theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

, the Chan–Paton factor (named after Jack E. Paton and Hong-Mo Chan)H. M. Chan, J. E. Paton, "Generalized Veneziano Model with Isospin", ''Nucl. Phys''. B10, 516 (1969). is a multivalued index associated with the endpoints of an open string. An open string can be interpreted as a flux tube connecting a

quark A quark () is a type of 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 nucleus, atomic nuclei ...

and its

antiparticle In particle physics, every type of particle of "ordinary" matter (as opposed to antimatter) is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the ...

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

tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...

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

isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetr ...

factors to be added to the Veneziano model is known as Chan–Paton rules or Chan–Paton method. After the

second superstring revolution The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum ...

in 1995, Chan–Paton factors are interpreted as labels that identify which (

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

-filling)

D-branes In string theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open string (physics), strings can end with Dirichlet boundary conditions, after which they are named. D-branes are typically classified by their ...

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

References

String theory {{string-theory-stub