Closed strings in a class of pp-wave spacetimes and the memory effect

We study closed string evolution in the pp-wave spacetime assuming different pulse shapes (square and sech-squared) in the exact gravitational wave metric. It is shown that the shape of a circular closed string deforms permanently, after the pulse has departed. The worldsheet geometry also displays characteristic permanent changes caused by the gravitational wave pulse. The above effects collectively demonstrate features akin to what is known as `memory’ in gravitational wave physics.