RGxGRAV · Non-relativistic Renormalization Group flows from supergravity

Non-relativistic Renormalization Group flows from supergravity

Understanding the dependence of physical systems on the length scale at which they are studied provides a powerful perspective formalised in the renormalization group (RG). This perspective can be used to reformulate this scale dependence as a flow in the space of quantum field theories. A remarkable feature of the renormalization group is its ability to characterise wildly different physical systems via a universal framework. Indeed, applications of the RG machinery appear across the energy spectrum, from electronic and atomic systems to the physics of interacting quarks and gluons. Despite its ubiquity in theoretical physics, some of the most interesting aspects of RG flow remain ill-understood. This is particularly true when the relevant deformation driving the RG flow explicitly breaks space-time symmetries of the UV theory. Such deformations have the potential to be of great phenomenological interest. They can be used to explore the low energy physics of UV fixed point theories deformed by a lattice, or placed on a curved background. Additionally, they describe theories with localised defects, such as impurities or interfaces, as well as systems with boundaries. These systems arise in nearly all disciplines of contemporary physics research, including condensed matter, high energy particle physics, and cosmology. Accordingly, it is highly desirable to develop and extend RG techniques that are well suited to this class of flows, and can subsequently inform and advance our expectations of the physics in these diverse theories. This is the primary objective of this proposal. In this action, we investigate such "non-relativistic RG flows" and advance our understanding of their properties along several significant directions. Among the most important conclusions of this research is the insight that techniques from supergravity can be used in concert with holographic duality to compute precision data for the IR endpoint of RG flows initiated by deforming superconformal theories with spatially varying couplings. Specifically, we showed that in such situations quantities like central charges which characterize the IR theory can be computed exactly without ever explicitly solving the gravitational equations. This surprising result represents not only an enormous technical simplification, but also extends and generalizes the validity of (defect) field theory results and hints at a more fundamental mathematical structure underlying such systems which has subsequently received considerable attention.

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