MIT Center for Theoretical Physics — a Leinweber Institute Publications

In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to explain thermalization. Consider a nearly integrable Sachdev-Ye-Kitaev model obtained by adding random all-to-all \(4\)-body interactions as a perturbation to a random free-fermion model. When the subsystem size is larger than the square root of but is still a vanishing fraction of the system size, we prove thermalization if the system is initialized in a random product state, while almost all eigenstates violate the ETH. In this sense, the ETH is not a necessary condition for thermalization.

The 2+1d continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. These are two different \(U(1)\) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton/lineon-elasticity dualities for the Lifshitz theory, scalar and vector charge gauge theories.

It has recently been argued that noisy intermediate-scale quantum computers may be used to optimize interpolating operator constructions for lattice quantum field theory (LQFT) calculations on classical computers. Here, two concrete realizations of the method are developed and implemented. The first approach is to maximize the overlap, or fidelity, of the state created by an interpolating operator acting on the vacuum state to the target eigenstate. The second is to instead minimize the energy expectation value of the interpolated state. These approaches are implemented in a proof-of-concept calculation in (1+1)-dimensions for a single-flavor massive Schwinger model to obtain quantum-optimized interpolating operator constructions for a vector meson state in the theory. Although fidelity maximization is preferable in the absence of noise due to quantum gate errors, it is found that energy minimization is more robust to these effects in the proof-of-concept calculation. This work serves as a concrete demonstration of how quantum computers in the intermediate term might be used to accelerate classical LQFT calculations.

We construct initial data violating the AdS Penrose inequality using scalars with various potentials. Since the Penrose inequality can be derived from basic entries in the AdS/CFT dictionary, we argue that it is a new swampland condition, ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for top-down potentials. In the special case where the dominant energy condition holds, we use GR techniques to prove the AdS Penrose inequality in all dimensions greater than two, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings and the exponential behavior of scalar potentials.

Strong gravitational lensing has emerged as a promising approach for probing dark matter models on sub-galactic scales. Recent work has proposed the subhalo effective density slope as a more reliable observable than the commonly used subhalo mass function. The subhalo effective density slope is a measurement independent of assumptions about the underlying density profile and can be inferred for individual subhalos through traditional sampling methods. To go beyond individual subhalo measurements, we leverage recent advances in machine learning and introduce a neural likelihood-ratio estimator to infer an effective density slope for populations of subhalos. We demonstrate that our method is capable of harnessing the statistical power of multiple subhalos (within and across multiple images) to distinguish between characteristics of different subhalo populations. The computational efficiency warranted by the neural likelihood-ratio estimator over traditional sampling enables statistical studies of dark matter perturbers and is particularly useful as we expect an influx of strong lensing systems from upcoming surveys.

Dwarf galaxies are small, dark matter-dominated galaxies, some of which are embedded within the Milky Way. Their lack of baryonic matter (e.g., stars and gas) makes them perfect test beds for probing the properties of dark matter -- understanding the spatial dark matter distribution in these systems can be used to constrain microphysical dark matter interactions that influence the formation and evolution of structures in our Universe. We introduce a new method that leverages simulation-based inference and graph-based machine learning in order to infer the dark matter density profiles of dwarf galaxies from observable kinematics of stars gravitationally bound to these systems. Our approach aims to address some of the limitations of established methods based on dynamical Jeans modeling. We show that this novel method can place stronger constraints on dark matter profiles and, consequently, has the potential to weigh in on some of the ongoing puzzles associated with the small-scale structure of dark matter halos, such as the core-cusp discrepancy.

The quantum chromodynamics axion with a decay constant near the Grand Unification (GUT) scale has an ultralight mass near a neV. We show, however, that axion-like particles with masses near the keV - PeV range with GUT-scale decay constants are also well motivated in that they naturally arise from axiverse theories with dark non-abelian gauge groups. We demonstrate that the correct dark matter abundance may be achieved by the heavy axions in these models through the misalignment mechanism in combination with a period of early matter domination from the long-lived dark glueballs of the same gauge group. Heavy axion dark matter may decay to two photons, yielding mono-energetic electromagnetic signatures that may be detectable by current or next-generation space-based telescopes. We project the sensitivity of next-generation telescopes including \(\textit {Athena,}\) AMEGO, and e-ASTROGAM to such decaying axion dark matter. If the dark sector contains multiple confining gauge groups, then the observed primordial baryon asymmetry may also be achieved in this scenario through spontaneous baryogenesis. We present explicit orbifold constructions where the dark gauge groups unify with the SM at the GUT scale and axions emerge as the fifth components of dark gauge fields with bulk Chern-Simons terms.

This work presents a determination of potential short-distance contributions to the unphysical \(\pi^-\rightarrow\pi^+ e^- e^-\) decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with \(N_f = 2 + 1\) quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory (\(\chi\mathrm{EFT}\)). This extrapolation also yields the relevant low-energy constants of \(\chi\mathrm{EFT}\), which are necessary input for \(\chi\mathrm{EFT}\) calculations of neutrinoless double beta decay of nuclei.

In gauge theory, it is commonly stated that time-reversal symmetry only exists at \(\theta=0\) or \(\pi\) for a \(2\pi\)-periodic \(\theta\)-angle. In this paper, we point out that in both the free Maxwell theory and massive QED, there is a non-invertible time-reversal symmetry at every rational \(\theta\)-angle, i.e., \(\theta= \pi p/N\). The non-invertible time-reversal symmetry is implemented by a conserved, anti-linear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar non-invertible time-reversal symmetries in non-Abelian gauge theories, including the \(\mathcal{N}=4\)\(SU(2)\) super Yang-Mills theory along the locus \(|\tau|=1\) on the conformal manifold.

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with \(N_f = 2+1\) dynamical quark flavors and \(m_{\pi}\) = 200 MeV. The \(s\)-wave scattering lengths with both total isospins \(I=1/2\) and \(I=3/2\) are inferred from the finite-volume spectrum below the inelastic threshold together with the \(I=3/2\) \(p\)-wave containing the \(\Delta(1232)\) resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels enabling a determination of the \(I=3/2\) scattering length with statistical errors below \(5\%\), while the \(I = 1/2\) is somewhat less precise. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a pathway for future computations down to the physical light quark masses with multiple lattice spacings and physical volumes.

This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical point. In this system, neural-network preconditioners are found to accelerate the convergence of the conjugate gradient solver compared with the solution of unpreconditioned systems or those preconditioned with conventional approaches based on even-odd or incomplete Cholesky decompositions, as measured by reductions in the number of iterations and/or complex operations required for convergence. It is also shown that a preconditioner trained on ensembles with small lattice volumes can be used to construct preconditioners for ensembles with many times larger lattice volumes, with minimal degradation of performance. This volume-transferring technique amortizes the training cost and presents a pathway towards scaling such preconditioners to lattice field theory calculations with larger lattice volumes and in four dimensions.

We consider the partition function for Euclidean \(SU(N)\) super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six ``fixed" three-spheres on the \(\mathbb{S}^7\). The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres. The full partition function on the \({\mathbb S}^7\) is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an \(SU(2)\) gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that the low energy phase in this regime is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.

We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits no chiral matter representations. We focus specifically on applications to realizations of the Standard Model gauge group and chiral matter spectrum through breaking of rigid exceptional gauge groups \(E_7, E_6\), which are ubiquitous in the 4D F-theory landscape. Supplemented by an intermediate \(\mathrm{SU}(5)\) group, these large classes of models give natural constructions of Standard Model-like theories with small numbers of generations of matter in F-theory.

We have performed a systematic study of the statistical behavior of non-Poissonian template fitting (NPTF), a method designed to analyze and characterize unresolved point sources in general counts datasets. In this paper, we focus on the properties and characteristics of the Fermi-LAT gamma-ray data set. In particular, we have simulated and analyzed gamma-ray sky maps under varying conditions of exposure, angular resolution, pixel size, energy window, event selection, and source brightness. We describe how these conditions affect the sensitivity of NPTF to the presence of point sources, for inner-galaxy studies of point sources within the Galactic Center excess, and for the simplified case of isotropic emission. We do not find opportunities for major gains in sensitivity from varying these choices, within the range available with current Fermi-LAT data. We provide an analytic estimate of the NPTF sensitivity to point sources for the case of isotropic emission and perfect angular resolution, and find good agreement with our numerical results for that case.

Thermal higgsino dark matter (DM), with mass around 1 TeV, is a well-motivated, minimal DM scenario that arises in supersymmetric extensions of the Standard Model. Higgsinos may naturally be the lightest superpartners in Split-supersymmetry models that decouple the scalar superpartners while keeping higgsinos and gauginos close to the TeV scale. Higgsino DM may annihilate today to give continuum gamma-ray emission at energies less than a TeV in addition to a line-like signature at energies equal to the mass. Previous searches for higgsino DM, for example with the H.E.S.S. gamma-ray telescope, have not reached the necessary sensitivity to probe the higgsino annihilation cross-section. In this work we make use of 14 years of \(\textit{Fermi}\) gamma-ray data at energies above \(\sim\)10 GeV to search for the continuum emission near the Galactic Center from higgsino annihilation. We interpret our results using DM profiles from Milky Way analogue galaxies in the FIRE-2 hydrodynamic cosmological simulations. We set the strongest constraints to-date on higgsino-like DM. Our results show a mild, \(\sim\)2\(\sigma\) preference for higgsino DM with a mass near the thermal higgsino mass and, depending on the DM density profile, the expected cross-section.

The Landau-Ginzburg-Wilson theory of phase transitions precludes a continuous transition between two phases that spontaneously break distinct symmetries. However, quantum mechanical effects can intertwine the symmetries, giving rise to an exotic phenomenon called deconfined quantum criticality (DQC). In this work, we study the ground state phase diagram of a one-dimensional array of individually trapped neutral atoms interacting strongly via Rydberg states, and demonstrate through extensive numerical simulations that it hosts a variety of symmetry-breaking phases and their transitions including DQC. We show how an enlarged, emergent continuous symmetry arises at the DQCs, which can be experimentally observed in the joint distribution of two distinct order parameters, obtained within measurement snapshots in the standard computational basis. Our findings highlight quantum simulators of Rydberg atoms not only as promising platforms to experimentally realize such exotic phenomena, but also as unique ones allowing access to physical properties not obtainable in traditional experiments.

This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as stochastic estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD. Methods by which flow-based sampling approaches can be improved via standard techniques such as even/odd preconditioning and the Hasenbusch factorization are also outlined. Numerical demonstrations in two-dimensional U(1) and SU(3) gauge theories with \(N_f=2\) flavors of fermions are provided.

We introduce two exotic lattice models on a general spatial graph. The first one is a matter theory of a compact Lifshitz scalar field, while the second one is a certain rank-2 \(U(1)\) gauge theory of fractons. Both lattice models are defined via the discrete Laplacian operator on a general graph. We unveil an intriguing correspondence between the physical observables of these lattice models and graph theory quantities. For instance, the ground state degeneracy of the matter theory equals the number of spanning trees of the spatial graph, which is a common measure of complexity in graph theory ("GSD = complexity"). The discrete global symmetry is identified as the Jacobian group of the graph. In the gauge theory, superselection sectors of fractons are in one-to-one correspondence with the divisor classes in graph theory. In particular, under mild assumptions on the spatial graph, the fracton immobility is proven using a graph-theoretic Abel-Jacobi map.

We show that Dense Neural Networks can be used to accurately model the cooling of high-energy particles in the early universe, in the context of the public code package DarkHistory. DarkHistory self-consistently computes the temperature and ionization history of the early universe in the presence of exotic energy injections, such as might arise from the annihilation or decay of dark matter. The original version of DarkHistory uses large pre-computed transfer function tables to evolve photon and electron spectra in redshift steps, which require a significant amount of memory and storage space. We present a light version of DarkHistory that makes use of simple Dense Neural Networks to store and interpolate the transfer functions, which performs well on small computers without heavy memory or storage usage. This method anticipates future expansion with additional parametric dependence in the transfer functions without requiring exponentially larger data tables.

Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of \(2\to 2\) scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to \(\mathcal{O}(\epsilon)\) in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e.~the terms \(\sim \alpha_s^{k+1}n_f^k\) for any \(k\), where \(n_f\) is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.