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DOE OSTI2025

Cornering relative symmetry theories

The symmetry data of a 𝑑-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory. In top-down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated (𝑑+1)-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in 𝐷 =𝑑 + 𝑚 dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this 𝐷-dimensional bulk system. We present a bottom-up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

M-theory↗

DOE OSTI2026

Proliferation transitions from a topological phase in 2+1 dimensions

We consider phase transitions out of a general topological phase in 2+1 dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as “condensation.”) We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U⁡(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Lastly, we demonstrate our construction with many specific examples.

Anyons↗

DOE OSTI2025

Additivity, Haag duality, and non-invertible symmetries

The algebraic approach to quantum field theory focuses on the properties of local algebras, whereas the study of (possibly non-invertible) global symmetries emphasizes global aspects of the theory and spacetime. We study connections between these two perspectives by examining how either of two core algebraic properties — “additivity” or “Haag duality” — is violated in a 1+1D CFT or lattice model restricted to the symmetric sector of a general global symmetry. For the Verlinde symmetry of a bosonic diagonal RCFT, we find that additivity is violated whenever the symmetry algebra contains an invertible element, while Haag duality is violated whenever it contains a non-invertible element. We find similar phenomena for the Kramers-Wannier and Rep(D 8 ) non-invertible symmetries on spin chains.

Discrete Symmetries↗

NASA NTRS1983

Four-dimensional symmetry from a broad viewpoint. II Invariant distribution of quantized field oscillators and questions on infinities

The foundation of the quantum field theory is changed by introducing a new universal probability principle into field operators: one single inherent and invariant probability distribution P(/k/) is postulated for boson and fermion field oscillators. This can be accomplished only when one treats the four-dimensional symmetry from a broad viewpoint. Special relativity is too restrictive to allow such a universal probability principle. A radical length, R, appears in physics through the probability distribution P(/k/). The force between two point particles vanishes when their relative distance tends to zero. This appears to be a general property for all forces and resembles the property of asymptotic freedom. The usual infinities in vacuum fluctuations and in local interactions, however complicated they may be, are all removed from quantum field theories. In appendix A a simple finite and unitary theory of unified electroweak interactions is discussed without assuming Higgs scalar bosons.

Hsu, J. P.↗

DOE OSTI2025

Metric isometries, holography, and continuous symmetry operators

In the AdS/CFT correspondence, a topological symmetry operator of the boundary conformal field theory (CFT) is dual to a dynamical brane in the gravitational bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor 𝑋 of AdS × 𝑋. In the extra-dimensional geometry, these branes are associated with various metric singularities and do not arise from wrapped D-branes. Boosts relate configurations interpreted as topological symmetry operators and heavy defects in the CFT. From the perspective of the AdS factor, with gravity and bulk gauge fields, these are codimension-2 Gukov-Witten-like vortex configurations which are the gravity duals of 0-form symmetry operators. These effective branes come with an asymptotic tension and size which is also fully fixed by bulk dynamics. We use this higher-dimensional perspective to determine properties of the worldvolume theory for these branes. We also discuss how these considerations generalize to more general quantum field theories engineered via string theory which need not possess a semiclassical gravity dual.

anomalies↗

DOE OSTI2025

Quantum Anomalies in Condensed Matter

Quantum materials provide a fertile ground in which to test and realize unusual phenomena such as quantum anomalies predicted by quantum field theory. There are three important symmetries that are broken when classical field theory is moved into the quantum regime, the scale anomaly, the axial (chiral) anomaly, and the parity anomaly. Several potential device applications may be realized by the discovery of quantum anomalies in condensed matter, enabled by the new physics they embody, including ultra‐sensitive dark matter detectors, far infrared optical modulators, micro‐bolometric detectors, low‐dissipation ballistic transporters, terahertz‐based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions, and qubits topologically protected against decoherence. In this perspective article, the definition of these quantum anomalies is laid out, how little is known in the context of condensed matter, and how quantum anomalies are predicted to manifest as anomalous electronic, thermal, and magnetic behavior in experiments on topological quantum materials, including Weyl and Dirac semimetals. Furthermore, the importance that mechanical strain and defects will play in modifying signatures of quantum anomalies is discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2025

On the holographic dual of a symmetry operator at finite temperature

Topological symmetry operators of holographic large 𝑁 CFT 𝐷 ’s are dual to dynamical branes in the gravity dual AdS 𝐷+1 . We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFT 𝐷 and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of 0-form symmetry operators in the CFT 𝐷 are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS 3 , duality/triality defects in four-dimensional 𝒩 = 4 super Yang-Mills theory, and the dual of R-symmetry operators probing five-dimensional Bogomol’nyi–Prasad–Sommerfield black holes.

Anomalies↗

DOE OSTI2024

Robustness of quantum correlation in quantum energy teleportation

In this article, we explore a feedback-control protocol in different quantum field theories (QFTs) to study the quantum correlation in nonunitary evolution of quantum systems. Traditional studies on QFTs focus on quantum entanglement of pure states under the unitary evolution, however, we examine quantum correlation in mixed states using quantum energy teleportation (QET), which is an energy transfer protocol by utilizing ground state entanglement, and introduce quantum discord as a measure. QET involves a midcircuit measurement, which disrupts pure state entanglement. Despite this, our analysis demonstrates that quantum discord maintains the correlation throughout the QET process. We conducted numerical analyses with benchmark models including the Nambu-Jona-Lasinio (NJL) model, revealing that quantum discord consistently acts as an order parameter for phase transitions. The model is extended in a way that it has both the chiral chemical potential and the chemical potential, which are useful to study the phase structures mimicking the chiral imbalance between left- and right- quarks coupled to the chirality density operator. In all cases we studied, the quantum discord behaved as an order parameter of the phase transition. Published by the American Physical Society 2024

Ikeda, Kazuki (ORCID:0000000338212669)↗

DOE OSTI2025

Genesis: A Compiler Framework for Hamiltonian Simulation on Hybrid CV-DV Quantum Computers

We introduce Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems. Genesis is a two-level compilation system. At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer. At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level. Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CVDV gate set. Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, Z2−Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry. Our implementation is available at Genesis-CVDV-Compiler https://github.com/ruadapt/Genesis-CVDV-Compiler

Chen, Henry↗

DOE OSTI2026

IR side of bounds on theories with spontaneously broken Lorentz symmetry

In nature, some UV features of dynamics are reflected in IR quantities. In fully relativistic theories, this connection can be probed through the analyticity properties of scattering amplitudes, allowing one to understand which IR theories respect the UV assumptions of quantum field theory. The ensuing analyticity bounds can usually be rephrased as the absence of faster-than-light propagation for low-energy excitations. While it is interesting to understand these relations and their IR characterization for theories that have less idealized properties, it is also more difficult to derive analyticity bounds in these cases. For theories that spontaneously break Lorentz symmetry, recent progress was made by considering correlators of conserved currents and their analyticity properties. In this work, we focus on such theories and work to close the gap from the IR side, finding a natural way to express the known analyticity bounds purely in terms of low-energy kinematical quantities. Our analysis shows that the bounds require gapped excitations to have a slower speed than the gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to interpret the UV/IR connection in more complex theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Variational neural network approach to QFT in the field basis

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.

Klein-Gordon model↗

DOE OSTI2026

Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model

Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Supersymmetric lattice theories on curved space

We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete Kähler-Dirac equations. The quantization of the fermions proceeds by imposing conventional anticommutation relations while the bosons require a modification of the usual canonical commutator. On regular lattices we construct parity, time reversal and translation-by-one (shift) symmetries. We argue that the latter are generically noninvertible symmetries. We also show how to couple these degrees of freedom to background gauge fields which leads to a theory with enhanced supersymmetry.

Anomalies↗

NASA NTRS1986

Generation of fluctuations in cosmological models

The initial production of classical matter fluctuations in a scalar quantum field theory in curved spacetime is discussed. It is shown how quantum fluctuations generate classical matter inhomogeneities, and that the resulting spectrum is scale invariant. The relevant events that occur before the scale leaves the Hubble radius are studied.

Brandenberger, Robert H.↗

DOE OSTI2025

Elastic cross section is entanglement entropy

We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the cross section, which is the primary observable for high-energy particle scattering, by employing a careful formulation of wave packets for the incoming particles. For 2-to-2 elastic scattering with no initial entanglement and subdividing the system along particle labels, we show that both the Rényi and Tsallis entropies in the final states are directly proportional to the elastic cross section in units of the transverse size for the initial wave packets, which is then interpreted as the elastic scattering probability. The relations do not depend on the underlying dynamics of the quantum field theory and are valid to all orders in coupling strengths. Furthermore, computing quantum correlations between momentum and nonkinematic data leads to entanglement entropies expressed as various semi-inclusive elastic cross sections. Our result gives rise to a novel “area law” for entanglement entropy in a two-body system. Published by the American Physical Society 2025

Low, Ian (ORCID:0000000275709597)↗

DOE OSTI2025

Inferring three-nucleon couplings from multi-messenger neutron-star observations

Understanding the interactions between nucleons in dense matter is an important challenge in theoretical physics. Effective field theories have emerged as the dominant approach to address this problem at low energies, with many successful applications to the structure of nuclei and the properties of dense nucleonic matter. However, how far into the interior of neutron stars these interactions can describe dense matter is an open question. Here, we develop a framework that enables the inference of three-nucleon couplings in dense matter directly from astrophysical neutron star observations. We apply this formalism to the LIGO/Virgo gravitational-wave event GW170817 and the X-ray measurements from NASA’s Neutron Star Interior Composition Explorer and establish direct constraints for the couplings that govern three-nucleon interactions in chiral effective field theory. Furthermore, we demonstrate how next-generation observations of a population of neutron star mergers can offer stringent constraints on three-nucleon couplings, potentially at a level comparable to those from laboratory data. Our work directly connects the microscopic couplings in quantum field theories to macroscopic observations of neutron stars, providing a way to test the consistency between low-energy couplings inferred from terrestrial and astrophysical data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Collective coordinate fix in the path integral

Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multivalued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multivaluedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be nonperturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates. Published by the American Physical Society 2024

Bhattacharya, Arindam (ORCID:0000000244578926)↗

DOE OSTI2024

Reviving QFT in ( 2 + 1 )-dimensional de Sitter spacetime

We consider a conformally coupled scalar quantum field theory (QFT) on ( 2 + 1 )-dimensional static Einstein universe R × S 2 and write down the free theory Hilbert space. We explain that this theory is secretly a QFT in ( 2 + 1 )-dimensional de Sitter space because all the quantum observables experience “quantum revivals,” which naturally restricts the timelike R to the appropriate de Sitter time range. Our construction circumvents the causal obstruction to formulating QFT in de Sitter due to event horizons. There are not any in static Einstein. The “unitary gauge” description of the theory is realized by the zonal harmonics P ℓ ( n ^ · n ^ ′ ) . We verify that interactions with conformally invariant external sources are mediated only by these modes. Hence these modes comprise the complete basis of the “bulk” theory. When the theory is cut off in the UV, the basis dimension scales as the Bekenstein-Hawking formula. Published by the American Physical Society 2024

D’Amico, Guido (ORCID:0000000281831214)↗