String Theory Demystified

CHAPTER 13 D-Branes 237
We consider the critical point ϕ * = 0 and fi nd
4
λϕ 0 2 2
V = − λϕ ϕ +
0
2
The mass term, which multiplies the quadratic term in the expansion is
m 2
2
=−λϕ0
This is a negative mass. So the critical point ϕ * = 0 corresponds to a tachyon.
Our description of the fascinating topic of D-branes in this chapter barely scratches
the surface, but it should help prepare you for more detailed and/or more advanced
treatments. We have followed the development by Zweibach in this chapter, so you
can see his book for a more detailed analysis, in particular including his discussion
of intersecting D6-branes and his accessible discussion of string charge and
electromagnetic fi elds on D-branes (see References). Another good book to consult
is the Szabo text listed in the References. For a really detailed (and advanced)
description of D-branes, see Clifford V. Johnson’s “D-Brane Primer” Johnson’s.
Quiz
A 2 2 1. Consider a potential given by V(
φ) = ( φ −1)
. What are the critical
points?
6
A 2 2
2. Consider V(
φ) = ( φ −1)
and expand to second order. Then identify the
6
mass in the case of each critical point found in Prob. 1. Are any of these
related to a tachyon?
3. What are the critical points?
4. Which critical point corresponds to a tachyon?
5. If a string is stretched between two parallel D-branes, the ground state
acquires mass. Why is that?
Summary