Which BPS Baryons Minimize Volume?

TL;DR

This paper investigates BPS 3-cycles in Sasaki-Einstein 5-manifolds, showing they do not always minimize volume but instead minimize D-brane energy through a generalized calibration, with examples on Y(p,q) manifolds.

Contribution

It introduces a generalized calibration framework for BPS cycles, demonstrating that they minimize D-brane energy rather than volume, with explicit examples on Y(p,q) manifolds.

Findings

BPS 3-cycles do not always minimize volume in their homology class.

Generalized calibration reproduces D-brane energy components.

Examples on Y(p,q) manifolds illustrate non-minimal volume BPS cycles.

Abstract

A BPS 3-cycle in a Sasaki-Einstein 5-manifold in general does not minimize volume in its homology class, as we illustrate with several examples of non-minimal volume BPS cycles on the 5-manifolds Y(p,q). Instead they minimize the energy of a wrapping D-brane, extremizing a generalized calibration. We present this generalized calibration and demonstrate that it reproduces both the Born-Infeld and the Wess-Zumino parts of the D3-brane energy.