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functorial quantum field theory
Reshetikhin?Turaev model? / Chern-Simons theory
FQFT and cohomology
black hole spacetimes | vanishing angular momentum | positive angular momentum |
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vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Beyond the speculative hypothesized 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. This entry lists such instances of string theory results having led 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 construction of efficient computational methods for field theory scattering amplitudes has benefited substantially from string theory input.
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.
Example:
The first calculation along these lines was actually done earlier in (Metsaev-Tseytlin 88), where the 1-loop beta function for pure Yang-Mills theory was obtained as the point-particle limit of the partition function of a bosonic open string in a Yang-Mills background field. This provided a theoretical explanation for the observation, made earlier in (Nepomechie 83) that when computed via dimensional regularization then this beta function coefficient of Yang-Mills theory vanishes in spacetime dimension 26. This of course is the critical dimension of the bosonic string.
R.I. Nepomechie, Remarks on quantized Yang-Mills theory in 26 dimensions, Physics Letters B Volume 128, Issues 3–4, 25 August 1983, Pages 177-178 Phys. Lett. B128 (1983) 177 (doi:10.1016/0370-2693(83)90385-4)
Ruslan Metsaev, Arkady Tseytlin, On loop corrections to string theory effective actions, Nuclear Physics B Volume 298, Issue 1, 29 February 1988, Pages 109-132 (doi:10.1016/0550-3213(88)90306-9)
AdS/CFT correspondenceopen/closed string duality
talks at
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.
Example:
The first calculuation along these lines was actually done earlier in (Metsaev-Tseytlin 88), where the 1-loop beta function for pure Yang-Mills theory from the partition function of a bosonic open string in a Yang-Mills background field. This provided a theoretical explanation for the observation, made earlier in (Nepomechie 83) that when computed in via dimensional regularization then this beta function coefficient of Yang-Mills theory vanishes in spacetime dimension 26. This of course is the critical dimension of the bosonic string.
R.I. Nepomechie, Phys. Lett. B128 (1983) 177
{MetsaevTseytlin88} Ruslan Metsaev, Arkady Tseytlin, On loop corrections to string theory effective actions, Nuclear Physics B Volume 298, Issue 1, 29 February 1988, Pages 109-132 (doi:10.1016/0550-3213(88)90306-990306-9))
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.
The investigation specifically of N=1 D=4 super Yang-Mills theory and N=2 D=4 super Yang-Mills theory in this fashion has come to be known as geometric engineering of quantum field theory.
Montonen-Olive duality of (super) Yang-Mills theory derives from conformal invariance of the 6d (2,0)-supersymmetric QFT (see there) compactified on a torus.
gauge theory induced via AdS-CFT correspondence
M-theory perspective via AdS7-CFT6 | F-theory perspective |
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11d supergravity/M-theory | |
$\;\;\;\;\downarrow$ Kaluza-Klein compactification on $S^4$ | compactificationon elliptic fibration followed by T-duality |
7-dimensional supergravity | |
$\;\;\;\;\downarrow$ topological sector | |
7-dimensional Chern-Simons theory | |
$\;\;\;\;\downarrow$ AdS7-CFT6 holographic duality | |
6d (2,0)-superconformal QFT on the M5-brane with conformal invariance | M5-brane worldvolume theory |
$\;\;\;\; \downarrow$ 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 |
$\;\;\;\;\; \downarrow$ topological twist | |
topologically twisted N=2 D=4 super Yang-Mills theory | |
$\;\;\;\; \downarrow$ KK-compactification on Riemann surface | |
A-model on $Bun_G$, Donaldson theory |
$\,$
gauge theory induced via AdS5-CFT4 |
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type II string theory |
$\;\;\;\;\downarrow$ Kaluza-Klein compactification on $S^5$ |
$\;\;\;\; \downarrow$ topological sector |
5-dimensional Chern-Simons theory |
$\;\;\;\;\downarrow$ AdS5-CFT4 holographic duality |
N=4 D=4 super Yang-Mills theory |
$\;\;\;\;\; \downarrow$ topological twist |
topologically twisted N=4 D=4 super Yang-Mills theory |
$\;\;\;\; \downarrow$ KK-compactification on Riemann surface |
A-model on $Bun_G$ and B-model on $Loc_G$, geometric Langlands correspondence |
See also
The realization of Yang-Mills theory that describes quarks and their interaction by the strong nuclear force carried by gluons is quantum chromodynamics (QCD).
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.
twistor string theory explains some (super) Yang-Mills theory scattering amplitudes
Precision scattering amplitudes in QCD use twistor string theory on-shell recursion methods,
This also goes by the term “on-shell methods”. See also at amplituhedron.
Reviews include
Matthew Strassler, From string theory to the large hadron collider (blog post)
Lance Dixon, Calculating Amplitudes, December 2013 (web)
Rutger Boels, On-shell recursion for string theory amplitudes on the disk and the sphere (pdf)
Original articles include
Zvi Bern, Lance Dixon, David Kosower, On-Shell Methods in Perturbative QCD (arXiv:0704.2798)
Joseph Polchinski, Matthew Strassler, Hard Scattering and Gauge/String Duality, Phys.Rev.Lett.88:031601,2002, (arXiv:hep-th/0109174)
See also
Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi, Elliptic polylogarithms and Feynman parameter integrals (arXiv:1902.09971)
reviewed in
Lorenzo Tancredi, Feynman integrals and higher genus surfaces, talk at Amplitudes 2019 (pdf)
See also below Application to gravity – Scattering amplitudes.
Properties of quark-gluon plasma from AdS/CFT-dual type II string theory
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)
Steven Gubser, Using string theory to study the quark-gluon plasma: progress and perils (arXiv:0907.4808)
Discussion of confinement in the context of the AdS-CFT correspondence is in
David Berman, Maulik K. Parikh, Confinement and the AdS/CFT Correspondence, Phys.Lett. B483 (2000) 271-276 (arXiv:hep-th/0002031)
Henrique Boschi Filho, AdS/QCD and confinement, Seminar at the Workshop on Strongly Coupled QCD: The confinement problem, November 2011 (pdf)
Seiberg duality in super Yang-Mills theory is conceptually explained by type II string theory on certain D-brane configurations (…)
open/closed string duality in string scattering amplitudes allows to compute gravity scattering amplitudes in terms of Yang-Mills theory scattering amplitudes: the KLT relations
Zvi Bern, Perturbative Quantum Gravity and its Relation to Gauge Theory, Living Rev Relativ. 2002; 5(1): 5. (arXiv:gr-qc/0206071, doi:10.12942/lrr-2002-5)
more on this string-organizatioon of graviton scattering amplitudes is in
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:
Application of the KLT relation/double copy-technique to computation of gravitational wave-signature of relativistic binary mergers:
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.
Reviews include
string theory “knows more mathematics than we do” and its study has led to the development of a large quantity of new mathematics: mirror symmetry (enumerative formulas, homological mirror symmetry, Bridgeland stability), new invariants (Gromov-Witten, Donaldson-Thomas, Gopakumar-Vafa, etc.), topological field theory and topological quantum gravity, etc. (Douglas 19, slide 30)
Reviews include
Gregory Moore, The Impact of D-Branes on Mathematics (2014), Physical Mathematics and the Future (2014)
Mina Aganagic, String Theory and Math: Why This Marriage May Last, (arXiv:1508.06642)
Ibrahima Bah, Daniel Freed, Gregory Moore, Nikita Nekrasov, Shlomo S. Razamat, Sakura Schafer-Nameki, A Panorama Of Physical Mathematics c. 2022 (arXiv:2211.04467)
For a review of prospects of computerized support for string theory, see
See also Fields medal (and other) work related to string theory
The string orientation of tmf was directly motivated from the index of the heterotic string (“Witten genus”).
The relation between Bruhat-Tits buildings and zeros of the Riemann zeta function, as described in Huang-Stoica-Yau.
mirror symmetry took complex geometers by complete surprise, but is easily seen from the 2d (2,0)-sigma model with target space the respective CY manifolds.
Morse theory of loop spaces via loop space supersymmetric quantum mechanics describing superstring propagation.
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Last revised on November 10, 2022 at 11:27:57. See the history of this page for a list of all contributions to it.