In theoretical physics

Theoretical physics

Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, the Chan–Paton factor is a multivalued index associated with the endpoints of an open string. An open string can be interpreted as a fluxtube connecting a quark

Quark

A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...

 and its antiparticle

Antiparticle

Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...

. The two Chan–Paton factors make the string transform as a tensor

Tensor

Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

 under a gauge group whose charges are carried by the endpoints of the strings.

After the Second Superstring Revolution in 1995, Chan–Paton factors are interpreted as labels that identify which (spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

-filling) D-branes the stringy endpoints are attached to. The Chan–Paton factors have become a special case of a more general concept.