A description of 1/4 BPS configurations in minimal type IIB SUGRA

TL;DR

This work extends the Lin–Lunin–Maldacena framework from 1/2 BPS to 1/4 BPS configurations in minimal type IIB supergravity by enforcing an $SO(4)\times SO(2)$ symmetry and applying the Killing spinor bilinear method. All bosonic fields are expressed in terms of a single scalar, the Kahler potential $K$, together with radius scalars $G$ and $H$, yielding a nonlinear PDE for $K$ that couples to the four-dimensional Kahler base via determinant-of-Hessian structures and a radial relation $z=-2y\partial_y((1/y)\partial_y K)$. The four-dimensional base is shown to be Kahler with equal complex structures, and the background is constrained by first-order SUSY equations whose integrability implies the Einstein equations once flux Bianchi identities are satisfied. The results establish a concrete path to a moduli space of regular 1/4 BPS solutions and motivate further study of their SYM dual description with multiple complex matrices, as well as regularity conditions. The central insight is that a single scalar Kahler potential, together with a pair of scalars governing radii, suffices to determine the full 1/4 BPS geometry in this setup, with the nonlinear relation governing $K$ playing the role of a generalized LLM-type equation.

Abstract

In this paper we present an effort to extend the LLM construction of 1/2 BPS states in minimal IIB supergravity to configurations that preserve 1/4 of the total number of supersymmetries. Following the same techniques we reduce the problem to that of a single scalar which satisfies a non-linear equation. In particular, the scalar is identified to be the Kahler potential with which a four dimensional base space is equipped.