Geometry from Gauge Theory

D.H. CORREA; G.A. SILVA

Buenos Aires, Argentina

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 dualoperators in  N=4 Super Yang-Mills. The type IIB solutionsare characterized by arbitrary droplet pictures in a plane and weconsider, in particular, axially symmetric droplets.  The 1-loopanomalous dimension of the dual gauge theory operatorsprobed with single traces is described by some bosonic latticeHamiltonians. These Hamiltonians are shown to encode the topology ofthe droplets. In appropriate BMN limits, theHamiltonians spectrum reproduces the spectrum of near-BPS stringexcitations propagating along each of the individualedges of the droplet. We also study semiclassicalregimes for the Hamiltonians. For droplets having disconnectedconstituents, the Hamiltonian admits different complimentarysemiclassical descriptions, each one replicating the semiclassicaldescription for closed strings extending in each of theconstituents.