Type IIB Flows with N=1 Supersymmetry

TL;DR

This paper derives explicit equations for $ =1$ supersymmetric type IIB string backgrounds with fluxes, enabling systematic study of diverse solutions and flows with specific properties.

Contribution

It generalizes previous equations to arbitrary spinor relations, providing a comprehensive framework for analyzing $ =1$ flux backgrounds in type IIB string theory.

Findings

Derived explicit supersymmetry equations for general $ =1$ backgrounds.

Explored specific flux flow classes with distinct properties.

Discussed features and relations of various flux solutions.

Abstract

We write general and explicit equations which solve the supersymmetry transformations with two arbitrary complex-proportional Weyl spinors on $\mathcal{N}=1$ supersymmetric type IIB strings backgrounds with all R-R $F_1$, $F_3$, $F_5$ and NS-NS $H_3$ fluxes turned on using SU(3) structures. The equations are generalizations of the ones found for specific relations between the two spinors by Grana, Minasian, Petrini and Tomasiello in [1] and by Butti, Grana, Minasian, Petrini and Zaffaroni in [2]. The general equations allow to study systematically generic type IIB backgrounds with $\mathcal{N}=1$ supersymmetry. We then explore some specific classes of flows with constant axion, flows with constant dilaton, flows on conformally Calabi-Yau backgrounds, flows with imaginary self-dual 3-form flux, flows with constant ratio of the two spinors, the corresponding equations are written down and some of their features and relations are discussed.