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Open strings attached to a pair of D-branes. In string theory, a string may be open (forming a segment with two endpoints) or closed (forming a closed loop). D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane.
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 ...
[6] [7] Gogberashvili also showed that the four-dimensionality of the Universe is the result of the stability requirement found in mathematics since the extra component of the Einstein field equations giving the confined solution for matter fields coincides with one of the conditions of stability.
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.
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
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.
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.
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.