Damodar Rajbhandari | Searcharxiv

arXiv2026

Bosonic Ghost Correlators: A Case Study

There has been a lot of recent work addressing the representation theory that underlies logarithmic conformal field theories. A full understanding of these models will however also need analytic data, in particular the correlation functions. Here, we explore the correlators of one of the most fundamental of all logarithmic models: the bosonic ghost system. In this first part, we use differential equations to show that certain correlation functions may be expressed using hypergeometric functions. Our main result is the consequent verification that there are four-point functions with logarithmic singularities. In a sequel, we will employ Coulomb gas and bootstrap methods to further refine the results presented here.

math.QA↗

arXiv2022

Generalised spectral dimensions in non-perturbative quantum gravity

The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories of quantum gravity has been shown to be a potential source of quantum gravity phenomenology. The scale-dependent effective dimension from quantum gravity has only been considered for scalar fields. It is however possible that the non-manifold like structures, that are expected to appear near the Planck scale, have an effective dimension that depends on the type of field under consideration. To investigate this question, we have studied the spectral dimension associated to the Laplace-Beltrami operator generalised to $k$-form fields on spatial slices of the non-perturbative model of quantum gravity known as Causal Dynamical Triangulations. We have found that the two-form, tensor and dual scalar spectral dimensions exhibit a flow between two scales at which an effective dimension appears. However, the one-form and vector spectral dimensions show only a single effective dimension. The fact that the one-form and vector spectral dimension do not show a flow of the effective dimension can potentially be related to the absence of a dispersion relation for the electromagnetic field, but dynamically generated instead of as an assumption.

gr-qc↗