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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a

superstring theory Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string t ...

in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

in 1996. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities and T-dualities. This effect can be expanded to string theory, 2 strings cross together resulting in the creation or destruction of a third string.

The original effect

The original Hanany–Witten transition was discovered in type IIB superstring theory in flat, 10-dimensional

Minkowski space In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a ...

. They considered a configuration of NS5-branes, D5-branes and D3-branes which today is called a Hanany–Witten brane cartoon. They demonstrated that a subsector of the corresponding open string theory is described by a 3-dimensional Yang–Mills gauge theory. However they found that the string theory space of solutions, called the

moduli space In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme (mathematics), scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of suc ...

, only agreed with the known Yang-Mills moduli space if whenever an NS5-brane and a D5-brane cross, a D3-brane stretched between them is created or destroyed. They also presented various other arguments in support of their effect, such as a derivation from the worldvolume Wess–Zumino terms. This proof uses the fact that the

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phe ...

from each brane renders the

action Action may refer to: * Action (philosophy), something which is done by a person * Action principles the heart of fundamental physics * Action (narrative), a literary mode * Action fiction, a type of genre fiction * Action game, a genre of video gam ...

of the other brane ill-defined if one does not include the D3-brane.

The S-rule

Furthermore, they discovered the S-rule, which states that in a supersymmetric configuration the number of D3-branes stretched between a D5-brane and an NS5-brane may only be equal to 0 or 1. Then the Hanany-Witten effect implies that after the D5-brane and the NS5-brane cross, if there was a single D3-brane stretched between them it will be destroyed, and if there was not one then one will be created. In other words, there cannot be more than one D3 brane that stretches between a D5 brane and an NS5 brane.

Generalizations

(p,q) 5-branes

More generally, NS5-branes and D5-branes may form bound states known as (p,q) 5-branes. The above argument was extended i
Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories
to the case of a (p,q) and a (p',q') 5-brane which cross. The authors found that the number of D3-branes created or destroyed must be equal to pq'-p'q. Furthmore they showed that this leads to a generalized S-rule, which states that in a supersymmetric configuration the number of D3-branes never goes negative upon crossing two 5-branes. If it does go negative, then the gauge theory exhibits spontaneous supersymmetry breaking.

Dual forms of the effect

Via a series of T-dualities one obtains the result that in any type II superstring theory, when an NS5-brane and a Dp-brane cross one necessarily creates or destroys a . Lifting this statement to

M-theory In physics, M-theory is a theory that unifies all Consistency, consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1 ...

one finds that when two M5-branes cross, one creates or destroys an M2-brane. Using S-duality one may obtain transitions without NS5-brane. For example, when a D5-brane and a D3-cross one creates or destroys a fundamental string.

References

{{DEFAULTSORT:Hanany-Witten transition Eponyms in physics String theory