MIT Center for Theoretical Physics — a Leinweber Institute Publications

In this talk, I describe some recent ideas relating to the spectral reconstruction inverse problem, which arises frequently in lattice QCD calculations of inclusive hadronic quantities, and provide some physical context for this work. Particular emphasis is given to a new method for rigorously bounding uncertainties using techniques from complex analysis.

Khovanov homology is a topological knot invariant that categorifies the Jones polynomial, recognizes the unknot, and is conjectured to appear as an observable in $4D$ supersymmetric Yang–Mills theory. Despite its rich mathematical and physical significance, the computational complexity of Khovanov homology remains largely unknown. To address this challenge, this work initiates the study of efficient quantum algorithms for Khovanov homology. We provide simple proofs that increasingly accurate additive approximations to the ranks of Khovanov homology are DQC1-hard, BQP-hard, and #P-hard, respectively. For the first two approximation regimes, we propose a novel quantum algorithm. Our algorithm is efficient provided the corresponding Hodge Laplacian thermalizes in polynomial time and has a sufficiently large spectral gap, for which we give numerical and analytical evidence. Our approach introduces a pre-thermalization procedure that allows our quantum algorithm to succeed even if the Betti numbers of Khovanov homology are much smaller than the dimensions of the corresponding chain spaces, overcoming a limitation of prior quantum homology algorithms. We introduce novel connections between Khovanov homology and graph theory to derive analytic lower bounds on the spectral gap.

Quantum computing and quantum sensing represent two distinct frontiers of quantum information science. In this work, we harness quantum computing to solve a fundamental and practically important sensing problem: the detection of weak oscillating fields with unknown strength and frequency. We present a quantum computing enhanced sensing protocol that outperforms all existing approaches. Furthermore, we prove our approach is optimal by establishing the Grover-Heisenberg limit — a fundamental lower bound on the minimum sensing time. The key idea is to robustly digitize the continuous, analog signal into a discrete operation, which is then integrated into a quantum algorithm. Our metrological gain originates from quantum computation, distinguishing our protocol from conventional sensing approaches. Indeed, we prove that broad classes of protocols based on quantum Fisher information, finite-lifetime quantum memory, or classical signal processing are strictly less powerful. Our protocol is compatible with multiple experimental platforms. We propose and analyze a proof-of-principle experiment using nitrogen-vacancy centers, where meaningful improvements are achievable using current technology. This work establishes quantum computation as a powerful new resource for advancing sensing capabilities.

We calculate the probability distribution $P\left(k\right)$ for a heavy quark with velocity $v$ propagating through strongly coupled $N=4$ SYM plasma in the ‘t Hooft limit at a temperature $T$ to acquire a momentum $k$ due to interactions with the plasma. This distribution encodes the well-known drag coefficient ${\eta }_D$ and the transverse and longitudinal momentum diffusion coefficients ${\kappa }_T$ and ${\kappa }_L$. Furthermore, our calculation determines all of the higher order and mixed moments to leading order in $1/\sqrt{\lambda }$ for the first time. These non-Gaussian features of $P\left(k\right)$ include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero $v$. We demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck (FP) equation when truncated to only include the effects of ${\eta }_D$, ${\kappa }_T$ and ${\kappa }_L$. Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this FP equation, we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with the all-order Kolmogorov equation we have derived. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled $N=4$ SYM plasma — as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For example, an effective sparsening of a quark propagator provides an efficient map from a quark propagator on a fine lattice geometry to a quark propagator defined on a coarser geometry in order to reduce storage and computational costs of subsequent calculational stages while maintaining long-distance correlations and corresponding low-energy physical information. Previous studies have focused on decimating lattice sites or randomly sampling lattice sites to reduce the size of the propagator and subsequent costs of Wick contractions. Here, we extend the study of sparsening to incorporate covariant averaging of spatial sites and examine the effects on two-point and three-point correlation functions involving various hadrons. We find that sparsening is most effective in reproducing the unsparsened versions of these correlation functions when weighted covariant-averaging is sequentially applied many times.

We provide a perturbative effective field theory (EFT) description for anisotropic (redshift-space) correlations between the Lyman alpha forest and a generic biased tracer of matter, which could be represented by quasars, high-redshift galaxies, or dark matter halos. We compute one-loop EFT power spectrum predictions for the combined analysis of the Lyman alpha and biased tracers’ data and test them on the publicly available high-fidelity Sherwood simulations. We use massive and light dark matter halos at redshift $z=2.8$ as proxies for quasars and high-redshift galaxies, respectively. In both cases, we demonstrate that our EFT model can consistently describe the complete data vector consisting of the Lyman alpha forest auto spectrum, the halo auto spectrum, and the Lyman alpha-halo cross spectrum. We show that the addition of cross-correlations significantly sharpens constraints on EFT parameters of the Lyman alpha forest and halos. In the combined analysis, our EFT model fits the simulated cross-spectra with a percent level accuracy at $k_{\max }=1h{\mathrm{Mpc}}^{-1}$, which represents a significant improvement over previous analytical models. Thus, our work provides precision theoretical tools for full-shape analyses of Lyman alpha-quasar cross-correlations with ongoing and upcoming spectroscopic surveys.

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer $Ob$ in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly $e^{S_{Ob}}$, where $S_{Ob}$ is the number of degrees of freedom of $Ob$. Moreover we argue that the errors in this description are exponentially small in $S_{Ob}$. We give evidence for this proposal using the gravitational path integral and the coding interpretation of holography, and we explain how similar effects arise in black hole physics in appropriate circumstances.

Dualities of quantum field theories are challenging to realize in lattice models of qubits. In this work, we explore one of the simplest dualities, T-duality of the compact boson CFT, and its realization in quantum spin chains. In the special case of the XX model, we uncover an exact lattice T-duality, which is associated with a non-invertible symmetry that exchanges two lattice U(1) symmetries. The latter symmetries flow to the momentum and winding U(1) symmetries with a mixed anomaly in the CFT. However, the charge operators of the two U(1) symmetries do not commute on the lattice and instead generate the Onsager algebra. We discuss how some of the anomalies in the CFT are nonetheless still exactly realized on the lattice and how the lattice U(1) symmetries enforce gaplessness. We further explore lattice deformations preserving both U(1) symmetries and find a rich gapless phase diagram with special $Spin(2k{)}_1$ WZW model points and whose phase transitions all have dynamical exponent $z>1$.

We present the first results from the Quantum Resolution-Optimized Cryogenic Observatory for Dark matter Incident at Low Energy (QROCODILE). The QROCODILE experiment uses a microwire-based superconducting nanowire single-photon detector (SNSPD) as a target and sensor for dark matter scattering and absorption, and is sensitive to energy deposits as low as 0.11 eV. We introduce the experimental configuration and report new world-leading constraints on the interactions of sub-MeV dark matter particles with masses as low as 30 keV. The thin-layer geometry of the system provides anisotropy in the interaction rate, enabling directional sensitivity. In addition, we leverage the coupling between phonons and quasiparticles in the detector to simultaneously constrain interactions with both electrons and nucleons. We discuss the potential for improvements to both the energy threshold and effective volume of the experiment in the coming years.

In a seminal paper now a decade old, it was shown that dark matter detectors geared at probing interactions with nucleons could also be used to probe dark matter interactions with electrons. In this work, we show that new detector concepts designed to probe dark matter-electron interactions at low masses can similarly be used to probe new parameter space for dark matter-nucleon interactions. We demonstrate the power of this approach by using existing data from superconducting detectors to place new limits on the interactions of nuclei with MeV-scale dark matter. Further, we show that advances in detector technology that have been anticipated for electronic interactions will automatically extend sensitivity deep into uncharted territory for nuclear interactions. This doubles the effective science output of future low-threshold experiments.

A Muon (Synchrotron) Ion Collider (MuSIC) can be the successor to the Electron-Ion Collider at Brookhaven National Laboratory, as well as the ideal demonstrator facility for a future multi-TeV Muon Collider. Besides its rich nuclear physics and Standard Model particle physics programs, in this work we show that the MuSIC with a TeV-scale muon beam offers also a unique opportunity to probe New Physics. In particular, the relevant searches have the potential to surpass current experimental limits and explore new regimes of the parameter space for a variety of Beyond the Standard Model scenarios including: lepton-flavor violating leptoquarks, muonphilic vector boson interactions, axion-like particles coupling to photons, and heavy sterile neutrinos. Depending on the particular case, the sensitivity of the searches in the MuSIC may span a wide range of energy scales, namely from sub-GeV particles to the few TeV New Physics mediators. Our analysis demonstrates that the MuSIC can strike a powerful chord in the search for New Physics, thanks to unique combination of features that amplify its capabilities.

Understanding the mechanism of high-temperature superconductivity is among the most important problems in physics, for which quantum simulation can provide new insights. However, it remains challenging to characterize superconductivity in existing cold-atom quantum simulation platforms. Here, we introduce a protocol for measuring a broad class of observables in fermionic quantum gas microscopes, including long-range superconducting pairing correlations (after a repulsive-to-attractive mapping). The protocol only requires global controls followed by site-resolved particle number measurements — capabilities that have been already demonstrated in multiple experiments — and is designed by analyzing the Hilbert-space structure of dimers of two sites. The protocol is sample efficient and we further optimize our pulses for robustness to experimental imperfections such as lattice inhomogeneity. Our work introduces a general tool for manipulating quantum states on optical lattices, enhancing their ability to tackle problems such as that of high-temperature superconductivity.

We study the confining and deconfining phases of pure $SU\left(3\right)$ lattice gauge theory with topological data analysis. This provides unique insights into long range correlations of field configurations across the confinement-deconfinement transition. Specifically, we analyze non-trivial structures in electric and magnetic field energy densities as well as Polyakov loop traces and a Polyakov loop-based variant of the topological density. The Betti curves for filtrations based on the electric and magnetic field energy densities reveal signals of electromagnetic dualities. These dualities can be associated with an interchange in the roles of local lumps of electric and magnetic energy densities around the phase transition. Moreover, we show that plaquette susceptibilities can manifest in the geometric features captured by the Betti curves. We also confront the results obtained for $SU\left(3\right)$ with that for $SU\left(2\right)$ and elaborate on the significant differences. Our results demonstrate that topological data analysis can discriminate phase transitions of different order for non-Abelian lattice gauge theories. Moreover, it provides unprecedented insights into the relevant structures in their vicinity.

We report on an instance in quantum gravity where a topological expansion resums into an effective description on a single geometry. The original theory whose gravitational path integral we study is JT quantum gravity with one asymptotic boundary at nonperturbatively low temperatures. The effective theory we derive is a deformation of JT gravity by a highly quantum and nonlocal interaction for the dilaton, evaluated only on a disk topology. This emergent description addresses a strongly quantum gravitational regime where all genera contribute at the same order, successfully capturing the doubly nonperturbative physics of the original theory.

The SU(2) gauge group with two fundamental flavors is a candidate for a composite Higgs extension of the Standard Model. Central to Higgs phenomenology is a non-perturbative determination of observables of the theory, such as the decay constant of the pseudo-Nambu-Goldstone Bosons. We present preliminary results for the continuum limit of the pseudoscalar decay constant using a mixed-action setup, with non-perturbatively improved stabilized Wilson Fermions on the sea, and maximally twisted valence quarks. Pivotal to this study is the recent porting of our simulation suite HiRep to GPU architecture.

We present precision measurements of the bias parameters of the one-loop power spectrum model of the Lyman-$\alpha$ (Ly-$\alpha$) forest, derived within the effective field theory (EFT) of large-scale structure. We fit our model to the three-dimensional flux power spectrum measured from the ${\mathrm{ACCEL}}^2$ hydrodynamic simulations. The EFT model fits the data with an accuracy of below 2% up to $k=2h{\mathrm{Mpc}}^{-1}$. Further, we analytically derive how nonlinearities in the three-dimensional clustering of the Ly-$\alpha$ forest introduce biases in measurements of the baryon acoustic oscillations (BAOs) scaling parameters in radial and transverse directions. From our EFT parameter measurements, we obtain a theoretical error budget of $\Delta {\alpha }_{\parallel }=-0.2\%$ ($\Delta {\alpha }_{\perp }=-0.3\%$) for the radial (transverse) parameters at redshift $z=2.0$. This corresponds to a shift of $-0.3\%$ (0.1%) for the isotropic (anisotropic) distance measurements. We provide an estimate for the shift of the BAO peak for Ly-$\alpha$ -quasar cross-correlation measurements assuming analytical and simulation-based scaling relations for the nonlinear quasar bias parameters resulting in a shift of $-0.2\%$ ($-0.1\%$) for the radial (transverse) dilation parameters, respectively. This analysis emphasizes the robustness of Ly-$\alpha$ forest BAO measurements to the theory modeling. We provide informative priors and an error budget for measuring the BAO feature—a key science driver of the currently observing Dark Energy Spectroscopic Instrument (DESI). Our work paves the way for full-shape cosmological analyses of Ly-$\alpha$ forest data from DESI and upcoming surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.

We analyze the computation of $n$-point correlation functions in de Sitter spacetime, including loop corrections, using the wavefunction of the universe approach. This method consists of two stages employing distinct Feynman rules. First, one must compute the wavefunction coefficients using interactions as vertices. Then, in the second stage, one computes correlation functions using wavefunction coefficients as vertices. For massless fields, loop corrections in the first stage are free of infrared (IR) divergences, which leads to the question of how this matches the well-known IR behavior of correlators obtained via other methods. By considering a scalar field with an arbitrary potential, we compute $n$-point correlation functions to first order in the potential but to all orders in loops. We find that, although loop integrals in the first stage are indeed IR convergent, the second procedure reintroduces the IR divergence. We discuss how this induces renormalization of the interaction potential such that the final result combining both steps exactly matches the form of $n$-point functions previously calculated with other methods.

Cosmological analyses of redshift space clustering data are primarily based on using luminous red” galaxies (LRGs) and blue” emission line galaxies (ELGs) to trace underlying dark matter. Using the large high-fidelity high-resolution MillenniumTNG (MTNG) and Astrid simulations, we study these galaxies with the effective field theory (EFT)-based field level forward model. We confirm that both red and blue galaxies can be accurately modeled with EFT at the field level and their parameters match those of the phenomenological halo-based models. Specifically, we consider the state of the art Halo Occupation Distribution (HOD) and High Mass Quenched (HMQ) models for the red and blue galaxies, respectively. Our results explicitly confirm the validity of the halo-based models on large scales beyond the two-point statistics. In addition, we validate the field-level HOD/HMQ-based priors for EFT full-shape analysis. We find that the local bias parameters of the ELGs are in tension with the predictions of the LRG-like HOD models and present a simple analytic argument explaining this phenomenology. We also confirm that ELGs exhibit weaker non-linear redshift-space distortions (fingers-of-God”), suggesting that a significant fraction of their data should be perturbative. We find that the response of EFT parameters to galaxy selection is sensitive to assumptions about baryonic feedback, suggesting that a detailed understanding of feedback processes is necessary for robust predictions of EFT parameters. Finally, using neural density estimation based on paired HOD-EFT parameter samples, we obtain optimal HOD models that reproduce the clustering of Astrid and MTNG galaxies.

We supplement the string field theory action with boundary terms to make its variational principle well-posed. Central to our considerations is the violation of the stress-energy tensor conservation in non-compact CFTs due to the boundary terms. This manifests as the failure of the cyclicity of the BRST operator, which encodes the target space integration by parts identities at the level of the worldsheet. Using this failure, we argue that the free closed string field theory action admits a well-posed variational principle upon including an additional boundary contribution. We explicitly work out the resulting action up to the massless level and show that it is related to the expansion of the low-energy effective string action endowed with the Gibbons-Hawking-York term on a flat background. We also discuss the structure of the boundary terms in the interacting theory.