Brane intersections, anti-de Sitter spacetimes and dual superconformal theories

TL;DR

Problem: classify intersecting brane configurations whose near-horizon spacetimes contain AdS factors and connect them to dual 2D SCFTs with extended large N=4 symmetry. Approach: construct a family of solutions from M2, M5, Dp-branes, waves, and KK monopoles; formulate a wave/monopole rule; analyze supersymmetry enhancement and AdS/CFT dualities. Findings: all AdS near-horizon geometries exhibit supersymmetry doubling; the dual SCFTs possess the A_gamma algebra (and related products in the maximal AdS3 case); the results imply new gauged supergravity vacua and a concrete AdS/CFT framework in 2D. Significance: provides exact AdS backgrounds with tractable CFTs enabling precise tests of holography and suggesting rich interplays among dualities, brane intersections, and gauged supergravities.

Abstract

We construct a class of intersecting brane solutions with horizon geometries of the form adS_k x S^l x S^m x E^n. We describe how all these solutions are connected through the addition of a wave and/or monopoles. All solutions exhibit supersymmetry enhancement near the horizon. Furthermore we argue that string theory on these spaces is dual to specific superconformal field theories in two dimensions whose symmetry algebra in all cases contains the large N=4 algebra A_{gamma}. Implications for gauged supergravities are also discussed.

Figures (8)

• Figure 1: The wave/monopole rule for standard intersections. Starting from solution (a) one can obtain solutions (b), (c), (d) by adding a wave and/or a monopole. The lower-case letters in brackets refer to the four standard intersections listed in table 2.
• Figure 2: Interpolating structure of solution (A). Keeping one of the radial coordinates fixed while the other tends to infinity we recover solution (a), which itself interpolates between $adS_3 \times E^5 \times S^3$ and Minkowski. In addition, in the limit $r$ and $r'$ go to zero, (A) approaches $adS_3 \times E^2 \times S^3 \times S^3$. The horizontal and vertical axes correspond to a solution ((A) with the $1$ removed from one of the harmonic functions) which interpolates between the supersymmetric vacua with geometries $adS_3 \times E^2 \times S^3 \times S^3$ and $adS_3 \times E^5 \times S^3$. The subscripts denote the fractions of unbroken supersymmetry.
• Figure 3: The wave/monopole rule for non-standard intersections. Starting from solution (A) one can obtain solutions (B), (C), (D), (E), (F) by adding a wave and/or monopole(s). The upper-case letters correspond to the solutions given in the text.
• Figure 4: Interpolating structure of solution (B).
• Figure 5: Interpolating structure of solution (C). Notice that in this case one obtains different standard intersections ((a) and (c)) depending on which radial coordinate is sent to infinity.