MIT Center for Theoretical Physics — a Leinweber Institute Publications

We study the mixed-state entanglement structure of chaotic quantum many-body systems at late times using the recently developed \(\textit{equilibrium approximation}\). A rich entanglement phase diagram emerges when we generalize this technique to evaluate the logarithmic negativity for various universality classes of macroscopically thermalized states. Unlike in the infinite temperature case, when we impose energy constraints at finite temperature, the phase diagrams for the logarithmic negativity and the mutual information become distinct. In particular, we identify a regime where the negativity is extensive but the mutual information is sub-extensive, indicating a large amount of \(\textit{bound entanglement}\). When applied to evaporating black holes, these results imply that there is quantum entanglement within the Hawking radiation long before the Page time, although this entanglement may not be distillable into EPR pairs.

Astrometry -- the precise measurement of positions and motions of celestial objects -- has emerged as a promising avenue for characterizing the dark matter population in our Galaxy. By leveraging recent advances in simulation-based inference and neural network architectures, we introduce a novel method to search for global dark matter-induced gravitational lensing signatures in astrometric datasets. Our method based on neural likelihood-ratio estimation shows significantly enhanced sensitivity to a cold dark matter population and more favorable scaling with measurement noise compared to existing approaches based on two-point correlation statistics, establishing machine learning as a powerful tool for characterizing dark matter using astrometric data.

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for high-energy exclusive processes in quantum chromodynamics. In this article, the second Mellin moment of the pion LCDA is determined as a proof-of-concept calculation for the first numerical implementation of the heavy-quark operator product expansion (HOPE) method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of \(m_\pi=550\) MeV at a factorization scale of 2 GeV is \( \langle \xi^2 \rangle = 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}\). This result is compatible with those from previous determinations of this quantity.

I look at propagation of jets that act as a probe of the medium in the phenomenologically relevant case of a short lived dilute Quark Gluon Plasma(QGP) created during heavy ion collisions. Working in the regime where the lifetime of the medium is of the order or smaller than the formation time of the energetic jet, I derive a factorization formula with a manifest separation of scales for an illustrative jet substructure observable using the Open Quantum system Effective Field Theory(EFT) approach developed in \cite{Vaidya:2020lih}, in terms of a medium structure function and a medium induced jet function . The medium structure function or the "PDF of the medium" that describes the observable independent physics of the QGP remains identical to that in a dilute long lived medium considered in \cite{Vaidya:2021vxu}, while the medium induced jet function is modified and incorporates quantum interference between the hard interaction that creates the jet and subsequent medium interactions. The medium jet function continues to enjoy a BFKL rapidity evolution just as for a long lived medium, albeit with a modified renormalization scale that now depends on the medium lifetime.

It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an otherwise Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localization are lost.

We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking.

One of the most important properties of neural networks is the clustering of local minima of the loss function near the global minimum, enabling efficient training. Though generative models implemented on quantum computers are known to be more expressive than their traditional counterparts, it has empirically been observed that these models experience a transition in the quality of their local minima. Namely, below some critical number of parameters, all local minima are far from the global minimum in function value; above this critical parameter count, all local minima are good approximators of the global minimum. Furthermore, for a certain class of quantum generative models, this transition has empirically been observed to occur at parameter counts exponentially large in the problem size, meaning practical training of these models is out of reach. Here, we give the first proof of this transition in trainability, specializing to this latter class of quantum generative model. We use techniques inspired by those used to study the loss landscapes of classical neural networks. We also verify that our analytic results hold experimentally even at modest model sizes.

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under the Complexity=Volume proposal, this constitutes a positive holographic complexity theorem. The result features a number of parallels with the positive energy theorem, including the assumption of an energy condition that excludes false vacuum decay (the AdS weak energy condition). Our proof is rigorously established in broad generality in four bulk dimensions, and we provide strong evidence in favor of a generalization to arbitrary dimensions. Our techniques also yield a holographic proof of Lloyd's bound for a class of bulk spacetimes. We further establish a partial rigidity result for wormholes: wormholes with a given throat size are more complex than AdS-Schwarzschild with the same throat size.

In this paper we use Euclidean gravity methods to show that charged black holes which are sufficiently close to extremality must be able to decay. The argument proceeds by showing that Euclidean gravity would otherwise imply a violation of charge quantization. As this is the assumption which leads to the weak gravity conjecture, our argument gives a derivation of that conjecture. We use a small negative cosmological constant as an infrared regulator, but our argument applies to near-extremal black holes which are arbitrarily small compared to the \(AdS\) curvature scale. We also give a universal formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero fraction, this gives a new proof of the completeness hypothesis for finite gauge fields. Based on these observations we make two conjectures about many-body quantum physics: we propose a lower bound on the critical temperature for the instability of a semi-local quantum liquid, and we propose that our formula for the density of black hole microstates in each representation of a finite gauge group also applies at high energy to any quantum field theory with a finite group global symmetry.

We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order \(m^2\) gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green's functions and Green's functions at coinciding points on the manifold.

These lectures, presented at the 2021 Les Houches Summer School on Dark Matter, provide an introduction to key methods and tools of indirect dark matter searches, as well as a status report on the field circa summer 2021. Topics covered include the possible effects of energy injection from dark matter on the early universe, methods to calculate both the expected energy distribution and spatial distribution of particles produced by dark matter interactions, an outline of theoretical models that predict diverse signals in indirect detection, and a discussion of current constraints and some claimed anomalies. These notes are intended as an introduction to indirect dark matter searches for graduate students, focusing primarily on intuition-building estimates and useful concepts and tools.

The low-energy spectrum and scattering of two-nucleon systems are studied with lattice quantum chromodynamics using a variational approach. A wide range of interpolating operators are used: dibaryon operators built from products of plane-wave nucleons, hexaquark operators built from six localized quarks, and quasi-local operators inspired by two-nucleon bound-state wavefunctions in low-energy effective theories. Sparsening techniques are used to compute the timeslice-to-all quark propagators required to form correlation-function matrices using products of these operators. Projection of these matrices onto irreducible representations of the cubic group, including spin-orbit coupling, is detailed. Variational methods are applied to constrain the low-energy spectra of two-nucleon systems in a single finite volume with quark masses corresponding to a pion mass of 806 MeV. Results for S- and D-wave phase shifts in the isospin singlet and triplet channels are obtained under the assumption that partial-wave mixing is negligible. Tests of interpolating-operator dependence are used to investigate the reliability of the energy spectra obtained and highlight both the strengths and weaknesses of variational methods. These studies and comparisons to previous studies using the same gauge-field ensemble demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and non-variational methods, including missing energy levels and other discrepancies. While this study is inconclusive regarding the presence of two-nucleon bound states at this quark mass, it provides robust upper bounds on two-nucleon energy levels that can be improved in future calculations using additional interpolating operators and is therefore a step toward reliable nuclear spectroscopy from the underlying Standard Model of particle physics.

Motivated by questions related to the landscape of flux compactifications, we combine new and existing techniques into a systematic, streamlined approach for computing vertical fluxes and chiral matter multiplicities in 4D F-theory models. A central feature of our approach is the conjecturally resolution-independent intersection pairing of the vertical part of the integer middle cohomology of smooth elliptic CY fourfolds, relevant for computing chiral indices and related aspects of 4D F-theory flux vacua. We illustrate our approach by analyzing vertical flux backgrounds for F-theory models with simple, simply-laced gauge groups and generic matter content, as well as models with U(1) gauge factors. We explicitly analyze resolutions of these F-theory models in which the elliptic fiber is realized as a cubic in \(\mathbb P^2\) over an arbitrary (e.g., not necessarily toric) smooth base, and confirm the resolution-independence of the intersection pairing of the vertical part of the middle cohomology. In each model we study, we find that vertical flux backgrounds can produce nonzero multiplicities for all anomaly-free chiral matter field combinations, suggesting that F-theory geometry imposes no additional linear constraints beyond those implied by anomaly cancellation.

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for \(h^{(1,1)}\) and 97% for \(h^{(2,1)}\) (100% for both), 81% (96%) for \(h^{(3,1)}\), and 49% (83%) for \(h^{(2,2)}\). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.

In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite \(N\) corrections are taken into account by interactions (non-Gaussian terms in the action). In this paper, we study two related aspects of this correspondence. First, we comment on the concepts of locality and power-counting in this context. Indeed, these usual space-time notions may not hold for neural networks (since inputs can be arbitrary), however, the renormalization group provides natural notions of locality and scaling. Moreover, we comment on several subtleties, for example, that data components may not have a permutation symmetry: in that case, we argue that random tensor field theories could provide a natural generalization. Second, we improve the perturbative Wilsonian renormalization from arXiv:2008.08601 by providing an analysis in terms of the nonperturbative renormalization group using the Wetterich-Morris equation. An important difference with usual nonperturbative RG analysis is that only the effective (IR) 2-point function is known, which requires setting the problem with care. Our aim is to provide a useful formalism to investigate neural networks behavior beyond the large-width limit (i.e.~far from Gaussian limit) in a nonperturbative fashion. A major result of our analysis is that changing the standard deviation of the neural network weight distribution can be interpreted as a renormalization flow in the space of networks. We focus on translations invariant kernels and provide preliminary numerical results.

We study which bulk couplings contribute to the \(S^3\) free energy \(F(\mathfrak{m})\) of three-dimensional \({\cal N} = 2\) superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters \(\mathfrak{m}\). In particular, we show that \(F(\mathfrak{m})\) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, \(F(\mathfrak{m})\) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, \(\mathfrak{osp}(2|4)\). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that \(F(\mathfrak{m})\) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that \(F(\mathfrak{m})\) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar \({\cal N} = 2\) superconformal multiplets.

This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV \(< q_T < 1.7\) GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass, \(m_\pi=538(1)\) MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.

The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, \(\rho\) meson, and \(\Delta\) baryon as functions of the squared momentum transfer \(t\) in the region \(0 \leq -t < 2 \; \text{GeV}^2\), as determined in a lattice QCD study with pion mass \(m_{\pi} = 450(5) \; \text{MeV}\). By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for the corresponding gluon mechanical and mass radii, as well as the forward-limit gluon contributions to the momentum fraction and angular momentum of the hadrons.

There is a growing use of neural network classifiers as unbinned, high-dimensional (and variable-dimensional) reweighting functions. To date, the focus has been on marginal reweighting, where a subset of features are used for reweighting while all other features are integrated over. There are some situations, though, where it is preferable to condition on auxiliary features instead of marginalizing over them. In this paper, we introduce neural conditional reweighting, which extends neural marginal reweighting to the conditional case. This approach is particularly relevant in high-energy physics experiments for reweighting detector effects conditioned on particle-level truth information. We leverage a custom loss function that not only allows us to achieve neural conditional reweighting through a single training procedure, but also yields sensible interpolation even in the presence of phase space holes. As a specific example, we apply neural conditional reweighting to the energy response of high-energy jets, which could be used to improve the modeling of physics objects in parametrized fast simulation packages.