Types of quantum field thories
FQFT and cohomology
Beyond the speculative hypothetized role of string theory as a physical theory of fundamental strings that constitute the observed fundamental particles in the standard model of particle physics, the theory has shed light on many aspects of quantum field theory as such, both on the conceptual structure of QFT as well as on concrete theories and their concrete properties such as of. This entry lists such instances of string theory results having lead to insights in non-stringy physics and in particular into experimentally confirmed physics, such as QCD in the standard model of particle physics.
Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.
The two basic theories that underlie observed fundamental physics – and which string theory unifies at least qualitatively and in perturbation theory – are Yang-Mills theory and Einstein gravity/general relativity.
Many of the insights are based on the gauge/gravity duality in string theory:
The worldline formalism for expressing QFT scattering amplitudes in an effective gauge invariant way (different from but equivalent to the Feynman rules) was originally found by taking the point-particle limit of the expressions for string scattering amplitudes. See at worldline formalism for more.
By embedding quantum field theories in string theory (typically as the worldvolume theories of various branes) the various dualities of string theory will relate different QFTs in ways that are typically far from obvious from just looking at these QFTs themselves.
|M-theory perspective via AdS7-CFT6||F-theory perspective|
|Kaluza-Klein compactification on||compactificationon elliptic fibration followed by T-duality|
|7-dimensional Chern-Simons theory|
|AdS7-CFT6 holographic duality|
|6d (2,0)-superconformal QFT on the M5-brane with conformal invariance||M5-brane worldvolume theory|
|KK-compactification on Riemann surface||double dimensional reduction on M-theory/F-theory elliptic fibration|
|N=2 D=4 super Yang-Mills theory with Montonen-Olive S-duality invariance; AGT correspondence||D3-brane worldvolume theory with type IIB S-duality|
|topologically twisted N=2 D=4 super Yang-Mills theory|
|KK-compactification on Riemann surface|
|A-model on , Donaldson theory|
|gauge theory induced via AdS5-CFT4|
|type II string theory|
|Kaluza-Klein compactification on|
|5-dimensional Chern-Simons theory|
|AdS5-CFT4 holographic duality|
|N=4 D=4 super Yang-Mills theory|
|topologically twisted N=4 D=4 super Yang-Mills theory|
|KK-compactification on Riemann surface|
|A-model on and B-model on , geometric Langlands correspondence|
The string scattering amplitudes exhibit certain relations due to the extended nature of the string which are retained in the point particle limit and hence explain and serve to discover subtle relations in QFT scattering amplitudes.
This also goes by the term “on-shell methods”. See also at amplituhedron.
Rutger Boels, On-shell recursion for string theory amplitudes on the disk and the sphere (pdf)
Original articles include
See also below Application to gravity – Scattering amplitudes.
Pavel Kovtun, Quark-Gluon Plasma and String Theory, RHIC news (2009) (blog entry)
Makoto Natsuume, String theory and quark-gluon plasma (arXiv:hep-ph/0701201)
Henrique Boschi Filho, AdS/QCD and confinement, Seminar at the Workshop on Strongly Coupled QCD: The confinement problem, November 2011 (pdf)
David C. Dunbar, Paul S. Norridge, Calculation of Graviton Scattering Amplitudes using String-Based Methods, Nucl.Phys. B433 (1995) 181-208 (arXiv:hep-th/9408014)
KLT relations used for instance to demonstrate:
Semi-classical QFT computations suggest that there should be entropy associated with black holes, the Bekenstein-Hawking entropy, without however providing microscopic degrees of freedom of which this would be an entropy in the ordinary sense.
Since the quantum dynamics of general black holes is outside the reach of perturbative methods in string theory, certain supersymmetric black hole? solutions in supergravity have properties independent of the coupling and are known to be the strong-coupling limit of what at weak coupling is a certain configuration of branes in flat space. Therefore the ordinary entropy of these brane configurations should match the Bekenstein-Hawking entropy of the corresponding black holes, and this has been confirmed to good precision.
While this argument does not give direct information about the origin of the BH-entropy of physically observed black holes, it does show conceptually, in the general context of black holes in theories of gravity, BH-entropy can be accounted for by microscopic degrees of freedom in a theory of quantum gravity.
chapter 5 of