
$G\mu<10^{-11}\sim10^{-10}$, which is more stringent by two orders of magnitude
than that obtained by the high-frequency LIGO-Virgo experiment for one model,
and less stringent for the other. The results provide the chance to test the
Grand unified theories, with the spontaneous symmetry breaking scale of $U(1)$
being two-to-three orders of magnitude below $10^{16}$ GeV. The pulsar timing
array experiments are thus quite complementary to the LIGO-Virgo experiment in
probing the cosmic strings and the underlying beyond standard model physics in
the early Universe.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory