Phase Structure of a Brane/Anti-Brane System at Large N

Abstract

We further analyze a class of recently studied metastable string vacua obtained by wrapping D5-branes and anti-D5-branes over rigid homologous S^2's of a non-compact Calabi-Yau threefold. The large N dual description is characterized by a potential for the glueball fields which is determined by an auxiliary matrix model. The higher order corrections to this potential produce a suprisingly rich phase structure. In particular, at sufficiently large 't Hooft coupling the metastable vacua present at weak coupling cease to exist. This instability can already be seen by an open string two loop contribution to the glueball potential. The glueball potential also lifts some of the degeneracy in the vacua characterized by the phases of the glueball fields. This generates an exactly computable non-vanishing axion potential at large N.

Figures (11)

• Figure 1: Depiction of the geometric transition from the open string picture with branes wrapped over minimal size $S^{2}$'s (top) to the large $N$ closed string dual where the branes and homologous $S^{2}$'s have been replaced by flux threading topologically distinct $S^{3}$'s of a new geometry (bottom). The lines with red crosses denote finite length branch cuts on the Riemann surface of the local geometry after the transition. In the open string picture the area of the $S^{2}$ in the middle of the bulge is approximately $|W^{\prime}(x)|$. When branes are wrapped over these minimal size $S^{2}$'s, the bare tension of the branes creates a potential barrier against brane/anti-brane annihilation.
• Figure 2: Depiction of the complex $x$-plane corresponding to the Riemann surface defined by equation (\ref{['defcon']}) with $uv=0$. The compact $A$-cycles reduce to counterclockwise contours which encircle each of the $n$ branch cuts of the Riemann surface. The non-compact $B$-cycles reduce to contours which extend from $x=\Lambda_{0}$ on the lower sheet (dashed lines) to $x=\Lambda_{0}$ on the upper sheet (solid lines).
• Figure 3: Topologically distinct one loop planar diagram contributions to the prepotential for the two cut matrix model. Solid lines denote branes and dashed lines denote anti-branes.
• Figure 4: Plot of $V_{\mathrm{eff}}/\left\vert \alpha\right\vert ^{2}$ in the one loop approximation along the locus $S_{1}/g\Delta^{3}=-S_{2}/g\Delta ^{3}>0$ for a flux configuration with $N_{1}=-N_{2}$. In this plot $\Lambda_{0}/\Delta\sim10^{4}$ and $\left\vert N_{1}/\alpha\right\vert \sim0.1$. In the neighborhood of the semi-classical expansion point there is a single critical point which is metastable.
• Figure 5: Two loop planar diagram contributions to the genus zero prepotential of the two cut geometry. Solid lines denote branes and dashed lines denotes anti-branes.