Making Quantum Gravity Computable

The gauge/gravity duality relates supersymmetric gauge theories to superstring/M-theory. Powerful Monte Carlo methods developed in lattice QCD can be applied to study the former,and from the simulation data we can extract the quantum gravitational effects. In this talk I will give a brief introduction to lattice gauge theory and supersymmetry on a lattice, and show some applications to quantum gravity via the gauge/gravity duality.

In the last decade various cosmological spacetimes have been quantized using the techniques of loop quantum gravity. To understand singularity resolution and decipher reliable Planck scale physics, development of new numerical methods and usage of high performance computing is critical in loop quantum cosmology. In recent years, these developments have robustly demonstrated resolution of singularities in quantum spacetimes. These methods have provided detailed understanding of the emergence of new physics at Planck scale, and of classicality when spacetime curvature becomes very small.  Further, they have validated an effective spacetime description of the underlying quantum geometry -- a key ingredient of phenomenological predictions in loop quantum cosmology. These lectures will introduce these numerical methods.

In the last decade various cosmological spacetimes have been quantized using the techniques of loop quantum gravity. To understand singularity resolution and decipher reliable Planck scale physics, development of new numerical methods and usage of high performance computing is critical in loop quantum cosmology. In recent years, these developments have robustly demonstrated resolution of singularities in quantum spacetimes. These methods have provided detailed understanding of the emergence of new physics at Planck scale, and of classicality when spacetime curvature becomes very small.  Further, they have validated an effective spacetime description of the underlying quantum geometry -- a key ingredient of phenomenological predictions in loop quantum cosmology. These lectures will introduce these numerical methods.

Functional renormalization group techniques based on Wetterichs equation provide a powerful tool for studying the properties of gravity in the quantum regime and its connection to the observable low-energy world. Explicit computations in this framework require the evaluation of functional traces over operator-valued functions. In these lectures I will give a pedagogical introduction to the Universal Renormalization Group Machine, a combinatorial algorithm which allows evaluating such traces in a systematic way. Moreover, I will discuss flow equations for “composite operators” which may pave the route towards developing a microscopic description of quantum spacetime within the Asymptotic Safety approach.

Functional renormalization group techniques based on Wetterichs equation provide a powerful tool for studying the properties of gravity in the quantum regime and its connection to the observable low-energy world. Explicit computations in this framework require the evaluation of functional traces over operator-valued functions. In these lectures I will give a pedagogical introduction to the Universal Renormalization Group Machine, a combinatorial algorithm which allows evaluating such traces in a systematic way. Moreover, I will discuss flow equations for “composite operators” which may pave the route towards developing a microscopic description of quantum spacetime within the Asymptotic Safety approach.