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Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge . Mathematically, branes can be represented within categories , and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry .
The arrangement of D-branes constricts the types of string states which can exist in a system. For example, if we have two parallel D2-branes, we can easily imagine strings stretching from brane 1 to brane 2 or vice versa. (In most theories, strings are oriented objects: each one carries an "arrow" defining a direction along its length.) The ...
For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p, these are called p-branes. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics.
The M2-brane solution can be found [1] by requiring () symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three-form gauge field which, in isotropic coordinates, can be written as
The Calabi–Yau manifolds used in string theory are of interest in pure mathematics, and mirror symmetry allows mathematicians to solve problems in enumerative algebraic geometry, a branch of mathematics concerned with counting the numbers of solutions to geometric questions.
As such, it can be described explicitly as a black brane solution [1] to eleven-dimensional supergravity, the low-energy limit of M-theory. In particular, it carries a magnetic charge under the 3-form gauge field of the 11-dimensional supergravity multiplet. The M5-brane is the electric-magnetic dual of the M2-brane.
Investigating theories of higher dimensions often involves looking at the 10 dimensional superstring theory and interpreting some of the more obscure results in terms of compactified dimensions. For example, D-branes are seen as compactified membranes from 11D M-theory. Theories of higher dimensions such as 12D F-theory and beyond produce other ...
The worldvolume theory on a stack of N D2-branes is the string field theory of the open strings of the A-model, which is a U(N) Chern–Simons theory. The fundamental topological strings may end on the D2-branes. While the embedding of a string depends only on the Kähler form, the embeddings of the branes depends entirely on the complex structure.