arXiv subjects

Saswato Sen

Publications and source records attributed to Saswato Sen.

4 recordsLinked to original sources

arXiv2026

Critical Phenomena on the Bethe Lattice

We investigate the critical behavior of a family of $\mathbb{Z}_2$-symmetric scalar field theories on the Bethe lattice (the tree limit of regular hyperbolic tessellations) using both the non-perturbative Functional Renormalization Group and lattice perturbation theory. The family is indexed by the parameter $\zeta \in (0,1]$, which determines the range of the theory via the kinetic term constructed from the graph Laplacian raised to the power $\zeta$. Specifically, $\zeta=1$ is the short-range theory, while $0<\zeta<1$ defines the long-range model. Due to the hyperbolic nature of Bethe lattices, the Laplacian lacks a zero mode and exhibits a spectral gap. We find that upon closing this spectral gap by a modification of the Laplacian, the scalar field theories exhibit novel critical behavior in the form of non-trivial fixed points with critical exponents governed by $\zeta$ and the spectral dimension $d_s=3$. In particular, our analysis indicates the presence of a Wilson-Fisher fixed point for the short range $\zeta =1$ theory. In contrast, the nearest-neighbor Ising model on the Bethe lattice is known to exhibit mean-field critical exponents. To the best of our knowledge, this work provides the first evidence that a scalar $\phi^4$ theory and the discrete Ising model on the same underlying lattice may lie in distinct universality classes.

hep-th↗

arXiv2024

Dirac walks on regular trees

The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two point function as a sum over random walks. An analogous expansion for Fermions on non-Euclidean geometries is still lacking. Casiday et al. [\textit{Laplace and Dirac operators on graphs}, Linear and Multilinear Algebra (2022) 1] proposed a classical "Dirac walk" diffusing on vertices and edges of an oriented graph with a square root of the graph Laplacian. In contrast to the simple random walk, each step of the walk is given a sign depending on the orientation of the edge it goes through. In a toy model, we propose here to study the Green functions, spectrum and the spectral dimension of such "Dirac walks" on the Bethe lattice, a $d$-regular tree. The recursive structure of the graph makes the problem exactly solvable. Notably, we find that the spectrum develops a gap and that the spectral dimension of the Dirac walk matches that of the simple random walk ($d_s=1$ for $d=2$ and $d_s=3$ for $d\geq 3$).

cond-mat.stat-mech↗

arXiv2023

Scaling solutions for asymptotically free quantum gravity

We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to perturbation theory, to the non-perturbative infrared region. The existence of such scaling solutions is necessary for a renormalizable quantum field theory of gravity. If the proposed scaling solution is confirmed beyond our approximations asymptotic freedom is a viable alternative to asymptotic safety for quantum gravity.

hep-th↗

arXiv2022

Asymptotic freedom and safety in quantum gravity

We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $β$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a scalar field. Quantum gravity can be asymptotically free, based on a flow trajectory from the corresponding ultraviolet fixed point to the infrared region. This flow can also be realized by a scaling solution for varying values of a scalar field. As an alternative possibility, quantum gravity can be realized by asymptotic safety at the other fixed point. There may exist a critical trajectory between the two fixed points, starting in the extreme ultraviolet from asymptotic freedom. We compute critical exponents and determine the number of relevant parameters for the two fixed points. Evaluating the flow equation for constant scalar fields yields the universal gravitational contribution to the effective potential for the scalars.

hep-th↗