Search results
Results from the WOW.Com Content Network
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 ...
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
That type of solution would be called a black p-brane. [1] In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. [2] With the notion of a horizon in mind as well as identifying points as zero-branes, a generalization of a black hole is a black p-brane. [3]
Some important examples of Freund–Rubin compactification come from looking at the behavior of branes in string theory.Similar to the way that coupling to the electromagnetic field stabilizes electrically charged particles, the presence of antisymmetric tensor fields of various rank in a string theory stabilizes branes of various dimensions.
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.
In this section we present the dHYM equation as explained in the mathematical literature by Collins-Xie-Yau. [3]The deformed Hermitian–Yang–Mills equation is a fully non-linear partial differential equation for a Hermitian metric on a line bundle over a compact Kähler manifold, or more generally for a real (,)-form.
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.