Quantum Fields and Strings

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.

I will explain a recently proposed holographic scenario for pure dS3 Einstein quantum gravity. The dual description is a double-scaled matrix model, which is capable of capturing bulk cosmological correlators integrated over the metric at future infinity in order to define gauge-invariant observables. Moreover the matrix model has precisely the right number of degrees of freedom to account for the de Sitter entropy associated with the cosmological horizon seen by an observer. A key step in the logic is a reformulation of the gravity theory in terms of a novel topological quantum field theory. Based on work with Lorenz Eberhardt, Beatrix Mühlmann, building on previous work with Victor Rodriguez.

In 1914, Ramanujan wrote down 17 intriguing formulas for 1/pi, which motivated the modern-day machinery of computing trillions of digits of pi. Most of these formulas lay unproven until the 1980s. The Canadian Borwein brothers wrote a comprehensive treatise proving these formulas in the 1980s. We can now ask, “What is the physics behind Ramanujan’s pi”? I will argue that the physics connection can be found via logarithmic conformal field theories, for instance, those studied in the fractional quantum hall effect, polymers, and percolation. The CFT connection gives rise to an infinite number of new formulas for pi. In contrast, the myriad Ramanujan formulas provoke us into looking into faster converging basis for conformal correlators, which is, in turn, provided by the stringy dispersion relation mentioned above.