Geometry from Gauge Theory

D.H. CORREA; G.A. SILVA

Buenos Aires

Workshop; Ten years of AdS/CFT; 2007

Strings@ar

We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB  geometries are captured by  their dual operators in  N=4 Super Yang-Mills. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets.  The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.