Holographic duals of 3d S-fold CFTs
- Assel, Benjamin et al
- arXiv:1804.06419CERN-TH-2018-087
 | \footnotesize a) Picture of $\Sigma$ (yellow strip) for the Janus solution with asymptotic axio-dilaton values $\tau_\pm$. b) $J$-folding of the extremal Janus solution. This involves an $SL(2,\bR)$ transformation before taking the $J$-fold quotient. The resulting solution has a cut (green) with $J$ monodromy. |
 | \footnotesize Quiver description of the $J_n$ theories and their brane realization. The subscript $n$ is the Chern--Simons level of the $U(N)$ node. |
 | \footnotesize Quiver description of a $J$ theory, with $J=J_{n_1}J_{n_2}J_{n_3}$, and its brane realization. Subscripts of gauge nodes indicate Chern--Simons levels. |
 | \footnotesize a) Half-ABJM quiver and its brane realization. b) Half-ABJM mirror and its brane realization. |
 | \footnotesize A mirror quiver of the ABJM theory at level $k=1$. The S-quotient of its brane realization leads to the brane realization of the half-ABJM theory. |
 | \footnotesize On the left: the $\Sigma$ annulus (yellow) with a D5 (red) and an NS5 (blue) singularity, corresponding to the initial ABJM ($k=1$) supergravity solution. On the right: the $\Sigma'$ M\"obius strip with a single D5 singularity and an S-interface (green dashed line), corresponding to the solution quotiented by $\cS$ in \ref{Saction}. |
 | \footnotesize A brane realization of a circular quiver invariant under the action of $\cS$ (translation + S-duality). The gauge theory data are read from the linking numbers of the five-branes: $\rho = (2,1,-1,-1,-1)$, $\hat\rho = (1,1,1,-1,-2)$. $N$ is the number of D3s stretched between the D5s and NS5s at the top, here $N=4$. On the right is the associated good circular quiver. |
 | \footnotesize An example of $\cS$-folding. The resulting S-flip solution has an S monodromy cut (green dashed line). |
 | \footnotesize a) An S-flip quiver and its brane realization. On the right: a canonical brane realization after Hanany--Witten moves, giving the quiver data $\rho_1 = (1,1,0)$, $\rho_2=(1,1)$, $N=3$ (number of D3s at the top). b) The parent circular quiver and its brane realization. On the right: the same brane configuration after Hanany--Witten moves, and the quotient by $\cS$. |
 | \footnotesize Quiver with gauge group $U(N)^{\wat M+1}$, $M$ fundamental hypermultiplets and a $T[U(N)]$ link. The corresponding brane realization has $\wat M$ NS5s, $M$ D5s and an $S$ interface. After moving the $S$ interface we can reach a description with $K=M+\wat M$ D5s, corresponding to a simpler quiver theory (pure D5 dual theory). |
 | \footnotesize $\cS$-quotient leading to the pure D5 theory. The double cover theory has $K$ $U(N)$ nodes and $K$ fundamental hypermultiplets in one node. The double cover supergravity solution has single stacks of $K$ D5s and $K$ NS5s. |