By Mariano Quiros, Rosa Dominguez Tenreiro
The booklet discusses, according to a sequence of lectures given by means of the authors on the Universidad Autonoma of Madrid discusses the relation among cosmology and particle physics at a pedagogical point. the themes coated include a lot worthy introductory fabrics. Very invaluable as a textual content for graduate scholars during this box.
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Extra info for An introduction to cosmology and particle physics
These are plane-wave normalizable at the horizon z → ∞, and correspond to a particle that comes out of the horizon, reflects off the boundary, and returns to the horizon. If conformal symmetry is broken in such a way that the space is cut off near the horizon at some large value of z, the effective four-dimensional mass spectrum becomes discrete. 4. Conformal field theories Now we discuss the field theory side of the duality. Again, gauge/gravity duality is much more general than AdS/CFT, but the conformal case gives the cleanest examples to start from, so I will start with few general comments about CFT.
53 Here the S 5 is replaced by a manifold T 1,1 . In fact one gets a solution to the supergravity field equations with just metric and five-form if S 5 is replaced by any Einstein space (Rmn = cgmn with c a positive constant). 54 The dual gauge theory can be determined in many cases by a combination of orbifolding, RG flow, moving to the Coulomb branch, and so on. 6. Nonconformal branes57 Suppose we try to repeat the near-horizon limit for D2-branes. Here the gauge theory is superrenormalizable: at high energy it is weak, and the 2 dimensionless coupling gYM N/E becomes small.
The relevant terms in the Euclidean action in AdS5 are L3 ˆ3 4L P,5 d4 x dz (∂z h∂z h + k 2 h2 ) . 64) This is exactly like the massless Klein-Gordon field. The usual gravitational extrinsic curvature term has been included implicitly to make the action first order,32 but no additional surface term is needed because ∆− = 0. The extremum can again be written as a surface term, Scl = − L3 −3 ǫ ˆ3 8L dd x ∂ǫ (h2 (ǫ)) . 65) P The classical solution that approaches hb at the boundary and remains bounded at z = ∞ is k2 z 2 hcl (z) = hb K2 (kz) .
An introduction to cosmology and particle physics by Mariano Quiros, Rosa Dominguez Tenreiro