Novel Representation of an Integrated Correlator in N=4 Supersymmetric Yang-Mills Theory.

An integrated correlator of four superconformal stress-tensor primaries of N=4 supersymmetric SU(N) Yang-Mills theory (SYM), originally obtained by localization, is reexpressed as a two-dimensional lattice sum that is manifestly invariant under SL(2,Z) S duality. This expression is shown to satisfy a novel Laplace equation in the complex coupling constant τ that relates the SU(N) integrated correlator to those of the SU(N+1) and SU(N-1) theories. The lattice sum is shown to precisely reproduce known perturbative and nonperturbative properties of N=4 SYM for any finite N, as well as extending previously conjectured properties of the large-N expansion.

Resurgence in quantum field theory: nonperturbative effects in the principal chiral model.

We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory.

Volume independence in the large N limit and an emergent fermionic symmetry.

Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories is believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius.