basics of physics in extra dimensions. motivation for extra dimensions hierarchy problem –vast...
TRANSCRIPT
![Page 1: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/1.jpg)
Basics of Physics in Extra Dimensions
![Page 2: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/2.jpg)
Motivation for extra dimensions
• Hierarchy problem– Vast expanse between the scales of weak interactions and
gravitational interactions is not aesthetic. 16 orders of magnitude.
• Dark Matter– WMAP results indicate that 23% of the mass/energy
required to close the universe is in the form of cold dark matter (CDM).
– Some models naturally provide a candidate for dark matter
![Page 3: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/3.jpg)
Common Factors in XD Models• Small or large, extra dimensions are usually
compactified– radius of compactification ranges from 10-33 cm → 10-1
cm, depending on model and assumptions
• Extra dimensions manifest themselves in (3+1)-dimensions as Kaluza-Klein towers of states– Our universe consists of the zero-modes of SM fields– Higher tower states represent momentum states in the
extra dimensions.
• Gravity propagates in the extra dimensions– Dimensions in which neither gravity nor the SM fields
propagate are irrelevant
![Page 4: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/4.jpg)
Relate XDs to observation
• SM fields are constrained to live on the 3-brane– Charged SM fields cannot travel very far in extra
dimensions (~1 TeV ~ attometer ).– For small XD, this is naturally accounted for– For large XD, methods of constraint must be invented to
keep SM fields within an attometer of the brane
![Page 5: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/5.jpg)
toy derivation of the KK tower of states for a scalar field
• Heuristic derivation showing how mass terms appear – infinite tower of KK modes
• 5th dimension compactified implicitly
• Flat metric
2
2
in2
Rn
n 0
i(m n)2 in2 im2
R R Rn m n m
n 0 m 0 n 0 m 0
n n n nn 0 n 0
2 n
R
2
R
X x , x e
e in e im e
![Page 6: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/6.jpg)
Orbifolds
• An orbifold is the quotient of a space by its symmetries.– Doesn’t necessarily reduce the dimension of the space– Implicitly absorbs redundancies
![Page 7: Basics of Physics in Extra Dimensions. Motivation for extra dimensions Hierarchy problem –Vast expanse between the scales of weak interactions and gravitational](https://reader036.vdocument.in/reader036/viewer/2022082710/56649dd35503460f94aca6d7/html5/thumbnails/7.jpg)
• S1/Z2 orbifolds are convenient within XD because it provides a mechanism for generating boundary conditions.– The circle maps to an interval, whose endpoints are
identified as the fixed points