In theoretical physics, thesix-dimensional (2,0)-superconformal field theory is aquantum field theory whose existence is predicted by arguments instring theory. It is still poorly understood because there is no known description of the theory in terms of anaction functional. Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a variety of reasons, both physical and mathematical.[1]
The (2,0)-theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes a large number of mathematically interestingeffective quantum field theories and points to new dualities relating these theories. For example, Luis Alday,Davide Gaiotto, and Yuji Tachikawa showed that by compactifying this theory on asurface, one obtains a four-dimensional quantum field theory, and there is aduality known as theAGT correspondence which relates the physics of this theory to certain physical concepts associated with the surface itself.[2] More recently, theorists have extended these ideas to study the theories obtained by compactifying down to three dimensions.[3]
In addition to its applications in quantum field theory, the (2,0)-theory has spawned a number of important results inpure mathematics. For example, the existence of the (2,0)-theory was used byWitten to give a "physical" explanation for a conjectural relationship in mathematics called thegeometric Langlands correspondence.[4] In subsequent work, Witten showed that the (2,0)-theory could be used to understand a concept in mathematics calledKhovanov homology.[5] Developed byMikhail Khovanov around 2000, Khovanov homology provides a tool inknot theory, the branch of mathematics that studies and classifies the different shapes of knots.[6] Another application of the (2,0)-theory in mathematics is the work of Davide Gaiotto,Greg Moore, andAndrew Neitzke, which used physical ideas to derive new results inhyperkähler geometry.[7]
| Theories | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Models |
| ||||||||||||||||
| Related | |||||||||||||||||
See also:  Template:Quantum mechanics topics | |||||||||||||||||
