Links for [1] and [2] are below.(adsbygoogle = window.adsbygoogle || []).push({});

Please have a look here section 12.6 [1]. It says here that

Given the action of a supergravity theory, it is generally useful to search for solutions of the classical equations of motion. It is most useful to obtain solutions that can be interpreted as backgrounds or vacua. Fluctuations above the background are then treated quantum mechanically. The backgrounds that are considered have vanishing values of fermions, and are thus determined by a value of the metric, the vector fields (or higher forms) and scalar fields. One common background is Minkowski space, but there are others such as anti-de Sitter space, certain black holes, cosmic strings, branes or pp-waves, which are all supersymmetric, i.e. they‘preserve some supersymmetry’. This means that the background isinvariantunder a subset of the local supersymmetries of the supergravity theory.For a preserved supersymmetry, the local SUSY variations of all fields must vanish when the background solution is substituted. This leads to conditions of the generic form $$δ(\epsilon) \text{boson} = \text{fermion} = 0, \hspace{.5cm} δ(\epsilon)\text{fermion} = \text{boson} = 0. \tag{12.15}$$

I discussed this a little with ACuriousMind in this thread [2]. My question was if supersymmetric background means that itpreservessome supersymmetry, then as the text above says, the SUSY variations (12.15) must vanish. This results in for example that $$\delta \text{fermion}=0.$$ So, what does this equation imply? Does it imply that for a background to be supersymmetric, then fermions must not transform into bosons but rather stay fermions? I must be confused about this because this doesn't make much sense now does it?

Note: I would like to note ACuriousMind's answer there on where he said

"You're completely misunderstanding what a "preserved supersymmetry" is. That's not a requirementon the theory, it is just a requirement on theclassical solutions, that they be mapped onto themselves under thepreservedsupersymmetric transformation (i.e. δX=0 for all fields), and not onto another solution (this is just a weird way of stating that the solution doesn't break the supersymmetry)."

This got me confused, what does he mean by this answer?

[1]: http://books.google.com.lb/books?id=KFUhAwAAQBAJ&pg=PA249&lpg=PA249&dq=van proeyen freedman supergravity It is most useful to obtain solutions that can be interpreted as backgrounds or vacua.&source=bl&ots=vh-QrPO7je&sig=ZDggO4dPDDVcNeiqaC8ojY8clSQ&hl=ar&sa=X&ved=0ahUKEwjUzdDYj__JAhXG1BoKHaqyBX0Q6AEIGjAA#v=onepage&q=van proeyen freedman supergravity It is most useful to obtain solutions that can be interpreted as backgrounds or vacua.&f=false

[2]: http://physics.stackexchange.com/qu...etry/226342?noredirect=1#comment489467_226342

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What does ##\delta F=0## mean?

Loading...

Similar Threads - does ##delta F=0## | Date |
---|---|

I Mirror fermions / mirror families. How does it work? | Jan 21, 2018 |

I Does gravity just emerge out of all the quantum fields? | Jan 8, 2018 |

I How does gravitation fit into this picture of branes? | Oct 14, 2017 |

B Why does "gravity" need to be unified? | Aug 29, 2017 |

Polchinski Excercise Question - delta function | Mar 7, 2004 |

**Physics Forums - The Fusion of Science and Community**