Supersymmetric AdS Solitons, Coulomb Branch Flows and Twisted Compactifications

Abstract

This work, which accompanies [1], is about constructing smooth solutions in type II and eleven dimensional supergravity which describe supersymmetry preserving RG flows from four-dimensional SCFTs in the UV to three-dimensional SQFTs in the IR, through holography. We show that all the different UV fixed points flow to theories which confine external quarks and have a mass gap. We proceed by presenting extended calculations of a plethora of observables and analyse the dual field theories in great detail. This includes a boundary analysis and application of holographic renormalization methods in the simplest case of the type IIB solution. Many of the observables computed here have a universal behaviour: they factorize into two parts, one of which includes information about the UV SCFTs, and the other describing the dynamics of the RG flow, which is the same regardless of the UV fixed point.

Figures (13)

• Figure 1: Invariants of the 5d geometry \ref{['5d_soliton']} for values of the parameter $\hat{\nu}$ close to $-1$. Approximately below the value $-0.95$ they start growing rapidly.
• Figure 2: Quiver diagram for the linear quiver described by the rank function \ref{['generic_R']} with $(P-1)$ gauge nodes. The balancing conditions enforce that $F_k= 2N_k - N_{k-1} - N_{k+1}$ for each node.
• Figure 3: Resulting plots using numerical integration regarding the WL embedding $\mathrm{I}$ for different values of $\hat{\nu}$. We notice the length gradually becoming double-valued as $\hat{\nu}\to-1$. We have set $\theta_0=0$.
• Figure 4: Wilson loop plots for embedding $\mathrm{I}$ using the approximate length and energy expressions \ref{['approximate_expressions']} for various values of $\hat{\nu}$ and the two options $\theta_0\in\{0,\pi/2\}$.
• Figure 5: We notice that for values of $\omega$ close to $0.99$ we get a single valued length and no phase transition, even when $\hat{\nu}=-0.99$ and $\theta_0=0$.