Super-Giants in Gutowski-Reall Black Hole

TL;DR

This work classifies all bosonic BPS D3-brane probe configurations—giants and dual-giants—in the Gutowski–Reall black hole background, preserving the two supersymmetries of the geometry. Using κ-symmetry, the authors derive embedding equations that reduce to holomorphic constraints, describing D3-brane world-volumes as zeros of holomorphic functions in carefully chosen complex coordinates; world-volume fluxes are constrained to pull-backs of closed 2-forms and are captured by holomorphic data. The dual-giant sector is encoded by a single holomorphic constraint $F(\Psi_0,\Psi_1,\Psi_2)=0$, while the giant sector admits a Kim–Lee-type description with three holomorphic constraints $F^{(I)}$ that depend on five complex harmonics and unify the giants and dual-giants. Turning on world-volume flux preserves the same SUSY and is governed by a holomorphic 2-form $\mathcal G$ in the same complex variables, reproducing known AdS$_5\times S^5$ results in the $\omega\to0$ limit and enabling a path toward quantization and state counting of 1/16-BPS sectors in the dual ${\cal N}=4$ SYM. The framework thus provides a comprehensive, holomorphic classification of BPS D3-brane probes in GR and related geometries, with clear connections to holography and black-hole microstate physics.

Abstract

We present all bosonic giant and dual-giant type configurations of a probe D3-brane in the BPS single-parameter Gutowski-Reall black hole in 10d type IIB supergravity that do not break any of its supersymmetries. The resulting D3-brane world-volumes can be given by the common zeros of three holomorphic functions of five complex scalar harmonics of the geometry. These probe branes support world-volume electromagnetic fields which we characterise completely in terms of pull-backs of closed 2-forms. Our configurations can be seen as natural generalisations of known supersymmetric D3-branes in $AdS_5 \times S^5$ and approach them far away from the black hole horizon.