Holograms of Strings - Department of Physics - University of Virginia

For closed strings, conformal (scale) invariance
S = − 1
[
4πα
∫ws
′ dτdσ ∂ α X µ ∂ α X ν g µν (X ) + i∂ α X µ ∂ β X µ ɛ αβ B µν (X )
]
+ α ′ Φ(X )R ws
requires that the space-time metric satisfies Einstein equations
R µν = B,Φ−sources,
R µν = 0 in vacuum
In general, conformal invariance implies the EOM of Einstein action
(+more)
[
]
√
L = 1
G N
− det ge
−2Φ
R − 1 2 H µνρH µνρ + 4∂ µ Φ∂ µ Φ
It’s the tail wagging the dog! the string cannot exist in other spacetimes
than those compatible with general relativity.