Giant Gravitons in Conformal Field Theory

Abstract

Giant gravitons in AdS 5 × S 5 , and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS 7 × S 4 and the dual (2, 0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

(Non)-integrability of geodesics in D-brane backgrounds

“…The most useful version of the AdS/CFT duality involves field theory on R × S 3 , then the bulk configurations satisfying (1.2) are represented by fundamental strings in the presence of giant gravitons [23,24]. The interactions between these objects can be very complicated [25][26][27], but additional simplifications occur for semiclassical configurations of giant gravitons with J ∼ N 2 , which can be viewed as classical geometries [28].…”

“…The Poincare and SO(m + 1) × SO(n + 1) symmetries of (3.21) lead to a partial separation of the Hamilton-Jacobi equation (1.3) for geodesics (this equation is a counterpart of (3.8)): 24) where…”

The Bethe ansatz equations for reflecting magnons

“…In the N = 4 super-Yang-Mills integrability is made manifest in the computation of anomalous dimensions of single trace operators. However, the gauge theory also contain baryonic operators [5] which, for instance, are given by determinants instead of traces. Such baryonic operators, i.e.…”

Bubbling AdS and vacuum string field theory

“…A giant graviton is represented by a single column Young diagram, whose maximum length is of course N . A giant graviton, [5,6,15] is a half-BPS state which can be described as a D3-brane wrapping around an S 3 cycles in the S 5 factor of AdS 5 × S 5 . Stability is guaranteed by the spinning of the brane around an axis in S 5 .…”

“…Under this correspondence the (x 1 , x 2 ) ↔ (q, p) plane becomes noncommutative. It is a well-known fact that, under this correspondence the classical Wigner distributions like (12,14,15) are mapped into projectors of the Moyal star algebra:…”