MIT Center for Theoretical Physics — a Leinweber Institute Publications

We introduce a procedure called random dimension reduction that simultaneously reduces the dimensions of many, potentially distinct quantum states while preserving properties invariant under the tensor power action of an isometry. This provides a black-box method to replace the dimension with the maximum rank in the sample complexity of learning symmetric properties, even those depending on multiple input states. We show that dimension reduction followed by full state tomography yields improved upper bounds for estimating distances, fidelities, and relative entropies between pairs of states. We also give an efficient quantum circuit implementation of the procedure using the Schur transform. Expressing the action of our procedure through the Choi-Jamiolkowski isomorphism reveals an intimate connection with the recently introduced random purification channel by Tang, Wright, and Zhandry. This perspective also completes an end-to-end analysis of sample-optimal tomography without requiring a reference to the Schur transform or Schur polynomials. Finally, we prove that there does not exist a random purification channel that simultaneously purifies copies of multiple, potentially different input states. Hence, random dimension reduction is related to, but distinct from, random purification.

We introduce the \emph{Centauric 1-jettiness}, $τ_1^C$, a generalized event shape for Deep Inelastic Scattering (DIS) with adjustable beam and jet reference vectors and thus beam and jet regions. We demonstrate that a specific choice of weights allows this observable to exactly reproduce the geometric boundaries of the Centauro jet algorithm in the Breit frame. Within the framework of Soft-Collinear Effective Theory (SCET), we derive a factorized cross section in the small-$τ_1^C$ region in terms of known perturbative ingredients. This allows the resummation of large logarithms to N$^3$LL accuracy, which we then match to fixed-order NLO QCD ($\mathcal{O}(α_s^2)$) predictions from \texttt{NLOJet++}. We establish that the soft measurement reduces to a rescaled hemisphere measurement, placing Centauric 1-jettiness in the same universality class, for the leading non-perturbative corrections, as DIS thrust and jet mass. As a consequence, the leading non-perturbative shift depends on the same universal first-moment-shift parameter $Ω_1$ and scales exactly as $1/R$ with the jet radius, thanks to the boost invariance of the Centauro algorithm along the photon axis in the Breit frame, a scaling that we test using \textsc{Pythia} simulations. These results open new strategies for determining the strong coupling from DIS event shapes, with $R$ providing a handle to break the degeneracy between $α_s$ and the universal non-perturbative shift parameter $Ω_1$.

We study two-point functions of half-BPS operators in maximally supersymmetric Yang-Mills theory continued to $d=4-2\,\varepsilon$ dimensions. Using supersymmetric localization on $S^d$, we derive perturbative matrix-model expressions for the $\varepsilon$-expansion of these correlators and obtain all-loop results at leading order in $\varepsilon$ in the planar limit, with extensions to finite-$N$ corrections and higher-charge operators. We compare the localization results with direct perturbative computations in flat space. At order $\varepsilon$ the two descriptions agree perfectly, while at higher orders our construction fails to reproduce the perturbative data due to the breaking of conformal symmetry away from four dimensions. Nevertheless, in the case of the dimension-two operator we conjecture an all-loop formula at order $\varepsilon^2$ by exploiting the precise form of the mismatch.

A principal lesson from recreating droplets of quark-gluon plasma (QGP) in heavy ion collisions is that it is a strongly coupled liquid, not a plasma of partons. The energy density and pressure of quarks and gluons confined within a proton are comparable to those of QGP at or just above the QCD transition temperature. Given this similarity between protons and QGP, we propose that the investigation of correlations between nearby partons within a proton must be a central goal for the future Electron-Ion Collider (EIC). Here, we ask how EIC measurements can discern such short-range correlations (SRCs) of quark pairs. Doing so would characterize the strongly coupled interior of a proton, augmenting the one-parton-at-a-time understanding of protons via (generalized) parton distribution functions, and could at the same time yield a key ingredient for the microscopic understanding of the liquid nature of QGP. Motivated by the experiments that have been used to demonstrate the existence of SRCs between nucleon pairs within a nucleus, we propose using EIC observables involving measurements of a jet and a pion, together with the scattered electron, to seek and quantify the possible existence of SRCs between quark pairs within a nucleon. The pronounced isospin dependence observed in the dominance of $np$ SRCs over $pp$ or $nn$ SRCs has played a central role in establishing the importance of SRCs among nucleons in nuclei. Analogously, the QCD attraction in the $ud$ diquark channel can make the $ud$ SRC stronger than the $uu$ and $dd$ SRCs, allowing a first observation of partonic SRCs.

Coulomb-gauge quasi-parton distributions can be computed directly in momentum space on a finite lattice, enabled by the commutativity of their renormalization and Fourier transform. This approach removes the formal inverse problem in coordinate-space methods. Our momentum-space pion quasi-distributions agree with coordinate-space results Fourier transformed with asymptotic extrapolation, indicating that the formal inverse problem in the latter is not a concern at this volume. We further extend the framework to higher dimensions and obtain the first 3D image of the pion directly from lattice QCD.

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

A key property of a global symmetry’s anomaly is its order: the smallest integer $n$ for which the diagonal symmetry of the $n$-copy system is anomaly-free. While many familiar lattice anomalies have finite order, perturbative anomalies in the continuum$-$those captured by Feynman diagrams$-$have infinite order. In this paper, we show that the Onsager symmetry, a lattice realization of the chiral symmetry of a 1+1d massless Dirac fermion, has an order-two anomaly. However, imposing lattice CPT symmetry enhances this anomaly from order two to infinite order, yielding a lattice chiral symmetry structure that more faithfully matches the continuum chiral anomaly. We also discuss the corresponding 2+1d symmetry-protected topological phases for these infinite-order lattice anomalies.

It is a long-standing problem to prove that the number of distinct topological types of Calabi-Yau threefolds is finite. A related proposition, Reid’s fantasy, conjectures that all Calabi-Yau threefolds are connected in a single moduli space through extremal transitions. Finiteness of topological types has been proven for the class of elliptic and genus one fibered Calabi-Yau threefolds, which recently have been shown to constitute the vast majority of known Calabi-Yau threefolds; the moduli space of elliptic CY3’s is connected. In this letter, we demonstrate that all non-fibered Calabi-Yau threefolds in two of the largest known classes (toric hypersurfaces and complete intersections in products of projective spaces) are connected to fibered Calabi-Yau threefolds through a simple class of geometric transitions involving the shrinking of a single divisor from a fibered geometry. This suggests that non-fibered Calabi-Yau threefolds are rare special cases that are reached by simplifying fibered Calabi-Yau threefolds, and points to a natural path towards proving finiteness and Reid’s fantasy for Calabi-Yau threefolds.

The couplings between hadrons encode the dynamics of quantum chromodynamics. While many couplings can be calculated from decay widths, in some cases the decays are kinematically forbidden and hence are not directly accessible. We use a Regge framework to determine these couplings from high-energy polarized scattering processes. We apply this to the $πΔ$ photoproduction that was recently studied at GlueX and provide the first determination of the complete set of $NΔ$ couplings to $ρ$, $b_1$, and $a_2$.

Differential cross sections are the currency of scientific exchange in particle and nuclear physics. Recently, machine learning methods have enabled unbinned and high-dimensional cross section measurements through new approaches to unfolding. A key challenge with unfolding is that it is a bi-level optimization problem where constraints are available at the detector level while the target is at the particle level, linked by a stochastic detector response. Further complications arise when the particle-level and detector-level distributions have non-overlapping or only partially overlapping support, which can destabilize training and degrade unfolding performance. In this paper, we introduce a new unbinned unfolding technique called the Reweighting Adversarial Network (RAN), which can be viewed as a generalization of the Moment Unfolding protocol to accommodate full phase-space unfolding. RANs address the bi-level optimization problem through a particle-level reweighting function steered by a Wasserstein critic at the detector level. RANs do not require overlapping support at the detector level, nor multiple iterations of training. We evaluate the performance of RANs with Gaussian data and jet substructure studies, including cases specifically designed to stress test the method under vanishing support overlap. We demonstrate that RANs outperform state-of-the-art methods in accuracy and have a lower computational overhead.

We study the stochastic dynamics of heavy quarks propagating through the strongly coupled plasma of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory at nonzero temperature in terms of the corresponding Kolmogorov equation, which correctly describes their kinetic equilibration and the non-Gaussian fluctuations in their momenta without having to restrict their velocity to the non-relativistic regime. Leveraging the heavy quark limit, we show that the evolution of the momentum space distribution function can be reformulated as a Hamilton-Jacobi problem, and therefore can be solved in terms of first-order ordinary differential equations. We solve these evolution equations in an infinite thermal plasma with a constant temperature for initial conditions specified by spherically symmetric heavy quark momentum distributions with a phenomenologically motivated shape that is steeply falling at large momentum. To highlight the distinctive features of the kinetic equilibration process, we compare their solutions with Fokker-Planck dynamics with the same drag coefficient and fluctuations chosen by hand to guarantee equilibration. We find qualitatively similar dynamics at small momentum, and very different dynamics at large momentum, where, much like in jet quenching phenomena, the steepness of the momentum distribution gives a larger relevance to unlikely events in which a heavy quark loses little momentum in a given time step. Such events are much less unlikely in the Kolmogorov evolution than in Fokker-Planck evolution with the same mean energy loss, meaning that equilibration at large momentum is significantly delayed. Our results provide a systematic description of heavy quarks propagating through strongly coupled plasma from the ultra-relativistic to the non-relativistic regime and point the way towards implementation in phenomenological studies.

We present the next-to-next-to-leading logarithmic (NNLL) collinear resummation of projected $N$-point energy correlators (ENCs) up to $N=6$, matched to fixed-order predictions at NLO, in both electron-positron annihilation and Higgs decay to gluons. The key new ingredient is the two-loop jet function for $N=4,5,6$, which we compute semi-analytically using Integration-by-Parts and differential equations. We further include the leading non-perturbative corrections for ENCs, described by two universal soft matrix elements $\overlineΩ_{1q},\overlineΩ_{1g}$ of order $Λ_{\rm QCD}$, whose evolution is governed by anomalous dimensions for $(N-1)$-point correlators. The matched distributions are compared with parton-shower simulations from Pythia8 and Herwig7, and we study the sensitivity of both the absolute spectra and their ratios to the two-point energy correlator under variations of $α_s$ and $\overlineΩ_{1q,1g}$. Our results show that higher-point projected energy correlators are now under quantitative control at NNLL accuracy, opening the door to future $α_s$ extractions with complementary systematics.

The reliable treatment of highly boosted hadrons is crucial for many lattice QCD applications. For all these cases the kinematically enhanced interpolators promise very significant improvements and are, therefore, ever more often used in recent calculations, especially for highly boosted mesons like the pion. Motivated by, e.g., the physics program of the future Electron-Ion Collider (EIC) in the US and Electron-Ion collider in China (EIcC), we systematically benchmark our code for the unpolarized isovector nucleon quark matrix elements extracted at large source-sink separations, where excited state artifacts are significantly suppressed. We find that the precision of the renormalized nucleon matrix elements is typically improved by an order of magnitude at momentum $P_z\sim2.5$ GeV. By comparing the results from three CLS ensembles with different lattice spacings $a$ but the same pion mass, we observe no statistically significant dependence on $a$ in the renormalized matrix elements at nearly identical values of $P_z$. These encouraging results suggest that the use of kinematically improved operators is highly advantageous for parton physics calculations and can be extended to a broader class of baryon observables, making them a promising candidate for a standard component of modern lattice QCD.

Primordial black holes (PBHs) in the asteroid-mass range, with typical masses $10^{17}\,{\rm g}\lesssim M \lesssim 10^{23}\,{\rm g}$, have drawn significant recent attention as a viable dark matter candidate. The peak frequencies of photons emitted via Hawking radiation from asteroid-mass PBHs range from infrared to $γ$-ray bands. We calculate expected local transit rates for extended PBH mass distributions which could comprise all the dark matter. We evaluate prospects for detecting Hawking-radiated photons from local PBH transits through the inner Solar System and from PBH explosions in the far outer edges of the Solar System. We consider several existing and proposed ground-based and space-based instruments sensitive to photons from the radio band to ultrahigh energy $γ$-rays. We find that proposed instruments, such as the AMEGO-X satellite, could reliably detect PBH transits within ${\it O} (0.1 \, {\rm AU})$ of the Earth, while the HAWC and LHAASO observatories are both sensitive to PBH explosions out to ${\it O}(0.1 \, {\rm pc})$ and ${\it O}(0.5 \, {\rm pc})$ respectively. We conclude by specifically considering potential companion electromagnetic signatures in the case of a PBH explosion about $10^3\,{\rm AU}$ from Earth, which has been suggested as a potential source for the $\sim 220 \, {\rm PeV}$ ultrahigh-energy KM3-230213A neutrino event observed by the KM3NeT collaboration in 2023. Whereas we find that the recent KM3NeT event would not have yielded detectable electromagnetic signals — due to its location on the sky, proposed distance from Earth, and the offline status of the HAWC observatory at that time — we demonstrate that future PBH explosions at comparable distances could yield measurable electromagnetic signals at Earth, depending on alignment of the PBH burst with detector fields of view.

We investigate the interplay between the thermodynamic (Gibbs) entropy of quark-gluon plasma (QGP) and the quantum entanglement entropy characteristic of confined hadronic states across the quark-hadron phase transition. In the deconfined regime, entropy is well described by the statistical mechanics of colored quarks and gluons. Upon hadronization, however, the macroscopic Gibbs entropy of the plasma cannot simply vanish; instead, it is reorganized into the configurational entropy of a gas of colorless hadrons together with quantum correlations among the confined partons within each hadron. We show that the entanglement entropy of the internal partonic wave functions inside hadrons provides a natural repository for this “converted” thermodynamic entropy, reconciling the apparent reduction of macroscopic entropy with the second law of thermodynamics. Either by extrapolating from known facts about deep inelastic scattering, or starting from model descriptions of the proton wave function, or starting from the Hagedorn spectrum of its resonances, we provide three estimates of the magnitude of the entanglement entropy carried by a proton, with very different uncertainties. All three estimates indicate that the internal entanglement entropy of the proton is similar in magnitude to the Gibbs entropy of the QGP droplet from which the proton formed as QGP cools through the quark-hadron transition, as for example throughout the universe microseconds after the Big Bang. These results suggest that entanglement entropy offers a bridge between the quantum information content of hadronic states and the thermodynamic entropy of the quark-gluon plasma, providing a new lens on the microscopic mechanism of confinement and the nature of the QCD phase transition.

We revisit the Hartle-Hawking wave function in AdS spacetime, where natural spatial slices are open and require an additional spacetime boundary. This leads to two constructions: a fully gravitational wave function, in which the boundary configuration is integrated over, and a partially frozen one, in which it is fixed, as in AdS/CFT. To illustrate the fully gravitational construction, we explicitly analyze it in AdS$_3$ Einstein gravity and AdS$_2$ Jackiw-Teitelboim gravity. We then evaluate the one-loop correction to the hyperbolic-ball partition function in $D$-dimensional AdS Einstein gravity, expected to give the leading contribution to the wave-function norm. We demonstrate that the fully gravitational hyperbolic ball partition function, where the boundary fluctuates, develops a nontrivial one-loop phase of $(\mp i)^{D+1}$, analogous to that of the sphere partition function in dS gravity. By contrast, the partially frozen partition function, where the boundary is fixed, remains real and positive. Motivated by this AdS comparison, we conversely investigate a partially frozen dS sphere partition function where the metric on an equator is fixed, finding that its one-loop phase cancels nontrivially. Our results suggest that the phase problem is controlled by whether the gravitational path integral is fully dynamical or partially frozen.

Tidal stripping is a key feature of the evolution of dark matter (DM) halos, and has major implications for the population of low-mass galaxies. In the case of ultralight DM, tidal stripping proceeds not only classically, at the tidal radius, but also via a process analogous to quantum tunneling by long-wavelength particles out of the potential of a subhalo. This modified tidal stripping behavior leads to tight constraints on the particle mass as a function of subhalo and host properties. As many models of ultralight DM predict several independent species, it is crucial to understand how these constraints can be generalized to multifield halos with different particle masses. However, numerical challenges make it difficult to directly study the tunneling process in all but the simplest multifield scenarios. We introduce a simplified approach based on semiclassical methods that entirely sidesteps the most difficult aspects of the numerical problem, and we apply this to the study of tunneling in multifield halos. Our results significantly clarify the physics of tidal stripping for ultralight DM halos even in the single-field case: we provide first-principles derivations of features of the tunneling rate previously suggested by empirical fits. We then evaluate stability bounds on two-field halos for the first time, for a wide range of density and particle mass ratios. We show that for particular parameter combinations, the stability bounds in the two-field case can be somewhat relaxed relative to the single-field case, but for much of the parameter space, the constraints become more stringent. We discuss the path towards probing realistic multifield ultralight DM halos.

Today, the observable cosmos exhibits a remarkable degree of isotropy and plausibly began in a nearly isotropic initial state. The properties of the Lorentzian Chern-Simons-Kodama (CSK) functional can provide an understanding of this initial state. In gravity with a positive cosmological constant, the Chern-Simons-Kodama (CSK) wavefunctional is an exact, chiral solution of the quantum gravitational constraints. We suggest that the normalizability and other issues with this functional, if interpreted as a proper state of quantum gravity, instead suggest an embedding into a larger quantum gravitational completion, and recast the CSK functional as a gravitational sphaleron with observationally desirable properties. By perturbing around the dominant de Sitter saddle of the wavefunctional with appropriate quantum gravitational boundary conditions, we find that for a closed universe the system is dynamically driven to spatial isotropy, while all anisotropic modes acquire positive quadratic curvature and are Gaussian-suppressed. The decay of this sphaleron therefore proceeds along an isotropic channel, providing an intrinsic quantum-gravitational mechanism for dynamical isotropization. This isotropization effect is robust under the inclusion of a slow-roll inflaton, and no analogous isotropic sphaleron exists for spatially flat or hyperbolic geometries. Taken together, these results recast the Lorentzian CSK functional as a chiral sphaleron that naturally prepares an approximately isotropic de Sitter background for inflation. Beyond this phenomenological study, we further suggest that the CSK functional can be understood as a boundary functional for a class of anomaly-free objects, including a complexified generalization of the Hartle-Hawking state.

In his 1976 paper “More about the massive Schwinger model”, Coleman introduced $1+1$-dimensional Quantum Electrodynamics coupled to two charged massive fermions. By applying Abelian bosonization, he elucidated much of the physics of this two-flavor Schwinger model, but he listed three puzzles at the end of his paper. We present new analytical and numerical calculations to solve Coleman’s three puzzles and thereby deepen our understanding of this model. These puzzles pertain to the theory with equal fermion masses at $θ= 0$ and at $θ= π$, as well as the size of isospin-breaking effects when the fermion masses are unequal. For the puzzle at $θ= π$, the solution is related to the structure of the zero-temperature phase diagram arXiv:2305.04437: for equal fermion masses $m$, the model exhibits spontaneous breaking of charge conjugation symmetry and absence of confinement for any value of the gauge coupling $g$, so that there is a smooth interpolation from weak to strong coupling. Using two-loop Renormalization Group and integrability methods, we show that the mass gap behaves as $\sim m e^{-0.111 g^2/m^2}$ in the strong coupling regime $m\ll g$. Our numerical results using the lattice Hamiltonian are in good agreement with this behavior. For the puzzle at $θ= 0$, the solution is related to a level crossing between two isosinglet particles with different discrete quantum numbers; we demonstrate the necessity of such a crossing by comparing integrability and weak coupling calculations, and we also exhibit the crossing numerically. Finally, we provide a new estimate for the size of isospin-breaking effects caused by different fermion masses at strong coupling.

Recent developments have shown that some semiclassical spacetimes cannot emerge from a traditional application of the rules of holography, prompting proposals for restoring their emergence with “observer rules”. In this paper, we propose a general semiclassical diagnostic of such failures of emergence, and of the extent to which observer rules can fix them. Our diagnostic is the presence of certain “evanescent” quantum extremal surfaces, which are distinguished by an upper bound on their area rather than their generalized entropy. In particular, the generalized entropy of an evanescent QES may be large: even though its area term must be small, its bulk entanglement term is unconstrained. This feature is explained by an operational distinction between classical and quantum connectivity in semiclassical gravity, or equivalently between the two summands of the generalized entropy.