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Results for “field theories in higher dimensions”

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DOE OSTI2025

Five-dimensional spinor helicity for all masses and spins

We develop a spinor helicity formalism for five-dimensional scattering amplitudes of any mass and spin configuration. While five-dimensional spinor helicity variables have been previously studied in the context of $\mathcal{N}$ = 2, 4 supersymmetric Yang-Mills scattering amplitudes with spin less than two [1], we propose an alternative viewpoint that stems from d-dimensional spinor helicity variables avoiding the decomposition of a massive momentum into the sum of two massless momenta. By enumerating all possible independent little group tensors, we systematically build the full space of five-dimensional three-point tree-level scattering amplitudes for any configuration of spins and masses. Furthermore, we provide a prescription for computing the high energy limit of scattering amplitudes written in our spinor helicity variables. We also expect that our formalism will be applicable to effective field theories with higher spin, in particular, the scattering of highly spinning black holes in five dimensions.

Field Theories in Higher Dimensions↗

DOE OSTI2025

Multi-Galileons in curved space

Using the probe brane construction of higher derivative effective field theories, extended to higher co-dimensions and curved spaces, we construct galileon and DBI theories on de Sitter space with N fields and an so (N) internal symmetry, non-linearly realizing the symmetries of a higher dimensional de Sitter space. In some cases, the theory admits a non-trivial vacuum that spontaneously breaks the so (N) symmetry, and around this vacuum the Goldstone modes have vanishing kinetic terms and become infinitely strongly coupled. This gives an example of a scalar effective field theory with two de Sitter vacua, one of which appears to have Boulware-Deser-like ghosts, and one of which does not.

Cosmological models↗

DOE OSTI2025

Scalar-scaffolded gluons and the combinatorial origins of Yang-Mills theory

We present a new formulation for Yang-Mills scattering amplitudes in any number of dimensions and at any loop order, based on the same combinatorial and binary-geometric ideas in kinematic space recently used to give an all-order description of Tr Φ 3 theory. We propose that in a precise sense the amplitudes for a suitably “stringy” form of these two theories are identical, up to a simple shift of kinematic variables. This connection is made possible by describing the amplitudes for n gluons via a “scalar scaffolding”, arising from the scattering of 2n colored scalars coming in n distinct pairs of flavors fusing to produce the gluons. Fundamental properties of the “u-variables”, describing the “binary geometry” for surfaces appearing in the topological expansion, magically guarantee that the kinematically shifted Tr Φ 3 amplitudes satisfy the physical properties needed to be interpreted as scaffolded gluons. These include multilinearity, gauge invariance, and factorization on tree- and loop-level gluon cuts. Our “stringy” scaffolded gluon amplitudes coincide with amplitudes in the bosonic string for extra-dimensional gluon polarizations at tree-level, but differ (and are simpler) at loop-level. We provide many checks on our proposal, including matching non-trivial leading singularities through two loops. The simple counting problem underlying the u variables autonomously “knows” about everything needed to convert colored scalar to gluon amplitudes, exposing a striking “discovery” of Yang-Mills amplitudes from elementary combinatorial ideas in kinematic space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Quantum area fluctuations from gravitational phase space

We study the gravitational phase space associated to a stretched horizon within a finite-sized causal diamond in (d + 2)-dimensional spacetimes. By imposing the Raychaudhuri equation, we obtain its constrained symplectic form using the covariant phase space formalism and derive the relevant quantum commutators by inverting the symplectic form and quantizing. Finally, we compute the area fluctuations of the causal diamond by taking a Carrollian limit of the stretched horizon in pure Minkowski spacetime, and derive the relationship $\left\langle {\left(\Delta A\right)}^2\right\rangle \ge \frac{2\pi G}{d}\left\langle A\right\rangle$, showing that the variance of the area fluctuations is proportional to the area itself.

classical theories of gravity↗

DOE OSTI2025

Field redefinitions can be nonlocal

We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions can be nonlocal, symmetry breaking, or in certain cases have explicit dependence on spacetime. We address field redefinitions that can be resummed into the propagator, which demonstrates how to perform perturbative calculations away from the minimum in field space. Field redefinitions are used to derive higher-order Schwinger-Dyson equations, which imply multiparticle soft theorems. Non-standard field redefinitions are showcased using both relativistic and nonrelativistic examples.

effective field theories↗

DOE OSTI2024

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗

DOE OSTI2025

String membrane nets from higher-form gauging: An alternate route to 𝑝-string condensation

We present a new perspective on the $p$-string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in 3+1D that is generated by Abelian anyons in isotropic stacks of 2+1D topological orders naturally results in a 3+1D $p$-string condensed phase, providing a controlled non-perturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and one-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: in field theory, we derive the foliated field theory description of the $\mathbb{Z}_N$ X-Cube model by gauging a higher-form symmetry in stacks of 2+1D $\mathbb{Z}_N$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$-graded string-net models leads to string-membrane-nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d \geq 2$ and provides a step towards building an algebraic theory of $p$-string condensation.

Anyons↗

DOE OSTI2025

Energy-enhanced dimension eight SMEFT effects in VBF Higgs production

We study Higgs boson production via vector boson fusion at the LHC, focusing on the process pp → H + jj and capturing the leading energy-enhanced contributions within the Standard Model Effective Field Theory (SMEFT) up to order 1/Λ$^{4}$. Employing energy-scaling arguments, we predict the magnitude of each higher-dimensional operator’s contribution. Utilizing the geometric formulation of SMEFT, our analysis incorporates dimension-eight operators not previously considered. We find that the kinematics of vector boson fusion — characterized by two highly forward jets — tend to suppress contributions from higher-dimensional operators, requiring a lower scale Λ for SMEFT effects to become observable. This suggests that the SMEFT remains valid for lower Λ than expected. Combined with the fact that LEP constrains the dimension-six operators with the most considerable impact on vector boson fusion, a regime exists where dimension-eight operators can have significant effects. In many cases, these dimension-eight operators also influence associated production processes like pp → HV(jj), though differences in analysis cuts and kinematics mean this is not always the case. Our findings provide insights that could refine the search for SMEFT signals in collider experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

New avenues for |∆ B | = 2 processes beyond neutron-antineutron oscillations

We explore baryon-number-violating (|∆ B | = 2) processes beyond the well-known neutron-antineutron ($n - \bar{n}$) oscillations, focusing on the $Λ - \bar{Λ}$ system. The presence of a strange quark in the Λ baryon introduces a new set of six-quark operators roughly of the form (uds) 2 , which are different from the (udd) 2 operators responsible for oscillations. Using the Standard Model Effective Field Theory (SMEFT), we classify all dimension-9 operators that cause |∆ B | = 2 transitions and study their UV completions mediated by exotic scalar fields with trilinear interactions. We demonstrate that in these models, oscillations can occur at tree level, with $n - \bar{n}$ mixing potentially appearing at higher loop levels. We employ a chiral effective theory to constrain the effective mass mixing δm Λ , deriving bounds from current experimental limits on $n - \bar{n}$ oscillations and dinucleon decays such as pp → K + K + . These bounds indicate that $Λ - \bar{Λ}$ oscillations probe a complementary parameter space, sensitive to baryon-number violation at scales up to 10 2 − 10 3 TeV. We show that the existing indirect bounds make it challenging to provide a competitive bound on δm Λ at BESIII.

Baryon/Lepton Number Violation↗

DOE OSTI2025

Universality of Rényi Entropy in Conformal Field Theory

We use the thermal effective theory to prove that, for the vacuum state in any conformal field theory in 𝑑 dimensions, the 𝑛th Rényi entropy 𝑆$^{(𝑛)}_{𝐴}$ behaves as 𝑆$^{(𝑛)}_{𝐴}$ = [𝑓⁡/(2⁢𝜋⁢𝑛) 𝑑−1 ]⁢[Area⁡(∂𝐴)/(𝑑−2)⁢𝜀 𝑑−2 ]⁢(1+𝑂⁡(𝑛)) in the 𝑛 → 0 limit when the boundary of the entanglement domain 𝐴 is spherical with the UV cutoff 𝜀. The theory dependence is encapsulated in the cosmological constant 𝑓 in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain 𝐴. In two dimensions, we can use the hot spot idea, which describes the effective action in the high-temperature limit when the temperature is position-dependent, to derive more powerful formulas valid for arbitrary positive 𝑛. We discuss the difference between two and higher dimensions and clarify the applicability of the hot spot idea. We also use the thermal effective theory to derive an analog of the Cardy formula for boundary operators in higher dimensions.

Conformal field theory↗

DOE OSTI2026

Constraints on long-range forces in de Sitter space

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

AdS-CFT Correspondence↗

DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗

DOE OSTI2025

The gravitational path integral from an observer’s point of view

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with ${G}_{N}^{-1}$. Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

2D gravity↗

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 OSTI2024

Gauging staggered fermion shift symmetries

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an S U ( 4 ) flavor symmetry which plays a crucial role in showing that staggered fermions lead to a theory of four degenerate Dirac fermions in the continuum limit. They are associated with the appearance of certain Z 2 valued global parameters. We propose a strategy to try to partially gauge these translation symmetries by allowing these parameters to vary locally in the lattice. To maintain invariance of the action requires the addition of Z 2 valued higher form lattice gauge fields. An analogous procedure can be carried out for reduced staggered fermions where the shifts correspond to a discrete subgroup of an S O ( 4 ) flavor symmetry. Published by the American Physical Society 2024

Catterall, Simon (ORCID:0000000327352682)↗

DOE OSTI2025

Revisiting the connection of baryon number, lepton number, and operator dimension

The effects of heavy new particles beyond the Standard Model can be conveniently captured through higher-dimensional effective operators. As noted long ago by Weinberg, the amount of baryon and lepton number an operator can carry is intricately connected to its mass dimension. We derive an improved inequality for this connection and compare it to explicit operator constructions up to mass dimension 25. For the effective field theory of Standard Model plus right-handed neutrinos, our relationship is even an equality up to high mass dimension.

Baryon number violation↗

DOE OSTI2026

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED 2 ), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Generalized Hall conductivities in local commuting projector models: Generalized symmetries and protected surface modes

Hall conductivities are important characterizations of phases of matter. It is known that nonzero Hall conductivities are difficult to realize in local commuting projector lattice models due to no-go theorems in (2+1)⁢D. In this work we construct local commuting projector models in (2+1)⁢D and (3+1)⁢D with nonzero generalized Hall conductivities for ordinary and higher-form continuous symmetries on tensor product Hilbert space of finite local dimension. The model is given by a standard ℤ 𝑁 toric code, but the symmetries do not admit expression in terms of on-site charge operators. The symmetry do not have local charges or currents on the lattice in the absence of boundaries, but there is still a notion of Hall conductivities that coincide with the continuum field theories. We construct protected gapless boundaries of the lattice models using modified Villain formalism. The generalized Hall conductivities are computed by surface currents as well as bulk flux insertion and many-body Chern number.

Anomalies↗