Competing orders in asymptotic safety - from frustrated magnets to observational tests of quantum gravity

• Applicant: Dr. Shouryya Ray
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 518075237

The search for a theory of quantum gravity is one of the most profound challenges of fundamental physics: in view of Einstein's reformulation of gravity as a pseudoforce caused by spacetime curvature, it is tantamount to searching for a fundamental understanding of the microscopic structure of spacetime itself. An intriguing solution may be given by the asymptotic safety scenario, which posits that quantum scale symmetry is restored at and above the Planck scale and thereby recovers predictivity from the clutches of perturbative non-renormalizability. A direct observation of this scale symmetry by definition requires access to transplanckian energies, but there are ways in which the ideas of asymptotic safety can be tested also at low energies, at two different levels. On one hand, quantum scale symmetry as a symmetry is powerful enough to strongly constrain phenomenology at low energies where the symmetry is no longer intact; low-energy observations (e.g., at particle accelerators) can thus provide tests for asymptotically safe quantum gravity. More indirectly, some of the general ideas underpinning asymptotic safety can be tested in analogue systems: 2D quantum critical semimetals, where quantum scale symmetry effectively emerges over long wavelengths of the order of the correlation length. The scale symmetric regime can then in fact be accessed in experiments at terrestrial scales. This project aims at a thorough understanding of how the interplay of order-parameter fluctuations influences the low-energy matter spectrum of asymptotically safe quantum gravity. On the direct level, we wish to answer two questions: Which constraints must the theory space of asymptotically safe quantum gravity fulfil to ensure the absence of gravitational chiral symmetry breaking and planckian particle masses? What is the proton lifetime in completions of the Standard Model with asymptotically safe quantum gravity? Though some progress has been made previously in certain simplified settings, all possible condensation or decay channels still need to be carefully accounted for: it is a priori unclear, whether additional channels will cooperate or compete with each other and the ones studied hitherto. The importance of accounting for the interplay of condensation channels is particularly transparent in the case of analogue asymptotically safe systems like quantum critical semimetals. We shall hence begin by devoting some effort in computing precise critical exponents for the spontaneous breakdown of a certain kind of isospin symmetry in 2D Dirac semimetals at zero temperature. The absence of gauge fields allows an isolated study on the competing-order-parameter problem in asymptotic safety; the accessibility of quantum critical semimetals in the laboratory allows for direct experimental tests of predictions, thereby furnishing a useful sandbox for the quantum gravity problems we shall study subsequently.

• DFG Programme: WBP Fellowship
• International Connection: Denmark
• Host: Professorin Dr. Astrid Eichhorn