Self-duality in Dimensions $2n>4$: Equivalence of Various Definitions, and an Upper Bound for $p_2$

TL;DR

This paper establishes the equivalence of different notions of self-duality in higher even dimensions and provides an upper bound for the integral of the second Pontrjagin class over certain manifolds.

Contribution

It proves the equivalence between two definitions of self-duality in dimensions greater than four and derives an upper bound for the second Pontrjagin class integral.

Findings

Self-duality and strong self-duality are equivalent in dimensions 2n>4.

An explicit upper bound for the integral of (p_2)^n is obtained.

The results connect geometric duality concepts with topological invariants.

Abstract

We show that the self-duality defined in [Trautman, Int.J.Theor.Phys.,{\bf 16},561 (1977)] is equivalent to strong self-duality defined in [Bilge, Dereli and Kocak, Lett.Math.Phys., {\bf 36}, 301-309, (1996)] and we obtain an upper bound on $\int (p_2)^{n}$, where $p_2$ is the second Pontrjagin class of an $SO(N)$ bundle over a $8n$ dimensional manifold.