MIT Center for Theoretical Physics — a Leinweber Institute Publications

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.

In the early universe, neutrinos undergo many interactions with the particles in the plasma. Key processes are the scattering of neutrinos by free electrons and positrons. In this paper, we derive general expressions for the electron neutrino-electron scattering kernel in isotropic media, analytically simplifying the 5D collision integral to two dimensions. We follow a procedure that is similar to the derivation of the Compton scattering kernel to reduce the angular integrals, yielding a compact analytic expression in terms of elementary functions that can be easily evaluated. We illustrate the properties of this kernel and also compute its first moments analytically, providing insights into the energetics of the redistribution process. For comparison, we consider the photon-electron scattering kernel, highlighting differences and similarities. We then explain how the obtained expressions can also be applied to the $ν_{μ/τ}$-electron and neutrino-positron scattering processes. The results presented here may be useful in the context of Big Bang Nucleosynthesis and were added as an extension to the Compton scattering library CSpack for more general applications.

Providing a practical and hadron-level definition of multiple jet flavors has been a long-standing challenge in collider physics. Previous work has introduced a data-driven, operational definition of quark and gluon jets, but no robust generalization beyond two jet categories presently exists. To address this, we introduce a machine-learning framework called “simplex demixing” to extract $T$ jet flavors (or topics in the statistics literature) from $M$ data samples (or mixtures) with minimal constraints. Intuitively, our procedure identifies the maximally separable categories in the data, translating a multi-category classifier on the $M$ mixtures into a bounded geometric object with $T$ vertices. We first demonstrate our procedure on a toy problem to infer the truth-level fractions of down-quark, up-quark, and gluon jets from synthetic mixtures of the three pure samples. We then propose a tag-and-probe strategy to extract multiple light-flavor categories in a more realistic collider setting involving dijet production. As expected, the identifiability of jet flavors depends on their relative abundance in the samples and the hadron-level information available to the classifier architecture. Our work opens the door to data-driven extractions of multiple jet flavor properties at the Large Hadron Collider.

The gluon Collins-Soper kernel, which encodes the rapidity evolution of transverse-momentum-dependent gluon distributions, is constrained for the first time in the nonperturbative regime, for transverse momentum scales $q_{T} \in [ 300\text{ MeV}, 1.3\text{ GeV}]$. The constraints are determined in lattice QCD at a close-to-physical pion mass $M_π= 172(3)\text{ MeV}$, a single lattice spacing $a=0.15\text{ fm}$, and next-to-next-to-leading logarithmic matching in Large-Momentum Effective Theory. These results represent the first step toward a controlled determination of the gluon Collins-Soper kernel in QCD, with eventual phenomenological import and relevance to present and future experiments sensitive to the gluon structure of hadronic matter.

Likelihood-based inference in particle physics, and in the physical sciences more broadly, relies on the assumption that the model accurately describes the data. When the model is misspecified, though, standard confidence intervals shrink to zero width with increasing data, producing overconfident and potentially misleading constraints. We propose the well-tempered likelihood, which divides the likelihood-ratio test statistic by a goodness-of-fit (GOF) statistic evaluated at the best-fit point. Under correct specification, the GOF is $\mathcal{O}(1)$ and standard inference is recovered. Under misspecification, both the likelihood and the GOF scale as $\mathcal{O}(N)$ for $N$ data points, so their ratio remains $\mathcal{O}(1)$ and the resulting well-tempered confidence interval self-limits at a floor determined by the model’s inadequacy, essentially reducing the effective sample size. In other words, \textit{all models are correct, as long as your dataset is small enough}. We present binned and unbinned formulations of the well-tempered likelihood—the latter based on a classifier two-sample test—and demonstrate our method on a Gaussian example and on a measurement of the strong coupling constant using synthetic electron-positron collisions.

We explore the potential of multiple possible future 10 TeV wakefield colliders to measure electroweak couplings of the Higgs boson. We find that the beam-beam interactions are not an impediment to high precision measurements of the Higgs couplings, provided that the luminosity spectra can be measured or calculated to high accuracy. In addition to $e^+ e^-$ colliders, we also assess the effectiveness of alternatives such as $e^- e^-$ colliders or $γγ$ colliders, which by-pass the positron acceleration challenge for wakefield colliders. We find that a 10 $\text{ab}^{-1}$ dataset at a $γγ$ collider yields qualitatively similar sensitivity to 10 $\text{ab}^{-1}$ at a muon collider and 1 $\text{ab}^{-1}$ at an $e^+e^-$ wakefield collider.

We present new \compass high-statistics measurements of the peripheral production of $ηπ^-$ and $η^\prime π^-$ pairs in the reactions $π^- p \to η^{(\prime)}π^- p$. For the first time, we perform an unbinned analysis of the high-mass region of the $ηπ^-$ and $η^\primeπ^-$ systems, which allows us to disentangle the exchange mechanisms governing their production. We report the first observation in high-energy scattering of an exotic Reggeon with high significance exceeding $5\,σ$ for both channels, which is, most likely, related to the exotic $π_1(1600)$.8

Relativistic quantum field theory is the structure on which the Standard Model and beyond-Standard Model physics are built. One of its most striking predictions is the Unruh effect: an accelerating observer measures the Minkowski vacuum as a thermal bath at a fixed temperature. Despite decades of theoretical interest, this effect has never been directly observed. We propose to use the high acceleration gradients provided by wakefield accelerators, coupled with a forward laboratory-frequency ~THz detector array, to measure the resulting forward-beamed radiation, and outline the unique signature provided by quantum detailed balance to extract the signal from backgrounds. While challenging, such a measurement appears within reach of present-day accelerator and detector technologies.

Hydrodynamics is a macroscopic theory of long-wavelength dynamics around local thermal equilibrium. We develop attractodynamics, the analogous construction around a far-from-equilibrium attractor. Dynamics near a far-from-equilibrium attractor retains some non-hydrodynamic microscopic information, which attractodynamics systematically organizes. We move towards this general structure by starting in 0+1D, and consider a model for which an anisotropic far-from-equilibrium attractor solution is exactly known. This setting provides a clean benchmark in which the ideal attractodynamic equations and a leading transient residual extension can be compared directly with the full kinetic evolution. The resulting hierarchy gives an improvable description of near-attractor dynamics: the ideal theory captures evolution close to the attracting manifold, while retaining the leading off-attractor moments extends the regime of agreement until the finite truncation breaks down. This example identifies the ingredients needed for local 3+1D attractodynamics and for macroscopic attractodynamic theories not derived from an underlying kinetic description.

The worldsheet description of string amplitudes can be reinterpreted as a baby universe field theory. Under this reinterpretation, we determine the $α$-states of a topological string theory: the Hurwitz worldsheet. We find that their relation to the Hartle–Hawking state encodes foundational results in the asymptotic representation theory of the symmetric group. In the holographic dual, our results characterize the pseudorandom nature of an ensemble of cluster-decomposing correlators.

We study the algebra of observables of a semiclassical observer in de Sitter space. When operators are time-evolved by a scrambling time, out-of-time-ordered correlation functions (OTOCs) receive corrections due to shockwave scattering near the cosmological horizon. When the observer’s clock is treated classically, we show that the time advance effect implies the breakdown of the KMS condition for vacuum correlators of matter operators. When the observer’s clock is quantized, this implies that the Hartle-Hawking state is not a trace on the resulting crossed-product algebra. We conjecture that the observer’s algebra has a trivial commutant. When the time separation between operators exceeds the scrambling time, the OTOC decays to zero and a free product algebra emerges. We illustrate this using classical solutions of de Sitter JT gravity with shocks. We comment on how our results pose a challenge for observer-centric static patch holography.

The Standard Model prediction for the rare $K_L\toμ^+μ^-$ decay depends critically on the long-distance contribution coming from the exchange of two photons. Such a contribution can be computed using lattice QCD and an effective three-flavor theory including only the $u$, $d$ and $s$ quarks, provided terms falling as the inverse square of the omitted charm quark mass, $1/m_c^2$ are neglected. Because of the missing Glashow-Iliopoulos-Maiani cancelation, this three-flavor theory contains additional low-energy constants that depend on $m_c$. Here we show how these constants can be determined from a practical four-flavor lattice QCD calculation performed on a small volume with $u$ and $d$ quark masses that are heavier than physical.

Diffraction is characterized by forward scattering and a large rapidity gap. Ordinary hard scattering also produces gapped events and presents a significant background to identification of diffractively produced events. We present a fully differential factorization of gapped hard $ep$ scattering. We find that the unpolarized azimuthally-dependent structure functions $F_{3,4}^{\rm gap}$ and the longitudinal $F_L^{\rm gap}$ vanish at leading power for hard scattering. Azimuthal dependence is thus a pure diffractive signature. This is borne out in Monte Carlo simulations.

We use effective field theory techniques to factorize elastic, single, and double diffractive forward $pp$ scattering in the Regge limit $|t|\ll s$, where $t$ is the squared momentum transfer. These processes involve a large rapidity gap and comprise about half the total $pp$ cross section. We explain why the diffractive PDFs appearing in $ep$ diffraction do not appear as universal hadronic functions for $pp$ diffraction. For $|t|\sim Λ_{\rm QCD}^2$, we show that the hadronic functions in $ep$ and $pp$ diffraction differ, and hence are non-universal. In general, we prove that rapidity anomalous dimensions are universal between diffractive $ep$ and $pp$ processes, and that color-singlet (Pomeron) evolution equations can be determined at the amplitude level.

The measurement of the sum of neutrino masses is among the primary promises of precision cosmology, achievable by combining complementary early- and late-Universe probes. However, these datasets currently exhibit mild-to-strong disagreements within $Λ$CDM and its simplest extensions, giving rise to multiple tensions, including the Hubble tension, the preference for “negative” neutrino mass, and indications of evolving dark energy. It has recently been shown that these tensions can be alleviated by adopting a higher value of the optical depth to reionization parameter, $τ$, when large-scale cosmic microwave background (CMB) polarization data are ignored. We extend this proposal and show that an especially high prior on $τ= 0.11 \pm 0.006$ simultaneously addresses all three of these tensions, significantly reducing the need for new physics beyond $Λ$CDM. We determine the “concordance” value of $τ$ by requiring physical neutrino mass and consistency of the Hubble constant, $H_0$, inferred from the CMB and that preferred by the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) and full-shape measurements. Within this high-$τ$ Universe, we obtain the first $2σ$ detection of a positive neutrino mass, $Σm_ν = 0.10^{+0.04}_{-0.05}$~eV at 68% C.L., while restoring cosmological concordance between datasets within $Λ$CDM. In particular, low-redshift distance predictions are consistent with DESI BAO observations and the inferred dark-energy equation-of-state parameters are consistent with a cosmological constant, both with and without supernovae data. The concordance power of our $τ$ prior further motivates new measurements of $τ$, e.g., through large angular scale CMB polarization observations with the \textit{LiteBIRD}, CLASS, or proposed PICO experiments. (Abridged)