MIT Center for Theoretical Physics – a Leinweber Institute

We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $Vpropto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.

We study the growth of massive $SO(9)$ super-representations in type II and type I string theories. We do this first directly by finding an empirical formula that specifies which representations appear at any level, and then compute the multiplicities from a refined partition function evaluated over finite fields up to level 501 for individual representations, and level 226 for all representations. We then derive asymptotic formulae for the growth of any representation, which are constructed by integrating about the peaks of the refined partition function. Using a Rademacher sum we can find very accurate approximations for the multiplicities of the representations. Unlike the superstring partition function, which only receives contributions from the odd Rademacher terms, the multiplicities for any representation have contributions from both even and odd terms. Finally, we apply the same techniques to the ordinary representations, where a simplified refined partition function allows for better computational speed and simpler expressions for the asymptotic approximations.

Quantum thermalization explains how an isolated many-body system naturally evolves towards a thermal state, rendering information about the initial conditions inaccessible to local measurements. This is precisely the mechanism utilized in quantum error correction, where information is protected by design through a nonlocal encoding. In this work, we leverage this connection to port the rigorous framework of (approximate) quantum error correction to the study of quantum thermalization. Treating typical late-time states as codewords, we characterize the error-correcting properties of generic thermalizing dynamics. We numerically uncover a universal relationship between the encoding rate, distance, and thermal entropy density of the emergent code. At infinite temperature, this universal curve saturates the quantum Singleton bound, achieving the same optimal limit as Haar-random codes. At finite temperature, we introduce a code family based on the Scrooge ensemble, the natural thermal analogue of the Haar ensemble, and prove it saturates the entropic quantum Singleton bound, establishing this family as optimal within entropic constraints. Our extracted universal curve independently saturates this same bound, revealing that finite-temperature thermalization is itself optimal. Finally, we show how conserved quantities limit the error-correcting behavior of thermalization: codewords with differing energies, or other conserved charges, leak only classical information, and correctability persists until the difference reaches the scale of thermal fluctuations. Our results reveal a universal optimal coding structure in thermalizing dynamics, while introducing new optimal codes that achieve fundamental limits of approximate quantum error correction.

We present predictions for the collinear energy-energy correlator (EEC) measured inside $Z$-tagged jets in proton-proton collisions across the confinement transition. Our framework combines transverse-momentum-dependent factorization for back-to-back $Z+$jet production with an exclusive differential EEC jet function incorporating perturbative evolution and flavor-dependent non-perturbative fragmentation. The EEC jet function is evaluated at $mathrm{NLL}^{prime}$ accuracy, with separate quark and gluon non-perturbative scales constrained by existing $e^+e^-$ and inclusive-jet data. We provide predictions for forward $Z+$jet production at $sqrt{s}=8~mathrm{TeV}$ and $13~mathrm{TeV}$ in the jet transverse-momentum intervals $(20, 30)$, $(30, 50)$ and $(50, 100) , mathrm{GeV}$. The EEC distributions as functions of $z_χ$ exhibit finite plateaus at small $z_χ$, while the corresponding angular distributions display the characteristic turnover associated with the confinement transition. A flavor decomposition shows that this transition becomes increasingly dominated by quark-initiated jets as the jet transverse momentum increases. Forward $Z$-tagged jets therefore provide a clean probe of non-perturbative quark fragmentation and offer a direct test of whether the characteristic confinement scale extracted from $e^+e^-$ collisions remains universal in a hadronic environment.