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DOE OSTI2025

All-order splits and multi-soft limits for particle and string amplitudes

The most important aspects of scattering amplitudes have long been thought to be associated with their poles. But recently a very different sort of “split” factorizations for a wide range of particle and string tree amplitudes have been discovered away from poles. In this paper, we give a simple, conceptual origin for these splits arising from natural properties of the binary geometry of the curve integral formulation for scattering amplitudes for Tr(Φ 3 ) theory. The most natural way of “joining” smaller surfaces to build larger ones directly produces a choice of kinematics for which higher amplitudes factor into lower ones. This gives a generalization of splits to all orders in the topological expansion. These splits allow us to access and compute loop-integrated multi-soft limits for particle and string amplitudes, at all loop orders. This includes split factorizations and multisoft limits for pion and gluon amplitudes, that are related to Tr(Φ 3 ) theory by a simple kinematical shift.

Bosonic Strings↗

DOE OSTI2024

Treelike structure of symmetry topological field theories and multisector QFTs

The global symmetries of a D -dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( D + 1 )-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( D + 1 )-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large M averaging where the topological sectors of different large M replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2024

Physical Yukawa couplings in heterotic string compactifications

One of the challenges of heterotic compactification on a CalabiYau threefold is to determine the physical (27) 3 Yukawa couplings of the resulting four-dimensional $\mathcal{N}$ = 1 theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of the Calabi-Yau manifold. In various examples (the Fermat quintic, the intersection of two cubics in $\mathbb{P}$ 5 , and the TianYau manifold), we calculate the normalized Yukawa couplings for (2,1)-forms using the Weil-Petersson metric obtained from the Kodaira-Spencer map. In cases where $h^{1,1}$ = 1 , this is compared to a complementary calculation based on performing period integrals. A third expression for the normalized Yukawa couplings is obtained from a machine learned approximate Ricci-flat metric making use of explicit harmonic representatives. Finally, the excellent agreement between the different approaches opens the door to precision string phenomenology.

Butbaia, Giorgi↗

DOE OSTI2025

Precision string phenomenology

Calabi-Yau compactifications of the E 8 × E 8 heterotic string provide a promising route to recovering the four-dimensional particle physics described by the Standard Model. While the topology of the Calabi-Yau space determines the overall matter content in the low-energy effective field theory, further details of the compactification geometry are needed to calculate the normalized physical couplings and masses of elementary particles. In this work, we present numerical computations of physical Yukawa couplings in a number of heterotic models in the standard embedding and demonstrate the existence of natural hierarchies, a coveted feature in string model building. Published by the American Physical Society 2025

Berglund, Per (ORCID:0000000316754133)↗

DOE OSTI2024

Born-Oppenheimer potentials for $SU$(3) gauge theory

We develop parametrizations of eight of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation r of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure SU⁡(3) lattice gauge theory. The parametrizations have the correct limiting behavior at small r, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large r, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-r region between two potentials with the same Born-Oppenheimer quantum numbers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Cuts and contours

The traditional formulation of string amplitudes via worldsheet integrals provides a parametrization of the moduli space that fails to expose the complete singularity structure of the amplitudes. This problem is solved by the positive parametrization of string amplitudes given by surfaceology. In this work, we use this formalism to study a number of properties of string amplitudes at tree-level and one-loop. We introduce several global prescriptions for an integration contour for which the integrals are finite everywhere in kinematic space. At tree-level, this is done in two ways: one directly implements the Feynman iε to analytically continue from Euclidean to Lorentzian worldsheets; the other is a generalization of the closed Pochhammer contour to arbitrary number of points. At loop-level, we present a systematic way of extracting cuts directly from the worldsheet integrand. This provides a powerful set of unitarity constraints, which we use to test the consistency of different “stringy” UV regularizations of field theory amplitudes. In addition, we identify the massive threshold expansion of the integrand, which allows us to reduce the problem to a finite set of Feynman integrals in Schwinger parametrization and provide a straightforward contour prescription reminiscent of its field-theory version.

Bosonic Strings↗

DOE OSTI2025

Cosmological perturbations from a new approach to inflation

In a previous paper, we proposed a new approach to the beginning of inflation—a lingering universe [Melcher et al. Phys. Rev. D 110, 063517 (2024).]—that is a quasistatic phase prior to inflation. The Universe begins in a lingering state with a nearly vanishing Hubble parameter. This calls into question the absolute age of the Universe, as the Hubble time can be nearly infinite. It also provides promise for addressing the initial singularity of inflation and issues with quantum field theory in de Sitter spacetime. Such models arise in classical cosmologies with nonvanishing spatial curvature (inspired by PLANCK 2018 data) and independently by models that arise in string cosmology. Here, in this paper, we consider the importance of cosmological perturbations for the stability of the lingering phase and how this influences cosmological observations. Our goal is to establish observables in this new paradigm for the origin of inflation, which is in contrast to eternal inflation and cyclic cosmologies. We also address questions of stability and the transition to inflation.

cosmology↗

DOE OSTI2025

New state of matter between the hadronic phase and the quark-gluon plasma?

Lattice-quantum chromodynamics (QCD) simulations and theoretical arguments hint at the existence of an intermediate phase of strongly interacting matter between a confined hadron gas and a deconfined quark-gluon plasma (QGP). We qualitatively and semiquantitatively explore and differentiate the phase structures in the temperature window from the QCD pseudocritical temperature 𝑇 c ≃ 160 MeV to the pure gluonic deconfinement temperature 𝑇 d ≃ 285 MeV. We propose a three-regime picture using a hadron resonance gas description augmented with the exponential spectrum of strings, corresponding to highly excited mesons and glueballs, based on the analysis of a large number 𝑁 c of colors. We estimate the entropy density from our model to confirm that the lattice-QCD data are bracketed with three regimes, i.e., a hadron gas, a QGP, and a new phase for 𝑇 c ≲ 𝑇 ≲ 𝑇 d . In this new phase, which we name a spaghetti of quarks with glueballs (SQGBs), thermal degrees of freedom of quarks are liberated, yet gluons remain confined in glueballs. Since the Hagedorn temperature 𝑇 H ∼ 285 MeV is universal in the meson and the glueball sectors, in the infinite-𝑁 c limit, the phase diagram in the plane of the baryon chemical potential and the temperature is reduced to one with the confined and deconfined phases and quarkyonic matter at high density. At large but finite 𝑁 c , an SQGB window may open between these phases. We point out that the SQGB has interesting similarities with quarkyonic matter and that this matter in the large-𝑁 c limit is confined as measured by the interaction between heavy quarks, but behaves in other respects like a quasifree gas of quarks. As a result of the extrapolation to 𝑁 c = 3, we present a revised phase diagram with the SQGB phase bounded by thermal crossovers. Finally, we give a quantitative analysis of chiral-symmetry restoration in the SQGB phase.

Color confinement↗

DOE OSTI2025

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional SU⁡(𝑁) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) 𝑉 𝜆 of the SU⁡(𝑁) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {𝜆 ℓ } and monomer tensors on sites labeled by {𝜆 𝑠 }. These tensors naturally define a local site Hilbert space, ℋ$^𝑔_𝑠$, on which gauge transformations act. Gauss’s law introduces an additional index 𝛼 𝑠 =1,2,…,𝒟⁡(ℋ$^𝑔_𝑠$) that labels an orthonormal basis of the gauge-invariant subspace of ℋ$^𝑔_𝑠$. This monomer-dimer tensor-network (MDTN) basis, |{𝜆 𝑠 },{𝜆 ℓ },{𝛼 𝑠 }⟩, of the physical Hilbert space enables the construction of new qubit-regularized SU⁡(𝑁) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in 𝑑 =2 and 𝑑 =3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in 𝑑 =1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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 OSTI2025

Spatial String Tension and Its Effects on Screening Correlators in a Thermal QCD Plasma

We calculate the spatial Wilson line correlator for 2 +1 flavor QCD using highly improved staggered quark discretization for fermions and in quenched QCD for a wide range of temperatures, from the chiral crossover temperature 𝑇 pc ≃ 156 MeV or the deconfinement temperature ≃300 MeV, respectively, up to 2 GeV. Extracting the spatial string tension for different lattice cutoffs and by performing a continuum extrapolation of this observable, we show that the soft (magnetic) gluons interact nonperturbatively even at temperatures ≳1 GeV. We provide incriminating evidences to demonstrate that dimensionally reduced effective theories can describe these soft quark and gluon quasi-particles for both quenched and 2 +1 flavor QCD, at temperatures 𝑇 ≳ 5⁢𝑇 pc . We also show for the first time the imprints of the nonperturbative pseudopotential in the properties of mesonic screening masses for temperatures ranging from 0.8 to 164 GeV in the quark-gluon plasma.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Universal rapidity scaling of entanglement entropy inside hadrons from conformal invariance

When a hadron is probed at high energy, a nontrivial quantum entanglement entropy inside the hadron emerges due to the lack of complete information about the hadron wave function extracted from this measurement. In the high-energy limit, the hadron becomes a maximally entangled state, with a linear dependence of entanglement entropy on rapidity, as has been found in a recent analysis based on parton description. In this paper, we use an effective conformal field theoretic description of hadrons on the light cone to show that the linear dependence of the entanglement entropy on rapidity found in parton description is a general consequence of approximate conformal invariance and does not depend on the assumption of weak coupling. Our result also provides further evidence for a duality between the parton and string descriptions of hadrons. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Islands far outside the horizon

Information located in an entanglement island in semiclassical gravity can be nonperturbatively reconstructed from distant radiation, implying a radical breakdown of effective field theory. We show that this occurs well outside of the black hole stretched horizon. We compute the island associated to large-angular momentum Hawking modes of a four-dimensional Schwarzschild black hole. These modes typically fall back into the black hole but can be extracted to infinity by relativistic strings or, more abstractly, by asymptotic boundary operators constructed using the timelike tube theorem. Remarkably, we find that their island can protrude a distance of order $\sqrt{\ell_p{r}_{\textrm{hor}}}$ outside the horizon. This is parametrically larger than the Planck scale ℓ p and is comparable to the Bohr radius for supermassive black holes. Therefore, in principle, a distant observer can determine experimentally whether the black hole information paradox is resolved by complementarity, or by a firewall.

AdS-CFT correspondence↗

DOE OSTI2026

Projective Representations, Bogomolov Multiplier, and Their Applications in Physics

We present a pedagogical review of projective representations of finite groups and their physical applications in quantum many-body systems. Some of our physical results are new. We begin with a self-contained introduction to projective representations, highlighting the role of group cohomology, representation theory, and classification of irreducible projective representations. We then focus on a special subset of cohomology classes, known as the Bogomolov multiplier, which consists of cocycles that are symmetric on commuting pairs but remain nontrivial in group cohomology. Such cocycles have important physical implications: they characterize (1+1)D SPT phases that cannot be detected by string order parameters and give rise, upon gauging, to distinct gapped phases with completely broken non-invertible Rep(G) symmetry. We construct explicit lattice models for these phases and demonstrate how they are distinguished by the fusion rules of local order parameters. We show that a pair of completely broken Rep(G) SSB phases host nontrivial interface modes at their domain walls. As an example, we construct a lattice model where the ground state degeneracy on a ring increases from 32 without interfaces to 56 with interfaces.

Bogomolov multiplier↗

DOE OSTI2025

Attention to quantum complexity

The imminent era of error-corrected quantum computing demands robust methods to characterize quantum state complexity from limited, noisy measurements. We introduce the Quantum Attention Network (QuAN), a classical artificial intelligence (AI) framework leveraging attention mechanisms tailored for learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting permutation invariance. Combined with our parameter-efficient miniset self-attention block, this enables QuAN to access high-order moments of bit-string distributions and preferentially attend to less noisy snapshots. We test QuAN across three quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and toric code under coherent and incoherent noise. QuAN directly learns entanglement and state complexity growth from experimental computational basis measurements, including complexity growth in random circuits from noisy data. In regimes inaccessible to existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types, highlighting AI’s transformative potential for assisting quantum hardware.

Kim, Hyejin [Cornell Univ., Ithaca, NY (United Sta↗

DOE OSTI2025

Dark dimension and the grand unification of forces

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any grand unified theory (GUT) models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, 𝑀 GUT ≲ 10 16 GeV. Combined with the experimental bound on the proton lifetime, this predicts that the 𝑋 gauge boson mediating proton decay is a 5D solitonic string of Planckian tension stretched across a length scale 𝐿 ∼ (1–10 TeV) −1 ending on gauge branes of the same diameter ∼𝐿. This leads to a mass of 𝑀 𝑋 ∼ 10 15 –10 16 GeV. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1–10 TeV range. This suggests that the diameter/separation 𝐿 of the gauge branes correlates with both the weak scale ∼1/𝐿 near a TeV and the GUT scale ∼𝑀$^2_5$⁢𝐿 at 10 16 GeV.

branes↗

DOE OSTI2024

Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory

We construct a novel flux tube entanglement entropy (FTE 2 ), defined as the excess entanglement entropy relative to the vacuum of a region of color flux stretching between a heavy quark-anti-quark pair in pure gauge Yang-Mills theory. We show that FTE 2 can be expressed in terms of correlators of Polyakov loops, is manifestly gauge-invariant, and therefore free of the ambiguities in computations of the entanglement entropy in gauge theories related to the choice of the center algebra. Employing the replica trick, we compute FTE 2 for SU(2) Yang-Mills theory in (2+1)D and demonstrate that it is finite in the continuum limit. We explore the properties of FTE 2 for a half-slab geometry, which allows us to vary the width and location of the slab, and the extent to which the slab cross-cuts the color flux tube. Following the intuition provided by computations of FTE 2 in (1+1)D, and in a thin string model, we examine the extent to which our FTE 2 results can be interpreted as the sum of an internal color entropy and a vibrational entropy corresponding to the transverse excitations of the string.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗