A Non-perturbative Evidence toward the Positive Energy Conjecture for asymptotically locally AdS_5 IIB Supergravity on S^5

TL;DR

This paper provides non-perturbative evidence supporting the positive energy conjecture in type IIB supergravity on S^5 by analyzing classical solutions and identifying AdS solitons as the lowest energy, naked-singularity-free configurations.

Contribution

It demonstrates that among solutions with asymptotic AdS_5 geometry, only AdS black holes and solitons are free of naked singularities, supporting the positive energy conjecture.

Findings

AdS solitons are the unique lowest energy solutions without naked singularities.

Other solutions interpolating between black holes and solitons have naked singularities.

The results align with the positive energy conjecture for IIB supergravity on S^5.

Abstract

We consider the classical solution of the type IIB supergravity spontaneously compactified on S^5, whose metric depends only on the radial coordinate and whose asymptotic geometry is locally that of AdS_5, i.e., R \times S^1 \times T^2. We solve the equations of motion to obtain the general solutions satisfying these conditions, and find that the only naked-singularity-free solutions are the AdS black holes and AdS solitons. The other solutions, that smoothly interpolate these two solutions, are shown to have naked singularities even though their Ricci tensor is proportional to the metric with a negative constant. Thus, among the possible solutions of this type, the AdS solitons are the unique lowest energy solution; this result is consistent with the recently proposed positive energy conjecture for the IIB AdS supergravity on S^5.