This week

In this seminar, I will discuss two- and three-point correlation functions of chiral primary half-BPS operators in four-dimensional $\mathcal{N}=2$ superconformal circular, cyclic symmetric quiver theories. Using supersymmetric localization, these functions can be expressed as matrix integrals which, in the planar limit, reduce to Fredholm determinants of certain semi-infinite matrices. This powerful representation allows us to investigate the correlation functions across the parameter space of the quiver theory, including both weak and strong coupling regimes and various limits of the number of nodes and the operator scaling dimensions. At strong coupling, the standard semiclassical AdS/CFT expansion diverges in the long quiver limit. However, by incorporating both perturbative corrections (in negative powers of the 't Hooft coupling) and an infinite tower of nonperturbative, exponentially suppressed contributions, we derive a remarkably simple expression for the correlation functions in this limit.These functions exhibit exponential decay with increasing node separation and admit an interpretation within a five-dimensional effective theory.We determine the mass spectrum of excitations propagating along the emergent fifth dimension within this theory, finding it to be given by the zeros of Bessel functions.

The AdS/CFT correspondence permits the study of bulk duals to free CFTs with gauge symmetries, such as U(N) with large N. In free models CFT correlators are explicitly known. Thermal observables reveal a black hole-like character of massive bulk objects, indicating that classical spacetime emerges by assuming large N in free theories, while strong coupling of the boundary theory is mainly significant quantitatively. I review the origins and the evidence for the above assertions, with future developments in mind. In general, it is important to consider finite but large N to capture non-perturbative gravity effects.

The period between inflation and nucleosynthesis can last for thirty orders of magnitude of time and represent half the lifetime of the universe on a logarithmic scale. But yet, there are minimal observational constraints on this epoch. String cosmologies motivate a rich set of modifications from the standard radiation-dominated post-inflationary assumption of Lambda CDM. In particular, string cosmology suggests the likelihood of moduli-dominated cosmologies through kination, tracker and matter epochs. I review the possible scenarios and observational possibilities, including a novel percolation scenario for formation of cosmic string networks.