(0,2) SCFTs from the Leigh-Strassler Fixed Point

TL;DR

The paper demonstrates a new class of two-dimensional $(0,2)$ SCFTs arising from twisted compactifications of the four-dimensional Leigh–Strassler fixed point on a closed hyperbolic Riemann surface. It computes the IR central charges via ’t Hooft anomaly matching and $c$-extremization, establishing a one-parameter family of fixed points characterized by a background flavor flux $\mathfrak{b}$ with $c_r(\mathfrak{b})=\tfrac{3}{8}\,\eta_{\Sigma}\,d_G\,(3+4\mathfrak{b}^2)$ and $\epsilon=2\mathfrak{b}$. On the holographic side, a consistent truncation of ${\cal N}=8$, $d=5$ gauged supergravity yields supersymmetric $AdS_3\times\Sigma_{\mathfrak{g}}$ vacua whose central charges match field theory, and the authors construct holographic RG flows from the 4D LS (or ${\cal N}=4$) fixed points to these 2D IR fixed points, including analytic and numerical examples. The results provide a controlled holographic realization of a broader landscape of $(0,2)$ fixed points and illustrate how flavor flux drives IR symmetry mixing and fixed-point structure in lower dimensions. The work also sets the stage for uplifts to ten dimensions and a three-dimensional gauged supergravity formulation, suggesting rich connections to 3D/4D dualities and 2D compactifications.

Abstract

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.

Figures (6)

• Figure 1: The superpotential $\mathcal{V}(\alpha,\beta,\chi,h)$ in the $(\alpha,\chi)$-plane with $\beta=\beta_{\frak a}$ and $h=h_{\frak a}$ kept constant at their critical values \ref{['AdS3sol']} for $\frak a=0$, $0.20$ and 0.248. The orange line denotes the position of the $AdS_3\times \Sigma_{\frak g}$ critical points for $0\leq |\frak a|<1/4$. The end point denoted by the blue dot is the KPW point, the red dot is the critical point for the corresponding value of $\frak a$, and the black dot is the $SO(6)$ point.
• Figure 2: Eigenvalues of the mass matrix $M_{ij}$.
• Figure 3: The radial variable and the two metric functions $f$ and $h$ for the analytic solution in \ref{['analytic']} and \ref{['rrho']}.
• Figure 4: Examples of flows from the $SO(6)$ point to different $AdS_3\times \Sigma_{\frak g}$ solutions projected onto the $(\alpha,\chi)$-plane for $\frak a=0.001,\,0.1,\, 0.15,\, 0.2$, and $0.22$ from left to right.
• Figure 5: Solutions of the flow equations \ref{['BPSeqnV']} projected onto the $(\alpha,\chi)$-plane for $\frak a=0.20$. The curves between the $SO(6)$ point (black dot) and the $AdS_3\times \Sigma_{\frak{g}}$ point (red dot) are representatives of the one-parameter family of holographic RG flows labelled by the parameter $c_0$ in \ref{['sersolso6']} corresponding to the mass $m$ in \ref{['LSsuperpot']}. The red curve connecting the blue and red dots is the unique holographic RG flow between the KPW point and the $AdS_3\times \Sigma_{\frak{g}}$ solution.