Geometrically Induced Phase Transitions at Large N

TL;DR

This paper explores phase transitions in a large N brane system within a Calabi-Yau threefold, revealing how geometric changes induce vacuum shifts and affect brane annihilation, with implications for vacuum stability.

Contribution

It introduces a detailed analysis of phase transitions caused by geometric rearrangements in a large N brane setup, including the effects of higher-order corrections on vacuum structure.

Findings

Degenerate vacua split at two-loop order, generating an axion potential.

Changing S^2 positions causes discrete jumps in the preferred vacuum.

Branes must hop between S^2's, increasing non-supersymmetric vacuum lifetimes.

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.