22/07/2016, 11:30 — 12:30 — Amphitheatre Ea1, North Tower, IST
Simeon Hellerman, Kavli IPMU, The University of Tokyo

Vacuum Manifolds from Local Operators

In this talk we consider ${\mathcal N}=2$ superconformal field theories in three dimensions with vacuum manifolds of a single complex dimension. In such theories we show there always exists a special one-complex-parameter family of normalizable states on the sphere with the property that expectation values of products of chiral primaries in these states are precisely products one-point functions. These states are themselves coherent superpositions of scalar chiral primaries, with coefficients that can be expressed in terms of conformal bootstrap data. We show that in a certain scaling limit, expectation values of local operators in these states become expectation values in a super-Poincaré invariant vacuum with nonzero vev for the complex modulus. Using this relationship, we express observables in states on the vacuum manifold in terms of bootstrap data. We also make certain observations about the analytic structure of observables as a function of the coherent state parameter, and use this relationship to draw conclusions about the convergence properties of the $1/J$ series expansion for observables in states with large R-charge $J$.