Perturbing AdS6 ×w S4: linearised equations and spin-2 spectrum

Abstract

We initiate the analysis of the Kaluza-Klein mass spectrum of massive IIA supergravity on the warped AdS 6 × w S 4 background, by deriving the linearised equations of motion of bosonic and fermionic fluctuations, and determining the mass spectrum of those of spin-2. The spin-2 modes are given in terms of hypergeometric functions and a careful analysis of their boundary conditions uncovers the existence of two branches of mass spectra, bounded from below. The modes that saturate the bounds belong to short multiplets which we identify in the representation theory of the f(4) symmetry superalgebra of the AdS 6 × w S 4 solution.

Spin-2 excitations in Gaiotto-Maldacena solutions

“…We restrict our attention to a consistent truncation, namely that of spin-2 excitations of the N = 2 geometries discussed above. As a result we have to deal with a second order differential equation which coincides with the analysis in [11] (see also [12,13,14,15,16] for similar studies of the spin-2 excitations). We provide a generic expression for the wave operator given in terms of the function that solves the axisymmetric Laplace equation.…”

“…This has exactly the same form as the operator L (1) in [12]. Also, since the indices of h µν are along the AdS 5 subspace we understand that h µν behaves like a scalar for the covariant derivative∇ m and the operator L. Now the action of L on a scalar f can be written as:…”

“…Let us start by writing the equations of motion for the type-IIA supergravity fields [12]: where ε M 1 ...M 10 is the totally antisymmetric Levi-Civita tensor.…”

Supersymmetric probes in warped AdS6

“…Using these backgrounds it had been possible to perform very detailed analysis of the dual 5d theories e.g. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

On minimal Type IIB AdS6 solutions with commuting 7-branes

“…Previous analyses of the BPS equations can be found in[15][16][17]. T-duals of a Type IIA solution[18], which has been studied extensively[19][20][21][22][23][24][25][26], have been discussed in[27,28].…”