M-Branes and Metastable States

TL;DR

This work analyzes metastable supersymmetry-breaking states in the M-theory CGLP/Stenzel background by placing p anti-M2 branes at the bottom of the warped throat, where flux induces polarization into an M5-brane wrapping an S^3 at fixed ψ. The authors derive a metastability window p/\tilde{M} \lesssim 0.054 and construct a smooth O(3)-symmetric Euclidean bounce to compute the decay rate, finding lifetimes exponentially long for small p; they also present a Type IIA reduction where anti-F1 strings puff into a D4-brane wrapping an S^3 inside the S^4, with equivalent tunneling dynamics. The results extend to the M-theory uplift, yielding an O(3) bounce with a decay exponent B ~ (4 \hat{H}_0^2 / 729) (\tilde{M}^4 / p^2) in the small-p limit, highlighting a robust, non-confining IR dynamics in the dual 2+1D N=2 theory. Overall, the paper provides a controlled holographic realization of long-lived metastable SUSY breaking via brane polarization and brane-flux annihilation, with concrete semiclassical decay rates and cross-checks between M-theory and Type IIA pictures.

Abstract

We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of R^{2,1} and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \tilde{M} units of 4-form flux. The dual (2+1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sphere. This supersymmetry breaking state turns out to be metastable for p / \tilde{M} < 0.054. We find a smooth O(3)-symmetric Euclidean bounce solution in the M5-brane world volume theory that describes the decay of the false vacuum. Calculation of the Euclidean action shows that the metastable state is extremely long-lived. We also describe the corresponding metastable states and their decay in the type IIA background obtained by reduction along one of the spatial directions of R^{2,1}.

Figures (5)

• Figure 1: The D4-brane potential given in eq. \ref{['LagDSimp']}. The potential has a metastable minimum marked by a black dot for $p/\tilde{M} \lesssim 0.0538$---see eq. \ref{['GotpMax']}.
• Figure 2: The angle $\psi_{\rm min}$ at which there is a metastable minimum as a function of $p/\tilde{M}$. The exact solution value of $\psi_{\rm min}$ found by solving eq. \ref{['QuarticEquation']} is plotted in solid black, and the small $p$ approximation \ref{['SmallpBehavior']} is plotted in dotted orange.
• Figure 3: A sample solution to the equation of motion following from \ref{['SERadialAgain']} for the case $p/\tilde{M} = 3/100$. The numerical solution is shown in black, and the asymptotic value it reaches as $r \to \infty$ is shown in dashed red.
• Figure 4: The on-shell action for the Euclidean bounce that mediates the decay of the metastable vacuum in the type IIA construction. The numerical results are shown in black, and the small $p$ approximation \ref{['GotrStar']} is shown in dashed red.
• Figure 5: The on-shell action for the Euclidean bounce that mediates the decay of the metastable vacuum in the M-theory construction. The numerical results are shown in black, and the small $p$ approximation \ref{['GotrStarM']} is shown in dashed red.