String Theory Demystified

Summary
262 String Theory Demystifi ed
In this chapter we provided a brief and heuristic introduction to two interesting
ideas that have sprung from string theory: the holographic principle and the AdS/
CFT correspondence. These two ideas are related. The holographic principle tells
us that for an enclosed volume, the informational content of the volume can be
described by an equivalent theory that lives on the bounding surface area. This
notion is codifi ed in black hole mechanics where the entropy of the black hole is
proportional to the area of the horizon, not the volume it encloses. The AdS/CFT
correspondence describes a fi ve-dimensional universe where fi ve-dimensional
supergravity in the bulk is equivalent to a super Yang-Mills conformal fi eld theory
on the boundary.
Quiz
A solution of supergravity gives the metric for a D-brane as:
⎛ ag N ⎞ s
where Fz () = +
⎝
⎜1
4
z ⎠
⎟
−
ds = F()( z dt −dx ) −F()
z dz
2 2 2 1 2
−1/
2
1. Find an expression for F(z) in the limit
.
agsN 4
z
1.
2. Using your answer to Prob. 1, fi nd a new expression for the metric.
3. The holographic principle can be best described by
(a) The informational content of a region is encoded in its volume.
(b) The informational content of a region can be described entirely by the
surface area.
(c) Fields living in the bulk are not equivalent to fi elds living on the
bounding surface.
4. In AdS/CFT correspondence, the number of degrees of freedom available
to the super Yang-Mills theory on the boundary is
(a) Independent of the AdS geometry.
(b) Related to the string coupling strength only.
(c) Is related to the string coupling strength and the fundamental string length.
(d) Is related to the fundamental string length only.