Tetrahedron instantons

TL;DR

This paper introduces tetrahedron instantons, a new class of instantons in string theory related to intersecting D-branes, and explores their moduli space, partition functions, and underlying symmetries.

Contribution

It constructs tetrahedron instantons as solutions to noncommutative instanton equations and analyzes their moduli space and partition functions, connecting to known invariants and proposing new symmetries.

Findings

Computed the instanton partition function via localization and elliptic genus methods.

Established the connection between tetrahedron instantons and higher-rank Donaldson-Thomas invariants.

Discovered a free field representation indicating a new symmetry acting on moduli space cohomology.

Abstract

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting real codimension-two supersymmetric defects. Moreover, we construct the tetrahedron instantons as particular solutions of general instanton equations in noncommutative field theory. We analyze the moduli space of tetrahedron instantons and discuss the geometric interpretations. We compute the instanton partition function both via the equivariant localization on the moduli space of tetrahedron instantons and via the elliptic genus of the worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes, obtaining the same result. The instanton partition function of the tetrahedron instantons lies between the higher-rank Donaldson-Thomas invariants on $\mathbb{C}^{3}$ and the partition function of the magnificent four model, which is conjectured to be the mother of all instanton partition functions. Finally, we show that the instanton partition function admits a free field representation, suggesting the existence of a novel kind of symmetry which acts on the cohomology of the moduli spaces of tetrahedron instantons.