Counting Wobbling Dual-Giants

TL;DR

This paper derives BPS equations for D3-branes in AdS_5 x S^5, classifies known giant and dual-giant graviton solutions, and quantizes dual-giant configuration spaces, matching previous partition function results.

Contribution

It introduces a unified framework for BPS D3-brane solutions, maps dual-giant configuration spaces to hyperbolic projective spaces, and quantizes these spaces to match known partition functions.

Findings

Derived BPS equations for D3-branes in AdS_5 x S^5.

Mapped dual-giant configuration spaces to hyperbolic projective spaces.

Quantized dual-giant spaces and matched existing partition functions.

Abstract

We derive the BPS equations for D3-branes embedded in AdS_5 X S^5 that preserve at least two supercharges. These are given in terms of conditions on the pullbacks of some space-time differential four-forms. Solutions to our equations are shown to describe all the known giant and dual-giant gravitons in AdS_5 X S^5. We then argue that the configuration spaces of dual-giants can be mapped to non-compact hyperbolic versions of complex projective spaces, in contrast with the giants, whose configuration spaces have been mapped to complex projective spaces. We quantize the configuration space of the 1/8-BPS dual-giants with two angular momenta in AdS_5 and one angular momentum in S^5 and find agreement with the partition function in the literature obtained both from counting appropriate 1/8-BPS configurations of giants and the boundary gauge theory considerations.