1. Basics of Physics in Extra Dimensions

2. 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

3. 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

4. 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

5. toy derivation of the KK tower of states for a scalar field Heuristic derivation showing how mass terms appear – infinite tower of KK modes 5 th dimension compactified implicitly Flat metric

6. Orbifolds An orbifold is the quotient of a space by its symmetries. –Doesn’t necessarily reduce the dimension of the space –Implicitly absorbs redundancies

7. S 1 /Z 2 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