Abstract:

In the context of gauge/string theory correspondences, the geometry of membranes and space-times must be seen as an emergent phenomenon arising from a strongly coupled quantum field theory with a large local symmetry or gauge group.

I shall discuss the dual description of membranes in terms of long, gauge-invariant, local operators in the Maldacena and ABJM correspondences, focusing primarily on a class of D-branes known as giant gravitons. These restricted Schur polynomial operators in the MSYM and ABJM theories form complete, exactly orthonormal bases with respect to the free field, two-point correlation functions and are built using the representation theory of the permutation group.

Various BPS, non-spherical, D3-brane and D4-brane giant graviton configurations, embedded into and moving on the compact spaces S⁵ and CP³, will be constructed in type IIB string theory on AdS₅xS⁵ and type IIA string theory on AdS₄xCP³ respectively. In the latter case, the D4-brane giants embedded into the complex projective space CP³ are descendants of M5-brane giant gravitons in S⁷ under the compactification on the S¹ Hopf fibre which takes S⁷ to CP³.

I shall finally discuss to what extent it has so far proven possible to view the non- trivial geometry of these membranes from the perspective of the dual operators.