MIT Center for Theoretical Physics — a Leinweber Institute Publications

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.

The strong coupling constant $α_s$ is a fundamental parameter of the Standard Model. Its precise determination is essential for accurately predicting, studying, and understanding processes at the Large Hadron Collider and future experiments such as the Future Circular Collider. Event shape and correlator observables measured at electron-positron colliders provide one of the cleanest environments for extracting $α_s$, thanks to their sensitivity to $α_s$ and the availability of high-precision data from the Large Electron-Positron Collider. More broadly, such observables provide an ideal setting to develop and test our understanding of the perturbative and non-perturbative elements of Quantum Chromodynamics, which will underpin the field's precision and discovery frontiers for decades to come. Despite these advances, significant discrepancies persist between different determinations of $α_s$ from event shapes, both in the extracted central values and estimated uncertainties. This document motivates the establishment of a dedicated Task Force to coordinate a community-wide effort addressing these open questions. We report on the first two-day meeting held at CERN in November 2025, summarizing the scientific discussion and documenting the experimental analyses identified as priorities during the meeting, as well as the concrete list of tasks to be carried out by the theory community in preparation for future meetings.

We present a robust protocol to reshape interactions in a spin ensemble based on global control pulse sequences applied to multiple subensembles in parallel. This setting arises naturally from ensembles of solid-state defects or multi-species atomic arrays. We show that it is provably computationally hard to find pulse sequences that simultaneously engineer interactions both within and between subensembles. Despite its formal hardness, we identify a set of necessary or sufficient conditions under which one can synthesize a target Hamiltonian from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer target Hamiltonians robust against common control imperfections. As a specific application, we discuss the robust generation of two-mode spin squeezing in dual-species atomic ensembles, which is a challenging task without subensemble control. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.

We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the entanglement-gap relation $S = Θ(Δ^{-1/2})$; this is believed to be optimal, but achieving it had been open. Second, we use it to provide a streaming protocol that tests for closeness to a class of 1D volume-law entangled states. Moreover, we extend our quantum expander to a constant-degree and constant-gap expander on the unitary group where each unitary is a single $T$ gate, a single $T^{dagger}$ gate, or a depth-$1$ Clifford circuit. This implies that a random sequence of unitaries from the expander yields a gapped walk on a dense subgroup of the unitary group. This improves upon previous work by Bourgain and Gamburd which did not control the dependence of the gap on the dimension.

Quantum anomalies strongly constrain the possible behavior of many-body systems. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which relates UV symmetry and filling constraints to IR features of the energy spectrum and ground-state structure. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the Liouvillian of a $d$-dimensional repeated quantum channel with a mixed anomaly between strong $S$ and weak $G$ symmetry can be mapped to a $(d{+}1)$-dimensional mixed-state symmetry-protected topological (mSPT) phase. Under this correspondence, the initial and steady states of the channel are identified with boundary states of the higher-dimensional mSPT in the presence of bulk projection. We further introduce the twisted Renyi-$N$ correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Finally, we identify the textit{Liouvillian singular spectrum}, rather than the Liouvillian spectrum itself, as a more fundamental diagnostic of quantum anomalies, and show that it is dual to the operator entanglement spectrum of the mSPT.

The dynamics of heavy quarks in quark-gluon plasma (QGP) formed in heavy ion collisions provide a unique window to characterize its properties. Existing approaches to describe heavy quarks in medium rely either on quasiparticle-based models of QGP, or on assuming that the momentum transfer from the medium follows Gaussian statistics. However, neither of these assumptions can be taken for granted in QCD. In fact, in the prototypical theory that is strongly coupled $mathcal{N}=4$ SYM, it has been long known there are no momentum-carrying quasiparticles, and furthermore, we have recently shown that the momentum transfer from the medium is far from being Gaussian [arXiv:2501.06289]. Since then, we showed that the asymmetry of said momentum transfer between energy loss and energy gain -- which affects all moments of the distribution, not only its Gaussian characteristics -- is, in fact, universal [arXiv:2504.21139]. Therefore, in order to connect the initial heavy quark production cross section with the final hadron spectrum in a way that is consistent with QFT principles, new methods are needed. In this talk, we present a new transport description of heavy quarks that encodes all of the non-Gaussian features of the momentum transfer from the medium, all of which can be defined and in principle calculated in QCD, without relying on any assumptions regarding the strength of the coupling. As a demonstrative example, we discuss heavy quark equilibration in $mathcal{N}=4$ SYM. This paves the way towards extracting novel information about fundamental properties of QGP.

We propose projected energy correlators measured on the recoiling QCD radiation of a $Z/γ$ as a benchmark observable for precision QCD at the LHC. Using the $Z/γ$ as a hard scale prevents the need for a jet algorithm, simplifying both the perturbative and non-perturbative corrections. We develop a framework to combine state-of-the-art fixed-order amplitudes, high order resummation, and universal non-perturbative matrix elements. Our approach is based on numerically computed inclusive hard functions, allowing flexibility in the process and the inclusion of realistic experimental cuts. We perform detailed numerical studies of the projected energy correlators at next-to-leading order + next-to-next-to-leading logarithm (NLO+NNLL) to verify the stability of our setup. We present numerical results at NLO+NNLL, which are the first complete matched predictions for energy correlators at the LHC at this order. We discuss the prospects for extensions to higher orders, outlining a path to NNLO calculations of energy correlators at the LHC.

We explain how the 'bar-cobar' construction for homotopy algebras reformulates the equations of motion of arbitrary gauge theories as gauge-covariant quadratic equations for an extended set of fields. The linear term of the new equations encodes the interactions of the original theory, while the quadratic term is universal. The extended fields include type-I multilocal fields, which depend on a set of coordinates and type-II multilocal fields, which depend on several sets of coordinates. The new equations of motion are the Maurer-Cartan equations of a differential graded associative algebra or Lie algebra. We show that every solution of the new equations is gauge equivalent to a solution with only type-I fields, that represents a solution of the original equations of motion. In string theory type-I fields are entangled states of the associated CFT, to be inserted across multiple punctures of a Riemann surface. General type-II states can also represent disconnected Riemann surfaces.

We propose a framework to determine the vacuum polarization functions in QED in the presence of an electromagnetic background field in the spacelike region on the lattice. This method consists in reweighting lattice Monte Carlo data generated without the background with the fermion determinant ratio evaluated in the continuous spacetime using worldline formalism. This proposal can be further extended to other applications in lattice gauge theory, such as QCD in finite chemical potential.

The Chinese remainder theorem is used in metrology for extending the range of quantum clocks/radar/interferometry, where the phase of a signal is known relative to a set of oscillators with different periods. This paper investigates the performance of a quantum-mechanical Chinese remainder clock, consisting of atoms/oscillators with pairwise coprime periods. We provide the optimal initial state and the optimal Heisenberg-limited quantum measurements for measuring time up to the product of the periods. We introduce a novel fault-tolerant post-processing protocol that allows reconstruction of the correct time even in the presence of errors in the remainders.

High-redshift spectroscopic galaxy surveys will be the scientific engines of the next generation of large-scale structure cosmology. The clustering signal of high redshift, star-forming Lyman-$α$ emitters (LAEs) will be of key importance for obtaining high-redshift constraints on the growth of structure and redshift-space distortions. The complex radiative transfer (RT) of Lyman-$α$ photons alters the symmetry group respected by the overdensity field constructed from these galaxies, and so the observed large-scale clustering of LAEs may have an angular dependence that differs significantly from that of linear theory, possibly biasing inference of cosmological parameters. While such an effect has been seen in simulations, its amplitude in nature and its detailed form remains unclear. In the restricted context of a linear, Gaussian model, we outline a procedure for pinning down the type and amplitude of such changes in angular dependence on large scales due to unknown RT or a more general unmodeled angular effect in the hypothetical scenario in which an observer is presented with LAE data containing such an effect. We show that if a second tracer without the modified angular dependence is available for cross correlation with the LAEs at the same redshifts (e.g., Lyman-break galaxies), then, with a high redshift survey of modest size, it is possible to rapidly identify: 1) the presence of a nontrivial angular functional form of radiative transfer (by a conditional field-level realization), 2) the functional form itself (with an optimal filter that we derive), and 3) the value of its amplitude with an uncertainty (via an adaptation of the standard quadratic estimator). Such sample-variance-cancellation strategies therefore provide a statistical solution to unknown astrophysical or systematic angular clustering dependence, including from RT.

It is often claimed Standard Model CP violation is insufficient for baryogenesis. We present a counterexample using minimal flavor violation (MFV) in which all CP-violating effects arise from the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Our scenario involves a leptoquark field with MFV-preserving interactions whose decays to Standard Model particles yield the observed baryon asymmetry in the early universe. Unlike previous efforts to realize baryogenesis through the CP violation of the CKM matrix, our scenario does not require any time-variation of model parameters.

We present a fermionic lattice Hamiltonian that exactly realizes the $mathrm{U(1)}_mathrm{L}times mathrm{U(1)}_mathrm{R}$ global symmetry and the associated chiral anomalies of a massless Dirac fermion in 1+1 dimensions. The construction couples Villain bosons to a Kitaev chain of Majorana fermions, where the bosonic fields are essential for evading Nielsen-Ninomiya-type no-go theorems. For two copies of our model, we realize the anomaly-free $mathrm{U(1)}_{3450}$ global symmetry and construct symmetric boundary conditions. We analytically demonstrate symmetric mass generation by mapping the symmetry-preserving six-fermion interactions to fermion bilinear terms using fermionic T-duality. Finally, by gauging general anomaly-free global symmetries, we obtain a broad class of lattice chiral gauge theories. As nontrivial applications, we compute the mass spectra of the lattice Schwinger model and the 3450 gauge theory, finding agreement with the corresponding continuum results.

Universal hallmarks of quantum chaos---such as the ramp and plateau in the spectral form factor---and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models---including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons---can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-$N$ limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in $1/N^2$. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects---such as baby-universe and wormhole condensates---which yield double exponential effects in $G_N$. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.

These notes are an introduction to non-linear perturbation theory for cosmological large-scale structure. They are aimed at undergraduate and beginning graduate students and do not require any cosmology or quantum field theory background. All necessary concepts are developed from scratch. The lectures are intended to explain all key ingredients needed to model the observed clustering of galaxies in real and redshift spaces. After a brief pedagogical introduction to the ideas of effective field theory (EFT), we develop large-scale structure EFT in the context of Newtonian cosmology using symmetry principles. We discuss in detail the shortcomings of Standard Perturbation Theory, the non-linear evolution of baryon acoustic oscillations and its relation to the equivalence principle, counterterms and renormalization of the loop diagrams, and stochastic effects. Then we develop EFT for galaxy bias and redshift space distortions. We also highlight some important facts about redshift-space stochasticity, relevant for ongoing and future galaxy surveys. Finally, we introduce Lagrangian Perturbation Theory.

We study the impact of spatial curvature ($Ω_k$) and dynamical dark energy (parametrized by $w_0$ and $w_a$) on the spectral index $n_s$ using a combination of cosmic microwave background datasets (Planck, SPT, and ACT), and spectroscopic galaxy samples from DESI, including both BAO and full-shape clustering measurements. We show that a small negative curvature, $Ω_k\simeq 3\times 10^{-3}$, lowers the value of $n_s$, bringing it closer to predictions of the Starobinsky, Higgs, and simplest $α$-attractor inflationary models. In particular, we find $n_s= 0.9667\pm0.0041$ (using Planck and DESI data) or $n_s= 0.9692\pm0.0035$ (adding ACT and SPT). Allowing for time-evolving dark energy also reduces the spectral index, leading to $n_s=0.9716\pm0.0032$ (from the combined dataset), or $n_s=0.9694\pm0.0035$ in combination with a small negative curvature. Our results demonstrate that the tension between current observational data and the Starobinsky, Higgs, and simplest $α$-attractor models holds only for $Λ$CDM, and can be mitigated in extended cosmological models. We discuss implications of these findings for inflationary models in an open universe and/or with dynamical dark energy, including scenarios with quantum tunneling and non-standard topology. Furthermore, we briefly describe a special class of $α$-attractor models, where one can make $n_s$ arbitrarily large, and we describe the $α$-attractor quintessence model. Such models may be of particular relevance when future data from DESI, as well as DESI-II, SPHEREx, Euclid, Rubin, and Roman, becomes available.

We explore the cosmological implications of combining dark dimension scenarios with an axiverse. If gauge sectors are realized on branes, towers of Kaluza-Klein (KK) excitations of closed string axions can propagate through the dark dimension in addition to the tower of graviton excitations. This modifies cosmology in two ways. First, if any of these axion towers interact with the standard model (SM) plasma, they can significantly alter the freeze-in production of the cosmological abundance of tower states. Freeze-in to graviton and axion towers can provide all of dark matter (DM) for an axion decay constant in $10^{12} \text{ GeV }\lesssim f_a\lesssim 10^{16}\,\text{ GeV }$ and reheating temperatures $5\text{ MeV }\lesssim T_{\rm RH} \lesssim O(1)\,\text{ GeV }$. Second, different towers fragment into each other and redistribute energy; each tower’s fraction of energy at late times is fixed by their interactions. If there are $N\gg1$ axion towers, the energy visibly injected into the SM by any decaying tower is diluted by a factor of $N$. This suppression offers a simple realization of how dark dimension dark matter can avoid strong cosmological constraints which rule out the simplest models. In the process of this exploration we develop a continuum approach to evaluating tower fragmentation which offers insight and aids numerical calculations by reducing the problem to quadrature.

The heavy jet mass distributions in hadronic Higgs decays are computed to next-to-next-to-next-to-leading logarithmic order (N${}^3$LL${}^\prime$) in the dijet limit and NNLL in the trijet limit, matched to the next-to-next-to-leading order (NNLO). Both resummation results are obtained from the factorization theorems in Soft-Collinear Effective Theory. In particular, we study the Sudakov shoulders in the trijet region, originating from the incomplete cancellation of infrared singularities between final states with different parton multiplicities, and resum the induced large logarithms to all orders. The shoulder resummation yields sizable corrections and improves the perturbative stability of the distribution. Our results provide state-of-the-art predictions for heavy jet mass in $H \to gg$ and $H\to q\bar{q}$ and can be applied to precision Higgs measurements at future $e^+e^-$ colliders.