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 natural phenomena. This is in contrast to experimental physics, which uses experim ...

, boundary conformal field theory (BCFT) is a

conformal field theory A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes ...

defined on a

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...

with a boundary (or boundaries). Different kinds of boundary conditions for the fields may be imposed on the fundamental fields; for example,

Neumann boundary condition In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative appl ...

Dirichlet boundary condition In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential ...

is acceptable for free

boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...

ic fields. BCFT was developed by

John Cardy John Lawrence Cardy FRS (born 19 March 1947, England)Guggenheim Foundation: Annual Report 1985. is a British-American theoretical physicist at the University of California, Berkeley. He is best known for his work in theoretical condensed matter ...

. In the context of

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

, physicists are often interested in two-dimensional BCFTs. The specific types of boundary conditions in a specific CFT describe different kinds of

D-branes In string theory, D-branes, short for ''Dirichlet membrane'', 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 Jin Dai, Leigh, and Polchi ...

. BCFT is also used in condensed matter physics - it can be used to study boundary critical behavior and to solve quantum impurity models.

See also

References

Further reading