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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.
Fundamental theorem of algebra – states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.
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.
Such stability conditions were introduced in a rudimentary form by Michael Douglas called -stability and used to study BPS B-branes in string theory. [1] This concept was made precise by Bridgeland, who phrased these stability conditions categorically, and initiated their study mathematically.
Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .
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.
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.