Figure 3.4: Plot of three solutions around the M = √$_{2 solution.}$ M GLYPH<Equal> GLYPH<Radical2> GLYPH<Radical2Extens> GLYPH<Radical2Extens> GLYPH<Radical2Extens> 2 GLYPH<Plus> 0.03 M GLYPH<Equal> GLYPH<Radical2> GLYPH<Radical2Extens> GLYPH<Radical2Extens> GLYPH<Radical2Extens> 2 M GLYPH<Equal> GLYPH<Radical2> GLYPH<Radical2Extens> GLYPH<Radical2Extens> GLYPH<Radical2Extens> 2 GLYPH<Minus> 0.03 0.5 1.0 1.5 2.0 Ρ GLYPH<Minus> 0.5 0.5 1.0 1.5 f GLYPH<LParen1> Ρ GLYPH<RParen1> A µ = g ( ρ ) e ik · $^{x}$ϵµ (3.20) M 2 n = 2 L R 2 √ ( n + 1)( n + 2) (3.21) 56 The process is identical to that in section 3.2.1 once we have made the following ans¨ atz for the holographic gauge field: ϵ µ is the polarization vector, defined only in the Minkowski directions. g ( ρ ) is determined from the equations of motion, just as f ( ρ ) was for the scalars. In this geometry, the mass spectrum of the vector mesons is exactly the same as that for the scalars: This is to be expected since they both form part of an N = 2 hypermultiplet. In the more complicated geometries that we will study later the N = 2 hypermultiplet will be broken, and then the masses will differ.