Proving a 40-year-old conjecture using lattice simulations

Proving a 40-year-old conjecture using lattice simulations

This project is focused on the study of field theories relevant for building holographic cosmological models. These models propose to use hypothetical theories dual to the unknown laws of gravity in the early universe and predict observable phenomena such as the cosmic microwave background (CMB). This allows to provide new models to consolidate current ones in observational cosmology, but also to constrain the existence of such dual theories.

Holographic cosmological models were shown [1,2] to describe well the CMB spectrum as measured by the Planck satellite. However, the observables from the dual theory were only computed in perturbation theory, which likely suffers from unphysical infrared divergences, limiting the predictivity of the model. It was conjectured in 1981 [3,4] that these divergences are just artefacts of perturbation theory, and do not exist in the full theory.

In this project we studied a specific class of field theories relevant for holographic models, scalar SU(N) theories in the adjoint representation and in a Euclidean three-dimensional space. We performed large-scale lattice simulations of the SU(2) and SU(4) theories on the DiRAC Data Intensive service in Cambridge University, and studied the phase diagram of the theory. We determined precisely the critical mass of the theory through finite-size scaling, in a completely non-perturbative manner. Through both frequentists and Bayesian hypothesis testing we found that our data strongly rejects the presence of infrared divergences in the critical mass, confirming the conjecture of Appelquist, Jackiw, Pisarski, and Templeton. Our result was published in the Physical Review Letters [5].

This important step sets the stage for using lattice simulations to understand the cosmological implications of holographic models, extending our knowledge of physics in the very early universe.

Figure 1 – Second-order phase transition in the dual SU(2) and SU(3) theories from the point of view of the Binder cumulant, which is the kurtosis of the magnetisation. The observed critical scaling with the simulation box size demonstrates the absence of infrared divergence as conjectured by Appelquist, Jackiw, Pisarski, and Templeton.


[1]: N. Afshordi, C. Corianò, L. D. Rose, E. Gould, and K. Skenderis, From Planck Data to Planck Era: Observational Tests of Holographic Cosmology, Phys.Rev.Lett. 118 (2017) 4, 041301.

[2]: N. Afshordi, E. Gould, and K. Skenderis, Constraining Holographic Cosmology Using Planck Data, Phys.Rev.D 95 (2017) 12, 123505.

[3]: R. Jackiw and S. Templeton, How Super-Renormalizable Interactions Cure Their Infrared Divergences, Phys.Rev.D 23 (1981), 2291.

[4]: T. Appelquist and R. D. Pisarski, High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics, Phys.Rev.D 23 (1981), 2305.

[5]: G. Cossu, L. D. Debbio, A. Juttner, B. Kitching-Morley, J. K. L. Lee, A. Portelli, H. B. Rocha, and K. Skenderis, Nonperturbative Infrared Finiteness in Super-Renormalisable Scalar Quantum Field Theory, Phys.Rev.Lett. 126 (2021) 22, 221601.