In physics , a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations. One analogy takes a person that can't go everywhere in an infinite field of graph paper, and this restriction doesn't change when the graph is moved a certain way that makes it smooth.
In string theory , D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions , after which they are named. D-branes were discovered by Dai, Leigh and Polchinski , and independently by Hořava in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity , a discovery that triggered the Second Superstring Revolution and led to both holographic and M-theory dualities.