# nLab duality in string theory

Contents

## Phenomenology

#### Duality in string theory

duality in string theory

general mechanisms

string-fivebrane duality

string-string dualities

M-theory

F-theory

string-QFT duality

QFT-QFT duality:

# Contents

## Idea

Whatever it is otherwise, string theory turns out to be an organizational principle that subsumes a wealth of effective quantum field theories together with hints for their UV-completion. As such, string theory reveals a multitude of equivalences between superficially very different-looking (classes of) quantum field theories, or between various limits (notably strong/weak coupling limits) of various different-looking quantum field theories. Large classes of these equivalences go by the name of “dualities”:

## Examples

duality in string theory

general mechanisms

string-fivebrane duality

string-string dualities

M-theory

F-theory

string-QFT duality

QFT-QFT duality:

## Overview

under construction

S-duality in string theory

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U-duality | $\updownarrow$ T-duality on $T^2$ |

| | D3-brane in IIB sugra | $\leftarrow$S-duality$\rightarrow$ | D3-brane in IIB sugra |

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

## References

### Original articles

The original article suggesting the relation of 11d sugra to string theory is

An original article collecting all the weak/strong electric/magnetic dualities is

### Surveys and lecture notes

More on dualities induced on K3-compactifications:

More in view of the landscape of string theory vacua:

Also

• Cumrun Vafa, around 3:30, 12:00 of On Mathematical Aspects of String Theory (video)

Discussion amplifying the role of category theory, and higher geometry is in

Last revised on February 14, 2023 at 05:16:16. See the history of this page for a list of all contributions to it.