Periodic Reporting for period 1 - RGxGRAV (Non-relativistic Renormalization Group flows from supergravity)
Reporting period: 2021-09-01 to 2023-08-31
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.
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.
Over the course of three work packages, new deformations of (super) conformal field theories were constructed, the holographic duals of these deformations were identified, and the phenomenolgy of these systems was explored. One class of deformations that played an important role in this work arises when the UV theory is placed on a curved manifold known as a "spindle". A spindle is topologically a two dimensional sphere, but "pinched" at its poles. By studying this deformed theory in its holographic limit, we constructed explicitly gravitational solutions that are dual to the putative IR endpoint of the RG flow from the deformed theory. Through application of modern field theory techniques such as "c-extremization" and anomaly polynomial reduction, we demonstrated that the holographic central charge of our gravitational solutions preceisly matched the field theory prediction. Surprisingly, we found that the holographic computation of these central charges depends only on the geometric data of the spindle on which the UV theory is compactified.
We further studied a distinct family of deformations known as "monodromy defects"--like vortices in four dimensional theories. Applying our methodology to these systems allowed for the construction of holographic duals to monodromy defect theories in a collection of interesting systems in three and four dimensions. Again, we investigated these gravitational duals with the full power of holography, and succeeded in verifying and extending conjectured relationships between correlation functions in these theories and defect anomaly coefficients.
These results were disseminated through various channels, including publication in high impact journals, invited seminar talks, and international conferences and workshops. Of particular note, the results of this project were presented in an invited seminar at the 2023 Defects, Strings, and Fields workshop for experts, held on Jeju island. They were also shown in the Iberian Strings conference in both 2022 and 2023, and the 12th Regional Meeting in String Theory. Moreover, this action was instrumental in the realisation of the workshop Conformal Field Theories and Quantum Gravity, held locally at the University of Crete. This one week event brought top researchers from throughout Europe to the host institution for an intensive program focused on various aspects of theoretical physics related to the central themes of this project.
The fundamental ideas driving this project were also presented in a variety of outreach activities. Specifically, the University of Crete hosts the "Particle Physics Masterclass" for high school physics learners. In this event, students from around Crete visit the university to attend lessons on aspects of theoretical physics (including those relevant to this project), and to participate in a mock analysis activity supervised by the members of the host institution and physicists from CERN. The core ideas of this action were also presented during the University of Crete Physics open house for prospective undergraduates. This particular event is designed to encourage the best students to enroll at the University of Crete by showcasing the most noteworthy research activities in the department.
We further studied a distinct family of deformations known as "monodromy defects"--like vortices in four dimensional theories. Applying our methodology to these systems allowed for the construction of holographic duals to monodromy defect theories in a collection of interesting systems in three and four dimensions. Again, we investigated these gravitational duals with the full power of holography, and succeeded in verifying and extending conjectured relationships between correlation functions in these theories and defect anomaly coefficients.
These results were disseminated through various channels, including publication in high impact journals, invited seminar talks, and international conferences and workshops. Of particular note, the results of this project were presented in an invited seminar at the 2023 Defects, Strings, and Fields workshop for experts, held on Jeju island. They were also shown in the Iberian Strings conference in both 2022 and 2023, and the 12th Regional Meeting in String Theory. Moreover, this action was instrumental in the realisation of the workshop Conformal Field Theories and Quantum Gravity, held locally at the University of Crete. This one week event brought top researchers from throughout Europe to the host institution for an intensive program focused on various aspects of theoretical physics related to the central themes of this project.
The fundamental ideas driving this project were also presented in a variety of outreach activities. Specifically, the University of Crete hosts the "Particle Physics Masterclass" for high school physics learners. In this event, students from around Crete visit the university to attend lessons on aspects of theoretical physics (including those relevant to this project), and to participate in a mock analysis activity supervised by the members of the host institution and physicists from CERN. The core ideas of this action were also presented during the University of Crete Physics open house for prospective undergraduates. This particular event is designed to encourage the best students to enroll at the University of Crete by showcasing the most noteworthy research activities in the department.
The results of this action are, in effect, now the state of the art for precision applications of holographic duality to theories deformed by spatially varying couplings. We have constructed new examples of such systems, developed novel tools for their analysis, and uncovered powerful and unexpected relationships between correlation functions in such theories and other observables. Independent of holography, we further advanced the state of the art for non-relativitsic RG flows, by providing explicit examples of large classes of such flows which are amenable to computation. Along the way, we have also furthered the active area of research devoted to constructing supersymmetric anti-de Sitter (AdS) solutions to the low energy limit of string/M-theory. This work sets the stage for extensions of all of these new lines of research, and can be expected to play an important role in subsequent investigations of such systems.
That this research has already garnered considerable attention in the published literature is indicative of its expected impact. Presently, work by other researchers applies our techniques to distinct systems of interest, enlarging the set of examples to include systems in other dimensions and with other field content. Moreover, insights from this project have played an important role in developing powerful new mathematical methods for extracting holographic observables from gravitational backgrounds. More broadly, this action has initiated and made important progress along a line of research that makes contact with diverse areas of contemporary physics research, from condensed matter to cosmology.
That this research has already garnered considerable attention in the published literature is indicative of its expected impact. Presently, work by other researchers applies our techniques to distinct systems of interest, enlarging the set of examples to include systems in other dimensions and with other field content. Moreover, insights from this project have played an important role in developing powerful new mathematical methods for extracting holographic observables from gravitational backgrounds. More broadly, this action has initiated and made important progress along a line of research that makes contact with diverse areas of contemporary physics research, from condensed matter to cosmology.