Abstract
In this paper we study spin-2 excitations for a class of N = 2 supersymmetric solutions of type-IIA supergravity found by Gaiotto and Maldacena. The mass spectrum of these excitations can be derived by solving a second order partial differential equation. As specific examples of this class we consider the Abelian and non-Abelian T-dual versions of the AdS5 × S5 and we study the corresponding mass spectra. For the modes that do not “feel” the (non-)Abelian T-duality transformation we provide analytic formulas for the masses, while for the rest we were only able to derive the spectra numerically. The numerical values that correspond to large masses are compared with WKB approximate formulas. We also find a lower bound for the masses. Finally, we study the field theoretical implications of our results and propose dual spin-2 operators.
Highlights
Product SU(Nc) gauge groups connected by bi-fundamental fields and SU(Nf ) fundamental matter for each gauge group associated to the D6-branes
We provide a generic expression for the wave operator given in terms of the function that solves the axisymmetric Laplace equation
In particular we studied the spin-2 excitations of the Gaiotto-Maldacena class of geometries
Summary
Primed symbols correspond to derivatives with respect to η while dotted symbols correspond to the action of the operator σ∂σ The geometry of this class of solutions is supported by a NS two-form and a set of RR potentials:. Where VolΩ2 = sin χdχ ∧ dξ is the volume form on the two-sphere Ω2 and the RR fields F2 and F4 are defined through the potentials C1 and C3 as F2 = dC1 and F4 = dC3 + C1 ∧ H3 with H3 = dB2 As it is understood by the previous expressions, any background that fits into the Gaiotto-Maldacena classification is fully determined by the function V (η, σ). The above equation is supplemented with boundary conditions for the function V (σ, η) and its derivatives that fully determine the solution and ensure the geometry and matter fields obtained via (2.2) are regular and properly quantised. In the section that follows we will study perturbations of the metric (2.1) along the AdS5 directions
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