Supertwistor Orbifolds: Gauge Theory Amplitudes and Topological Strings

TL;DR

This paper extends Witten's twistor string correspondence to less supersymmetric and more complex gauge theories via orbifolding supertwistor space, exploring their amplitudes, mirror symmetry, and topological string duals.

Contribution

It introduces an orbifolding method to construct and analyze gauge theories with reduced supersymmetry and complex matter content within the twistor string framework.

Findings

Constructed orbifolds of supertwistor space dual to N=2, 1, 0 quiver gauge theories.

Analyzed multiparton amplitudes involving fermions and U(1) interactions.

Explored mirror symmetry and parity in topological B-model on superorbifolds.

Abstract

Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space $CP^{3|4}$. We extend Witten's correspondence to gauge theories with lower supersymmetries, product gauge groups, and fermions and scalars in complex representations. Such gauge theories arise in high-energy limit of the Standard Model of strong and electroweak interactions. We construct such theories by orbifolding prescription. Much like gauge and string theories, such prescription is applicable equally well to topological string theories on supertwistor space. We work out several examples of orbifolds of $CP^{3|4}$ that are dual to N=2, 1, 0 quiver gauge theories. We study gauged sigma model describing topological B-model on the superorbifolds, and explore mirror pairs with particular attention to the parity symmetry. We check the orbifold construction by studying multiparton amplitudes in these theories with particular attention to those involving fermions in bifundamental representations and interactions involving U(1) subgroups.