what's supersymmetry?

What is Supersymmetry ?

1 kudayblog.wordpress.com What is

Supersymmetry ?

kudayblog.wordpress.com 2


Just a single ques:on for

crea:ng enough trouble.




….But since people keep asking me a lot about it, I feel like explaining it in the simplest form here.



4 kudayblog.wordpress.com

So let me try….


Supersymmetry:

Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.

kudayblog.wordpress.com 5 What is

Supersymmetry ?

Supersymmetry:



Scalars, vectors, extra dimensions, space, projec:on??

… Did you understand it

now??



Supersymmetry:


Me neither!!!



Supersymmetry:


Let’s draw a picture in other

words.



This is Bob. He lives in a 4 dimensional (x,y,z,t) world like us. This means he can measure length, height, width of an object at any time. Here he has 3 vectors called x,y,z.

This is Alice. She lives in a 5 dimensional world. Because she can measure one extra dimension θ in addition to x,y,z,t. So she has 4 vectors called x,y,z,θ.


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This is Bob. He lives in a 4 dimensional (x,y,z,t) world like us. This means he can measure length, height, width of an object at any time. Here he has 3 vectors called x,y,z.

This is Alice. She lives in a 5 dimensional world. Because she can measure one extra dimension θ in addition to x,y,z,t. So she has 4 vectors called x,y,z,θ.


Hushhhhh… Their rela:on has a strange story and I will tell you the reason why….


Assume that this axis represents Bob’s world: (x,y,z,t) = xμ where μ = 1,2,3,4 So that x1 = x , x2 = y , x3 = z , x4 = t BOB

ALICE



…and assume that this axis represents Alice’s world: (θ,x,y,z,t) = θa where a = 1,2,3,4,5 So that θ1 = θ , θ2 = x , θ3 = y , θ4 = z , θ5 = t

Xµ

BOB

ALICE



Xµ

θa

Whenever they decide to measure the dimensions of an object, they can not find the same results.

BOB

ALICE


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Xµ

θa

Because Bob was measuring 4 dimensions -width, length, height, time- but Alice was measuring one more dimension called θ in addition to width, length, height and time.

Y

BOB

ALICE

Yµ

Ya What is

Supersymmetry ?

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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

One day, Bob decided to do better than this. And he realised that he can also measure a scalar called Mass.

Mass of Y


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

He called up Alice and asked if she can measure any scalar feature of the same object Y. Alice told “What is a scalar?”

Mass of Y


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

She was completely unaware of SCALAR features of Y !!

Mass of Y


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Bob thought “That is too much. She must have been LYING!! And this relation cannot go on with lies.”

Mass of Y


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Then a physicist appeared. And warned Bob..

Mass of Y

Hey my friends, You’r ventured into Uncharted waters.


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Mass of Y

There is a simple solution and hence the facts are always simple and understandable:


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Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Mass of Y

“Alice” lives in an extra dimensional world so that she measures scalars (like mass) as vectorial dimensions.



Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Mass of Y

…But Bob measures some of her vectorial dimensions as scalars. So there is a naïve relation between Mass and θ.



Xµ

θa

Y

BOB

ALICE

Yµ

Mass of Y

Years ago, Bob was living in Alice’s Extradimensional World. But his θ has collapsed into a scalar axis.



Xµ

θa

Y

BOB

ALICE

Yµ

Ya

Mass of Y

Now you learned everything and i will tell you how you can relate your two different worlds with one equation.



Xµ

θa

BOB

ALICE

Mass

Assume that a particle travel with a constant speed and it’s momentum is “p”. So length of its momentum vector will be |p|2 = 0



Xµ

θa

BOB

ALICE

Mass

But Alice will write it as papa =0 and Bob will write it as pµpµ-m2 = 0 .

€

pa pa = 0

€

pµ pµ −m2 = 0



Xµ

θa

BOB

ALICE

Mass

If we transform Bob’s scalar axis to Alice’s vectorial axis θ, only Alice’s equation would be valid and it means “supersymmetric transformation”.

€

pa pa = 0

€

pµ pµ −m2 = 0



As a natural consequence of supersymmetry:

We should observe “scalar and vectorial partners” of elementary particles.

Vectorial Particle Scalar Particle electron selectron u, d, c, s – quark u, d, c, s – squark top quark stop bottom quark sbottom …(Fermions) ….(Bosons)

SUSY Transformations



Supersymmetry:


I hope it is more apparent now.


The End


what's supersymmetry?

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