# nLab Scherk-Schwarz mechanism

Contents

## Spin geometry

spin geometry

Dynkin labelsp. orth. groupspin grouppin groupsemi-spin group
SO(2)Spin(2)Pin(2)
B1SO(3)Spin(3)Pin(3)
D2SO(4)Spin(4)Pin(4)
B2SO(5)Spin(5)Pin(5)
D3SO(6)Spin(6)
B3SO(7)Spin(7)
D4SO(8)Spin(8)SO(8)
B4SO(9)Spin(9)
D5SO(10)Spin(10)
B5SO(11)Spin(11)
D6SO(12)Spin(12)
$\vdots$$\vdots$
D8SO(16)Spin(16)SemiSpin(16)
$\vdots$$\vdots$
D16SO(32)Spin(32)SemiSpin(32)

string geometry

# Contents

## Idea

The Scherk-Schwarz mechanism (Scherk-Schwarz 79) is the spontaneous supersymmetry breaking by KK-compactification on a circle whose spin structure imposes anti-periodic boundary conditions for fermion fields.

## Examples and applications

### Witten-Sakai-Sugimoto brane model for quantum chromodynamics

In the Witten-Sakai-Sugimoto model non-supersymmetric QCD is geometrically engineered from the D=5 super Yang-Mills theory on D4-branes by wrapping these on a Scherk-Schwarz circle (Witten 98, p. 19)

## References

### General

The original articles:

### Examples and applications

In geometrically engineering of non-supersymmetric QCD from the D=5 super Yang-Mills theory on D4-branes by wrapping these on a Scherk-Schwarz circle (the Witten-Sakai-Sugimoto model):

• Edward Witten, p. 19 of: Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories, Adv. Theor. Math. Phys.2:505-532, 1998 (arXiv:hep-th/9803131)

Last revised on September 10, 2019 at 07:21:56. See the history of this page for a list of all contributions to it.