Bulk thimbles dual to trace relations

TL;DR

This paper explores the duality between bulk trace relations and boundary operators using the maximal giant graviton in AdS/CFT, revealing its instability and the role of quantized imaginary phase space in boundary-bulk correspondence.

Contribution

It introduces a novel connection between trace relations and bulk duals via the quantization of an imaginary phase space associated with the maximal giant graviton.

Findings

Maximal giant is an unstable saddle point in the partition function.

Quantization of the imaginary phase space contributes negatively to the partition function.

Proposes a model connecting different components of the bulk half-BPS field space.

Abstract

The maximal giant graviton is a D-brane wrapping a maximal $S^3\subset S^5$ within $\text{AdS}_5\times S^5$. It represents an upper bound on the $R$ charge that can be carried by certain bulk states. We study the maximal giant and its half-BPS fluctuations, motivated by a recent proposal \cite{Lee:2023iil} connecting these fluctuations to trace relations in the boundary theory. In a computation of the partition function of half-BPS states, we find that the maximal giant is an unstable saddle point and that its Lefschetz thimble corresponds to the quantization of an imaginary phase space. The states resulting from the quantization of this phase space contribute negatively to the partition function and can be regarded as bulk duals of trace relations. Finally, we study a model for a path integral that would connect together components of the bulk half-BPS field space with different numbers of giants.