Extended fermion representation of multi-charge 1/2-BPS operators in AdS/CFT — towards field theory of D-branes

We extend the fermion representation of single-charge 1/2-BPS operators inthe 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 onan equal footing. This enables us to construct a field-theorecticrepresentation for a second-quantized system of spherical D3-branes in the1/2-BPS sector. The Fock space of D3-branes is characterized by a novelexclusion principle (called `Dexclusion' principle), and also by a nonlocalitywhich is consistent with the spacetime uncertainty relation. The Dexclusionprinciple is realized by composites of two operators, obeying the usualcanonical anticommutation relation and the Cuntz algebra, respectively. Thenonlocality appears as a consequence of a superselction rule associated with asymmetry which is related to the scale invariance of the super Yang-Millstheory. The entropy of the so-called superstars, with multiple charges, whichhave been proposed to be geometries corresponding to the condensation of giantgravitons is discussed from our viewpoint and is argued to be consistent withthe Dexclusion principle. Our construction may be regarded as a first steptowards a possible new framework of general D-brane field theory.Comment: 43 pages, 4 figures; version 2, corrected typos and added reference