Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus

TL;DR

The authors construct an infinite family of regular, half-BPS Type IIB solutions on AdS4 × S2 × S2 × Σ, parameterized by genus g hyperelliptic surfaces with real branch points, via two locally harmonic functions h1,h2. These solutions describe fully back-reacted AdS5 × S5 (or Janus) geometries doped with D5 and/or NS5 branes, featuring 2g+2 asymptotic AdS5 × S5 regions and g homology 3-spheres carrying RR or NSNS flux. Regularity and topology impose a precise ordering of branch points and real zeros of ∂h1, ∂h2, along with period relations that fix the complex zeros; genus-1 solutions are given explicitly in terms of elliptic functions, with higher-genus cases treated analytically and numerically. The results illuminate the holographic duals as multi-interface CFTs with 2g+2 copies of N=4 SYM joined by a 2+1d interface, and establish a bridge to probe-brane limits via branch-cut collapses that yield D5/NS5 brane configurations in the back-reacted geometry.

Abstract

Regularity and topology conditions are imposed on the exact Type IIB solutions on $AdS_4 \times S^2 \times S^2 \times Σ$ with 16 supersymmetries, which were derived in a companion paper. We construct an infinite class of regular solutions with varying dilaton, and non-zero 3-form fluxes. Our solutions may be viewed as the fully back-reacted geometries of $AdS_5 \times S^5$ (or more generally, Janus) doped with D5 and/or NS5 branes. The solutions are parametrized by the choice of an arbitrary genus $g$ hyper-elliptic Riemann surface $Σ$ with boundary, all of whose branch points are restricted to lie on a line. For genus 0, the Janus solution with 16 supersymmetries and 6 real parameters is recovered; its topology coincides with that of $AdS_5 \times S^5$. The genus $g\geq 1$ solutions are parametrized by a total of $4g+6$ real numbers, $2g-1$ of which are the real moduli of $Σ$. The solutions have $2g+2$ asymptotic $AdS_5 \times S^5$ regions, $g$ three-spheres with RR 3-form charge, and another $g$ with NSNS 3-form charge. Collapse of consecutive branch points of $Σ$ yields singularities which correspond to D5 and NS5 branes in the probe limit. It is argued that the AdS/CFT dual gauge theory to each of our solutions consists of a 2+1-dimensional planar interface on which terminate $2g+2$ half-Minkowski 3+1-dimensional space-time $\mathcal{N}=4$ super-Yang-Mills theories. Generally, the $\\mathcal{N}=4$ theory in each Minkowski half-space-time may have an independent value of the gauge coupling, and the interface may support various operators, whose interface couplings are further free parameters of the dual gauge theory.

Figures (10)

• Figure 1: The genus 1 solution has 4 distinct asymptotic $AdS_5 \times S^5$ regions, each with a different constant limit $\phi_1, \phi_2, \phi_3, \phi_4$ for the dilaton field. The radii $f_1$ and $f_2$ of the 2-spheres vanish on alternating segments of the boundary. The locations of the homology 3-spheres corresponding to RR and NSNS charges are also indicated.
• Figure 2: The cut plane for $h_1$ and $h_2$ of the Janus solution.
• Figure 3: Allowed parameter region for the complex zero $u_1=x+iy$ for given values of $\alpha_1$ and $\beta_2$ (equal to $(e_1+e_2)/2$ and $(e_2+e_3)/2$ in this case), and varying $\tau = i$ (black arcs), $1.2 i$ (blue arcs), and $1.6i$ (red arcs). The allowed regions are the trigons bounded by the real axis and arcs of the same color.
• Figure 4: The cut plane and fundamental domain of the elliptic solution.
• Figure 5: Field lines on the square of half-periods.