Generalized Born--Infeld Actions and Projective Cubic Curves

TL;DR

This paper explores complex supersymmetric Born-Infeld theories with multiple vector multiplets, classifying models via cubic prepotentials and linking their symmetries to projective cubic varieties.

Contribution

It provides an exact solution for quadratic constraints in multi-vector Born-Infeld models and classifies these models through cubic holomorphic prepotentials.

Findings

Exact solutions for quadratic constraints in three-vector models

Classification of models via cubic holomorphic prepotentials

Connection between symmetry structures and projective cubic varieties

Abstract

We investigate $U(1)^{\,n}$ supersymmetric Born-Infeld Lagrangians with a second non-linearly realized supersymmetry. The resulting non-linear structure is more complex than the square root present in the standard Born-Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties.