Geometrically Induced Phase Transitions at Large N

TL;DR

The paper investigates geometry-driven metastability in a large-N dual description of branes and anti-branes wrapped on rigid S^2's within a local Calabi-Yau, using a planar matrix model to compute the effective potential. Two-loop corrections lift vacuum degeneracies and generate an axion potential, with discrete jumps in the preferred confining vacuum as the S^2 positions change; additional unwrapped S^2's introduce new phase dynamics and hopping between sites that can slow annihilation and alter end states. The study also connects geometric positions to strong CP constraints via CP-invariant submanifolds and discrete symmetries, and it explores speculative mechanisms for stabilizing the radial mode through glueball-phase dynamics. Together, these results illuminate rich phase structure, metastability endpoints, and nontrivial decay channels in geometric engineering of non-supersymmetric vacua. The framework provides a tractable bridge between matrix-model techniques and geometric transitions in string theory, with potential implications for moduli stabilization and CP properties in compactifications.

Abstract

Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.

Figures (7)

• Figure 1: Depiction of flux line annihilation in a two cut geometry which initially consists of $N>0$ units of flux through one cut and $-N$ through the other. In the depiction on the left, $M>0$ D5-branes wrap the interpolating $3$-cycle between the two $S^{3}$'s supported by flux. In the Minkowski spacetime the stack of D5-branes separates a bubble of vacuum with flux numbers $(M-N,N-M)$ from one with flux numbers $(-N,N)$. The end of the annihilation process and the corresponding flux numbers are shown on the right.
• Figure 2: Two loop corrections to the glueball potential lift the degeneracy in energy density between the confining vacua of the theory. These vacua correspond to distinct orientations of the branch cuts in the closed string dual geometry. The metastable branch cut orientations denoted by dashed lines eventually decay to the energetically preferred configuration denoted by a solid line.
• Figure 3: Depiction of the complex $x$-plane corresponding to the Riemann surface defined by equation (\ref{['deformedcon']}) 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 4: Depiction of all Feynman diagrams which contribute to the $M_{i}^{2}M_{j}$ term of $\mathcal{F}_{pert}$ for $i\neq j$. In each diagram, ghost propagators are denoted by white and $\Phi$ propagators by dashed lines. The index loops of each diagram are also shown.
• Figure 5: Depiction of branch cut orientation in the lowest energy confining vacuum of the three cut system with $N_{1}>0$ units of flux through the cut near $x=a$, $N_{2}<0$ units of flux through the cut near $x=-a$ and $N_{3}=0$ units of flux through the cut near $x=iL$ with $L,a>0$. The presence of the additional minimal size $S^{2}$ at $x=iL$ causes the two cuts supported by flux to tip up.