Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --

TL;DR

This paper develops a new fermion-based framework for describing multi-charge 1/2-BPS operators in N=4 super Yang-Mills, leading to a second-quantized D3-brane theory with novel exclusion and nonlocality features.

Contribution

It introduces a generalized fermion representation for multi-charge BPS operators, incorporating a new Dexclusion principle and nonlocality, advancing towards a D-brane field theory.

Findings

Constructed a second-quantized D3-brane model with Dexclusion principle.

Linked nonlocality to spacetime uncertainty and symmetry considerations.

Supported the model's consistency with supergravity geometries like superstars.

Abstract

We extend the fermion representation of single-charge 1/2-BPS operators in the four-dimensional N=4 super Yang-Mills theory to general (multi-charge) 1/2-BPS operators such that all six directions of scalar fields play roles on an equal footing. This enables us to construct a field-theorectic representation for a second-quantized system of spherical D3-branes in the 1/2-BPS sector. The Fock space of D3-branes is characterized by a novel exclusion principle (called `Dexclusion' principle), and also by a nonlocality which is consistent with the spacetime uncertainty relation. The Dexclusion principle is realized by composites of two operators, obeying the usual canonical anticommutation relation and the Cuntz algebra, respectively. The nonlocality appears as a consequence of a superselction rule associated with a symmetry which is related to the scale invariance of the super Yang-Mills theory. The entropy of the so-called superstars, with multiple charges, which have been proposed to be geometries corresponding to the condensation of giant gravitons is discussed from our viewpoint and is argued to be consistent with the Dexclusion principle. Our construction may be regarded as a first step towards a possible new framework of general D-brane field theory.