Higgs Phase of Gravity in String Theory - LUTh

Action invariant under ξi ( ) 2
h00
( ) 2
OK
1
h0i 2
2, ij
K K K OK
ij
( )
K = ∂ h −∂ h −∂h
ij 0 ij j 0i i 0 j
( ) 2
4⎧α1 2 α2
ij ⎫
Leff = LEH+ M ⎨ h00 − K − K K
2 2 ij + ⎬
⎩ M M ⎭
Action for π
ξ 0 = π
h00 →h00 −2∂0π K → K +∂ ∂ π
ij ij i j
( ) ( ) 2
4⎧2α 1
2
Leff = LEH+ M ⎨ h00 −2 π − K +∇ π
2
⎩
M
α
2 ( ij i j
K )( K )
⎫
− +∇∇ π 2
ij +∇∇ i jπ
+ ⎬
M
⎭