# nLab string theory results applied elsewhere

## Surveys, textbooks and lecture notes

#### Gravity

gravity, supergravity

# Contents

## Idea

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.

## Examples

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:

### General relation between Yang-Mills theory and gravity

• Spenta R. Wadia, Gauge/Gravity Duality and Some Applications (arXiv:1009.0212)

talks at

• Zvi Bern, Thomas Gehrmann, Frank Petriello, Anastasia Volovich, The Harmony of Scattering Amplitudes KITP Program (2011) (web)

### Applications to Yang-Mills theory

#### Worldline formalism

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.

#### QFT Duality and specifically Montonen-Olive electric/magnetic duality

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

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 invarianceM5-brane worldvolume theory
$\;\;\;\; \downarrow$ KK-compactification on Riemann surfacedouble dimensional reduction on M-theory/F-theory elliptic fibration
N=2 D=4 super Yang-Mills theory with Montonen-Olive S-duality invariance; AGT correspondenceD3-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

$\,$

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

#### Application to QCD and experimental particle physics

The realization of Yang-Mills theory that describes quarks and their interaction by the strong nuclear force carried by gluons is quantum chromodynamics (QCD).

##### Scattering amplitudes

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.

Reviews include

• Rutger Boels, On-shell recursion for string theory amplitudes on the disk and the sphere (pdf)

Original articles include

##### Quark-gluon plasma

Properties of quark-gluon plasma from AdS/CFT-dual type II string theory

#### To the confinement problem

Discussion of confinement in the context of the AdS-CFT correspondence is in

• D. S. 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)

#### To super Yang-Mills theory

Seiberg duality in super Yang-Mills theory is conceptually explained by type II string theory on certain D-brane configurations (…)

### Applications to gravity

#### Black hole entropy

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

chapter 5 of

### Application to pure mathematics

#### Monstrous moonshine

• monstrous moonshine?

#### (…)

(…)

Revised on March 13, 2014 04:43:08 by Urs Schreiber (89.204.139.182)