Holographic Aspects of Four Dimensional ${\cal N }=2$ SCFTs and their Marginal Deformations

TL;DR

The paper develops a holographic dictionary for four-dimensional ${\

Abstract

We study the holographic description of ${\cal N}=2$ Super Conformal Field Theories in four dimensions first given by Gaiotto and Maldacena. We present new expressions that holographically calculate characteristic numbers of the CFT and associated Hanany-Witten set-ups, or more dynamical observables, like the central charge. A number of examples of varying complexity are studied and some proofs for these new expressions are presented. We repeat this treatment for the case of the marginally deformed Gaiotto-Maldacena theories, presenting an infinite family of new solutions and compute some of its observables. These new backgrounds rely on the solution of a Laplace equation and a boundary condition, encoding the kinematics of the original conformal field theory.

Figures (15)

• Figure 1: The quiver and Hanany-Witten set-up for a generic situation. The vertical lines denote individual Neveu-Schwarz branes extended on the $(x_4,x_5)$ space. The horizontal ones D4 branes, that extend on $x_6$, in between five branes and the crossed-circles D6 branes, that extend on the $(x_7,x_8,x_9)$ directions. All the branes share the Minkowski directions. This realises the isometries $SO(1,3) \times SO(3)\times SO(2)$.
• Figure 2: A generic quiver. The squares indicate flavour groups and the circles gauge groups.
• Figure 3: The quiver and Hanany-Witten set-up for the profile in eq.(\ref{['profile1']}). The vertical lines denote individual Neveu-Schwarz branes. The horizontal lines D4 branes and the crossed circles D6 branes.
• Figure 4: The quiver and Hanany-Witten set-up for the profile in eq.(\ref{['profile2']}).
• Figure 5: The two operations preserving conformality and $SU(2)_R\times U(1)_r$ as discussed in the text