In theoretical physics the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory 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 in 1996.[1] 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 Hanany–Witten transition was discovered in type IIB superstring theory in flat, 10-dimensional Minkowski space. 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, 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 from each brane renders the action of the other brane ill-defined if one does not include the D3-brane.
The S-ruleedit
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.
Generalizationsedit
(p,q) 5-branesedit
More generally, NS5-branes and D5-branes may form bound states known as (p,q) 5-branes. The above argument was extended in 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 effectedit
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 D(p-2)-brane. Lifting this statement to M-theory 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.
Referencesedit
^Hanany, Amihay; Witten, Edward (1997). "Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics". Nuclear Physics B. 492 (1–2): 152–190. arXiv:hep-th/9611230. doi:10.1016/S0550-3213(97)00157-0. S2CID 8791774.
May 02, 2024
hanany, witten, transition, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor,. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Hanany Witten transition news newspapers books scholar JSTOR February 2020 Learn how and when to remove this message In theoretical physics the Hanany Witten transition also called the Hanany Witten effect refers to any process in a superstring theory 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 in 1996 1 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 Contents 1 The original effect 1 1 The S rule 2 Generalizations 2 1 p q 5 branes 2 2 Dual forms of the effect 3 ReferencesThe original effect editThe original Hanany Witten transition was discovered in type IIB superstring theory in flat 10 dimensional Minkowski space 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 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 from each brane renders the action of the other brane ill defined if one does not include the D3 brane The S rule edit 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 edit p q 5 branes edit More generally NS5 branes and D5 branes may form bound states known as p q 5 branes The above argument was extended in 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 edit 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 D p 2 brane Lifting this statement to M theory 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 edit Hanany Amihay Witten Edward 1997 Type IIB superstrings BPS monopoles and three dimensional gauge dynamics Nuclear Physics B 492 1 2 152 190 arXiv hep th 9611230 doi 10 1016 S0550 3213 97 00157 0 S2CID 8791774 Retrieved from https en wikipedia org w index php title Hanany Witten transition amp oldid 1073180062, wikipedia, wiki, book, books, library,
