Multi-Spin Giants

TL;DR

This paper investigates multi-spin giant graviton solutions in AdS_m x S^n, analyzing their properties, supersymmetry, and quantization, revealing new insights into their spectra and BPS bounds.

Contribution

It constructs and analyzes two-spin giant solutions in AdS_m x S^n, exploring their supersymmetry, properties, and exact quantization of related sigma-models.

Findings

Two-spin giant solutions are 1/2 supersymmetric for specific (m,n)

Vibration modes have real, positive, evenly spaced frequencies

Exact quantization reveals Poschl-Teller potentials and anomalous dimensions

Abstract

We examine spherical p-branes in AdS_m x S^n, that wrap an S^p in either AdS_m (p=m-2) or S^n (p=n-2). We first construct a two-spin giant solution expanding in S^n and has spins both in AdS_m and S^n. For (m,n)={(5,5),(4,7),(7,4)}, it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, non-commutativity, zero-modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the (0+1)-dimensional sigma-models obtained by keeping generally time-dependent transverse coordinates, describing warped product of a breathing-mode and a point-particle on S^n or AdS_m x S^1. The BPS bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma-model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Poschl-Teller type potentials, and calculate its contribution to the anomalous dimension.