In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the

Pluggingtheseexpansionsinto(31)

one

cansolvefortheqiandEiiteratively.AtleadingorderE0=1(asitshouldfromthedualgaugetheoryperspective)andq0isimplicitlydeterminedthroughthe“ llingfraction”J2/J

J2

K(q0).(33)

The rstnon-trivialtermintheenergyisthenexpressedintermsofq0through

E=21

λλ2

832

λω1

ω21

λω1√qE(q 1)

Analogously(28)nowbecomes .

= 2π

dσ=4 π/2

2πdψ(q 1).

00sin2ψ0

Thecorrespondingrelationsto(29)and(30)then sin2ψ=4qKtaketheform

1√ω1qJ1

2K(q 1),2√

πJ

ω=2

21λq[K(q 1) E(q 1)].

(37)(38)(39)