A Landscape of Field Theories

TL;DR

This paper explores the vast landscape of possible backgrounds for quantum field theories, emphasizing the role of supergravity fluxes in string theory and demonstrating how different choices lead to diverse lower-dimensional theories.

Contribution

It introduces the concept of a landscape of field theory backgrounds, incorporating metric, symmetry backgrounds, and fluxes, with evidence from compactified six-dimensional theories.

Findings

Different background choices yield distinct 2D theories.

Flux choices influence supersymmetry preservation.

The landscape encompasses a wide variety of field theories.

Abstract

Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.