Two-dimensional SCFTs from wrapped branes and c-extremization

TL;DR

<p>The authors establish and test a robust c-extremization framework for 2d <em>N</em>=(0,2) SCFTs arising from wrapped D3- and M5-branes, enabling exact determination of the IR superconformal R-symmetry and central charges via anomaly data. They construct and match AdS$_3$ holographic duals in type IIB and eleven-dimensional supergravity for a wide class of twisted compactifications, confirming the field-theory results in the large- N limit. The work extends to several four-manifold geometries (Kähler, hyper-Kähler, and co-associative $G_2$ cases), providing explicit AdS$_3$ solutions and a unified gravity/field-theory dictionary for c-extremization in diverse holographic contexts. It also clarifies vector-field holography in AdS$_3$/CFT$_2$, including the relation between bulk CS levels and boundary anomalies and the role of boundary terms in the presence of branes and twists.</p>

Abstract

We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS_3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.

Figures (5)

• Figure 1: Regions of the parameter space $(a_1,a_2)$ (with $a_3 = -a_1-a_2 - \kappa$) where there exist good AdS$_3$ vacua, for genus $\mathfrak{g}=0,1,>1$ respectively. The boundaries are excluded, with the only exception of the three points where the regions touch (together with the circle) in the case $\mathfrak{g}>1$. The blue circle for $\mathfrak{g}=0, >1$ is the $\Theta=0$ locus; for $\mathfrak{g}=1$ it is collapsed at the origin.
• Figure 2: Numerical solutions for $g(\rho)$, $\phi_1(\rho)$ and $\phi_2(\rho)$ for some representative values of $a_1$ and $a_2$. The red, green, blue and purple curves refer to $(a_1,a_2) = (1,2), (2,3), (8,6), (15,7)$ respectively. We have chosen $\kappa=-1$ and $\mathfrak{g}=2$.
• Figure 3: Numerical solutions for $g_1(\rho)$, $g_2(\rho)$, $\lambda_1(\rho)$ and $\lambda_2(\rho)$ (clockwise from upper-left) for some representative values of $a_{\sigma}$ and $b_{\sigma}$. The red, green, purple and blue curves refer to $(z_1,z_2)=(3,-5), (11,-3), (15,-7), (23,-13)$, respectively. We have chosen $\kappa_1=\kappa_2=-1$ and $\mathfrak{g}_1 = \mathfrak{g}_2 =2$.
• Figure 4: Left: one-loop diagram for two-point functions, with a Weyl fermion running in the loop. When a scalar runs in the loop, there are no arrows and therefore there are two possible ways of contracting the operators. Right: tree level diagram for the two-point function.
• Figure 5: Regions of the parameter space $(z_1,z_2)$ where there exist good AdS$_3$ vacua. Boundaries are excluded. We have plotted the three cases $(\mathfrak{g}_1>1,\mathfrak{g}_2>1)$, $(\mathfrak{g}_1=1,\mathfrak{g}_2>1)$ and $(\mathfrak{g}_1=0,\mathfrak{g}_2>1)$ from left to right.

Theorems & Definitions (3)

• Theorem 1
• Theorem 2
• Theorem 3