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Abstract:

We study the prospects of detecting dark matter coupled to the spin of the electron, such that it may scatter and excite magnons—collective excitations of electronic spins. We show that materials exhibiting long-range magnetic order where the spins are coupled only along a plane may act as directional dark matter detectors. These quasi-two-dimensional materials possess anisotropic dispersion relations and structure functions which induce a sidereal modulation in the excitation rate. We calculate the expected signal rate for some candidate (anti)ferromagnets, demonstrating a possible route to the direct detection of spin-dependent dark matter in the keV to MeV mass range.

Abstract:

We investigate the interaction between matter and causal dynamical triangulations (CDT) in the context of two-dimensional quantum gravity. We focus on the Ising model coupled to CDT, contrasting this with Liouville gravity and the relation to the Knizhnik-Polyakov-Zamolodchikov (KPZ) formula. We demonstrate analytically for the quenched model that the conformal dimensions of fields on CDT align with those on a fixed lattice. We do this using a combination of lattice methods and adapting the Duplantier-Sheffield framework to CDT, emphasizing the one-dimensional nature of CDT and its description via a stochastic differential equation.

Abstract:

We show that the conformal data of a range of large-N CFTs, the melonic CFTs, are specified by constrained extremization of the universal part of the sphere free energy F = − log ZSd, called F~. This family includes the generalized SYK models, the vector models (O(N), Gross-Neveu, etc.), and the tensor field theories. The known F and a-maximization procedures in SCFTs are therefore extended to these non-supersymmetric CFTs in continuous d. We establish our result using the two-particle irreducible (2PI) effective action, and, equivalently, by Feynman diagram resummation. The universal part of F~ interpolates in continuous dimension between the known C-functions, so we can interpret this result as an extremization of the number of IR degrees of freedom, in the spirit of the generalized c, F, a-theorems. The outcome is a complete classification of the melonic CFTs: they are the conformal mean field theories which extremize the universal part of the sphere free energy, subject to an IR marginality condition on the interaction Lagrangian.