Debaditya Pramanik | Searcharxiv

arXiv2025

Integral constraints for $\mathcal{N}=4$ super-Yang-Mills from a squashed sphere

Supersymmetric localization and Ward identities have been used in the past several years to derive two integral constraints on the four-point function of the stress-tensor multiplet in $\mathcal{N} = 4$ super-Yang-Mills theory. These constraints are powerful tools for studying the theory, especially when used in tandem with analytic and/or numerical bootstrap techniques. In this paper, we consider three additional integral constraints that can be derived starting from the $\mathcal{N} = 4$ super-Yang-Mills theory placed on a squashed four-sphere. These constraints are technically much more challenging to derive than the ones in the literature, and much of the paper is devoted to developing techniques to make this computation tractable. Our end result is that these three constraints are implied by the two constraints already appearing in the literature.

hep-th↗

arXiv2021

Damping of Oscillations in Red Giants by Resonant Mode Coupling

Asteroseismic studies of red giants generally assume that the oscillation modes can be treated as linear perturbations to the background star. However, observations by the Kepler mission show that the oscillation amplitudes increase dramatically as stars ascend the red giant branch. The importance of nonlinear effects should therefore be assessed. In previous work, we found that mixed modes in red giants are unstable to nonlinear three-wave interactions over a broad range of stellar mass and evolutionary state. Here we solve the amplitude equations that describe the mode dynamics for large networks of nonlinearly coupled modes. The networks consist of stochastically driven parent modes coupled to resonant secondary modes (daughters, granddaughters, etc.). We find that nonlinear interactions can lower the energy of gravity-dominated mixed modes by $\gtrsim 80\%$ compared to linear theory. However, they have only a mild influence on the energy of pressure-dominated mixed modes. Expressed in terms of the dipole mode visibility $V^2$, i.e., the summed amplitudes of dipole modes relative to radial modes, we find that $V^2$ can be suppressed by $50-80\%$ relative to the linear value for highly-evolved red giants whose frequency of maximum power $ν_{\rm max} \lesssim 100\,μ\textrm{Hz}$. However, for less evolved red giants with $150\lesssim ν_{\rm max} \lesssim 200\,μ\textrm{Hz}$, $V^2$ is suppressed by only $10-20\%$. We conclude that resonant mode coupling can have a potentially detectable effect on oscillations at $ν_{\rm max} \lesssim 100\,μ\textrm{Hz}$ but it cannot account for the population of red giants that exhibit dipole modes with unusually small amplitudes at high $ν_{\rm max}$.

astro-ph.SR↗