Field Theory Research Articles

Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory

In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian. Our answer leads in particular to a well-defined composition law in a category of Lagrangian correspondences respecting given polarizations of the Hilbert spaces involved. As an application, we construct a functorial field theory on geometric spin manifolds with values in this category of Lagrangian correspondences, which can be viewed as a formal Wick rotation of the theory associated to a free fermionic particle in a curved spacetime.

Quantum critical phase of FeO spans conditions of Earth’s lower mantle

Seismic and mineralogical studies have suggested regions at Earth’s core-mantle boundary may be highly enriched in FeO, reported to exhibit metallic behavior at extreme pressure-temperature (P–T) conditions. However, underlying electronic processes in FeO remain poorly understood. Here we explore the electronic structure of B1-FeO at extreme conditions with large-scale theoretical modeling using state-of-the-art embedded dynamical mean field theory (eDMFT). Fine sampling of the phase diagram reveals that, instead of sharp metallization, compression of FeO at high temperatures induces a gradual orbitally selective insulator-metal transition. Specifically, at P–T conditions of the lower mantle, FeO exists in an intermediate quantum critical state, characteristic of strongly correlated electronic matter. Transport in this regime, distinct from insulating or metallic behavior, is marked by incoherent diffusion of electrons in the conducting t2g orbital and a band gap in the eg orbital, resulting in moderate electrical conductivity (~105 S/m) with modest P–T dependence as observed in experiments. Enrichment of solid FeO can thus provide a unifying explanation for independent observations of low seismic velocities and elevated electrical conductivities in heterogeneities at Earth’s mantle base.

FR,□R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R,\\square R\\right) $$\\end{document}-gravity and equivalency with the modified GUP Scalar field models

Inspired by the generalization of scalar field gravitational models with a minimum length we study the equivalent theory in modified theories of gravity. The quadratic generalized uncertainty principle (GUP) gives rise to a deformed Heisenberg algebra in the application, resulting in the emergence of additional degrees of freedom described by higher-order derivatives. The new degrees of freedom can be attributed to the introduction of a new scalar field, transforming the resulting theory into a two-scalar field theory. Thus, in order to describe all the degrees of freedom we investigate special forms of the sixth-order modify fR,□R-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R,\\square R\\right) -$$\\end{document}theory of gravity, where the gravitational Lagrangian has similar properties to that of the GUP scalar field theory. Finally, the cosmological applications are discussed, and we show that the de Sitter universe can be recovered without introducing a cosmological constant.

Smooth generalized symmetries of quantum field theories

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of ∞-categories. According to a geometric version of the cobordism hypothesis, such QFTs collectively assemble themselves into objects in an ∞-topos of smooth spaces. We show how this allows one to define and study generalized global symmetries of such QFTs. The symmetries are themselves smooth, so the ‘higher-form’ symmetry groups can be endowed with, e.g., a Lie group structure.Among the more surprising general implications for physics are, firstly, that QFTs in spacetime dimension d, considered collectively, can have d-form symmetries, going beyond the known (d−1)-form symmetries of individual QFTs and, secondly, that a global symmetry of a QFT can be anomalous even before we try to gauge it, due to a failure to respect either smoothness (in that a symmetry of an individual QFT does not smoothly extend to QFTs collectively) or locality (in that a symmetry of an unextended QFT does not extend to an extended one).Smoothness anomalies are shown to occur even in 2-state systems in quantum mechanics (here formulated axiomatically by equipping d=1 spacetimes with a metric, an orientation, and perhaps some unitarity structure). Locality anomalies are shown to occur even for invertible QFTs defined on d=1 spacetimes equipped with an orientation and a smooth map to a target manifold. These correspond in physics to topological actions for a particle moving on the target and the relation to an earlier classification of such actions using invariant differential cohomology is elucidated.

Uncertainty Analysis of Post-Failure Behavior in Landslides Based on SPH Method and Generalized Geotechnical Random Field Theory

In slope stability analysis, the inherent heterogeneity and spatial variability of soil significantly influence the aftermath of landslides, including critical aspects like runout distance, influence distance, and volume. This research integrates Smoothed Particle Hydrodynamics (SPH) with random field theory to precisely model the large deformation events in slopes with anisotropic shear parameters, while leveraging Graphics Processing Unit (GPU) parallel computing to expedite the generation of random field samples and SPH simulations. This approach meticulously examines how spatial heterogeneity of soil affects slope instability, simulating soil parameters across varied geological settings. It considers the fluctuation scale of anisotropy, the cross-correlation of cohesion and the angle of internal friction, along with their coefficient of variation (CV), to elucidate their impact on landslide magnitude and severity. This study furnishes a robust tool for a holistic assessment of slope impacts and landslide volumes. Additionally, by delineating the computational efficiency disparities between GPUs and Central processing units (CPUs), it underscores the pronounced efficiency benefits of GPU computing. The insights garnered offer fresh perspectives and methodologies in slope stability analysis and disaster risk evaluation, contributing to the finer prediction and management of this prevalent and grave geological hazard.

CP Conservation in the Strong Interactions

We discuss matters related to the point that topological quantization in the strong interaction is a consequence of an infinite spacetime volume. Because of the ensuing order of limits, i.e., infinite volume prior to summing over topological sectors, CP is conserved. Here, we show that this reasoning is consistent with the construction of the path integral from steepest-descent contours. We reply to some objections that aim to support the case for CP violation in strong interactions that are based on the role of the CP-odd theta-parameter in three-form effective theories, the correct sampling of all configurations in the dilute instanton gas approximation and the volume dependence of the partition function. We also show that the chiral effective field theory derived from taking the volume to infinity first is in no contradiction with analyses based on partially conserved axial currents.

Nonperturbative Second Law of Black Hole Mechanics in Effective Field Theory.

We describe a method for defining dynamical black hole entropy in gravitational effective field theories. The entropy is constructed order by order in derivatives. For any fixed number of derivatives, the entropy satisfies a nonperturbative second law of black hole mechanics if the black hole remains within the regime of validity of effective field theories. In equilibrium the entropy reduces to the Wald entropy. It reduces to the entropy defined by Hollands etal. in theories of vacuum gravity with up to ten derivatives.

Zeroth and second laws of black hole mechanics in Einstein-Maxwell-scalar effective field theory

There has been recent progress in extending the zeroth and second laws of black hole mechanics to gravitational effective field theories (EFTs). We generalize these results to a much larger class of EFTs describing gravity coupled to electromagnetism and a real scalar field. We also show that the zeroth law holds for the EFT of gravity coupled to electromagnetism and a charged scalar field. Published by the American Physical Society 2024

The quantum theory of gravitation, effective field theories, and strings: yesterday and today

The quantum theory of gravitation, effective field theories, and strings: yesterday and today

An Uneasy Peace: How STEM Progressive, Traditionalist, and Bridging Faculty Understand Campus Conflicts over Diversity, Anti-Racism, and Free Expression

AbstractIn recent years an uneasy peace has descended in U.S. academe between those who feel research universities have done too little to advance the representation of minority groups and women and those who feel that the administrative policies developed to improve representation can and sometimes do come into conflict with core intellectual commitments of universities. Using quantitative and qualitative evidence from interviews with 47 natural sciences, engineering, and mathematics faculty members at a U.S. research university, the paper examines the background characteristics of three sets of protagonists - academic progressives, academic traditionalists, and those whose views bridge the divide - and the way respondents discussed and justified their viewpoints. The paper draws on the theory of strategic action fields to illuminate the structure and dynamics of the conflict and suggests modifications to the theory that would improve its explanatory power for this case.

Surface tension of aqueous electrolyte solutions. A thermomechanical approach.

We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous fluid. To obtain the surface tension, we calculate both the normal and tangential pressures using the components of the stress tensor, recently derived by us [Y. A. Budkov and P. E. Brandyshev, J. Chem. Phys. 159, 174103 (2023)] within the framework of Wang's variational field theory. Using this approach, we derive an analytical expression for the surface tension in the linear approximation. At low ionic concentrations, this expression represents the classical Onsager-Samaras limiting law. By utilizing only one fitting parameter, which is related to the affinity of anions to the dielectric boundary, we successfully approximated experimental data on the surface tension of several aqueous electrolyte solutions. This approximation applies to both the solution-air and solution-dodecane interfaces, covering a wide range of electrolyte concentrations.

Impact of shell model interactions on nuclear responses to WIMP elastic scattering

Nuclear recoil from scattering with weakly interacting massive particles (WIMPs) is a signature searched for in direct detection of dark matter. The underlying WIMP-nucleon interactions could be spin and/or orbital angular momentum (in)dependent. Evaluation of nuclear recoil rates through these interactions requires accounting for nuclear structure, e.g., through shell model calculations. We evaluate nuclear response functions induced by these interactions for F19, Na23, Si28,29,30, Ar40, Ge70,72,73,74,76, I127, and Xe128,129,130,131,132,134,136 nuclei that are relevant to current direct detection experiments, and estimate their sensitivity to shell model interactions. Shell model calculations are performed with the NuShellX solver. Nuclear response functions from nonrelativistic effective field theory are evaluated and integrated over transferred momentum for quantitative comparisons. We show that although the standard spin-independent response is barely sensitive to the structure of the nuclei, large variations with the shell model interaction are often observed for the other channels. Significant uncertainties may arise from the nuclear components of WIMP-nucleus scattering amplitudes due to nuclear structure theory and modeling. These uncertainties should be accounted for in analyses of direct detection experiments. Published by the American Physical Society 2024

The framed and contested meanings of sport mega-event ‘legacies’: A case study of the Birmingham 2022 Commonwealth Games

This article examines the ways in which envisioned sport mega-event legacies are publicly framed, communicated and contested. By employing Bourdieusian field theory, the Birmingham 2022 Commonwealth Games (CWG) as a case, and drawing upon documentary and media analysis, this article questions how CWG 2022 legacies were framed in a pre-event context. The article makes two key arguments. First, dominant actors within the mega-event field framed a considerable part of their pre-event legacies in terms of intangible inclusivity legacies relating to the host city's local communities, workforce and volunteering practices. Second, alongside these framed legacies, counterclaims emerged from actors on a civil society level, illustrative of a wider scepticism toward mega-events’ effects in the present day. Whilst limited scholarship has examined CWG 2022 to date, this paper also advances scholarship on sport mega-events’ socio-political legacies whilst it, theoretically, unpacks Bourdieu's tools of ‘field’ and ‘doxa’ in a new context.

A confined rod: mean field theory for hard rod-like particles

ABSTRACT In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbours. By minimising the free energy in the model and performing molecular dynamics, where, in both cases, the shape of the cell is a free parameter, we obtain the equilibrium orientational order parameter, free energy and pressure of the system. Our model enables the calculation of anisotropic stresses exerted on the walls of the cell due to shape change of the rod in photoisomerisation. These results are a key step towards understanding molecular shape change effects in photomechanical systems under illumination.

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

We generalize the Hamiltonian picture of general relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a quantum field theory in curved spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important mathematical feature of this work is the use of Minlos’s theorem to characterize Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrödinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar’s complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

Interactions of the pseudoscalar meson octet and the baryon decuplet in the continuum and a finite volume

This study focuses on the interaction of the pseudoscalar meson octet and the baryon decuplet. In the continuum, it is observed that several JP=32-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{P}=\\frac{3}{2}^-$$\\end{document} baryon resonances can be produced by the Weinberg-Tomozawa interaction in unitarized chiral perturbation theory, including the N(1875), Σ(1670)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1670)$$\\end{document}, Σ(1910)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1910)$$\\end{document}, Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} and Ω(2012)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (2012)$$\\end{document}. Among them, the Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} and Σ(1670)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1670)$$\\end{document} may exhibit a potential two-pole structures. The unitarized chiral perturbation approach is then applied as the underlying theory to predict the energy levels of these systems in a finite volume. These energy levels are well described by the K-matrix parameterization constrained by flavor SU(3) symmetry. With the parameters from the best fits, the poles extracted from the K-matrix parameterization closely correspond to those derived from the underlying chiral effective field theory, as long as they are close to physical region and not significantly higher than the lowest relevant threshold.

Denoising and Extension of Response Functions in the Time Domain.

Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

Symmetry fractionalized (irrationalized) fusion rules and two domain-wall Verlinde formulae

We investigate the composite systems consisting of topological orders separated by gapped domain walls. We derive a pair of domain-wall Verlinde formulae, that elucidate the connection between the braiding of interdomain excitations labeled by pairs of anyons in different domains and quasiparticles in the gapped domain wall with their respective fusion rules. Through explicit non-Abelian examples, we showcase the calculation of such braiding and fusion, revealing that the fusion rules for interdomain excitations are generally fractional or irrational. By investigating the correspondence between composite systems and anyon condensation, we unveil the reason for designating these fusion rules as symmetry fractionalized (irrationalized) fusion rules. Our findings hold promise for applications across various fields, such as topological quantum computation, topological field theory, conformal field theory, and parton physics.

Cosmological constraints on early dark energy from the full shape analysis of eBOSS DR16

ABSTRACT We evaluate the effectiveness of early dark energy (EDE) in addressing the Hubble tension using the luminous red galaxy (LRG), quasar (QSO), and emission line galaxy (ELG) samples from the completed eBOSS survey. We perform cosmological parameter measurements based on full shape analysis of the power spectrum employing the effective field theory of large-scale structure (EFTofLSS). EDE is known to strongly suffer from volume projection effects, complicating cosmological constraints’ interpretation. To quantify the volume projection effects within an EDE full shape analysis, we explore the impact of different prior choices on the nuisance parameters of EFTofLSS through an extensive mock study. We compare classical Gaussian priors to the non-informative Jeffreys prior, known to mitigate volume projection effects in ΛCDM. Our full shape analysis combines eBOSS and BOSS data with Planck, external Baryon Acoustic Oscillation (BAO), PantheonPlus, and SH0ES supernova data. EDE reduces the tension from 5.2σ to 3σ compared to ΛCDM, yielding $H_0=71.73_{-0.86}^{+0.82}$ km s−1 Mpc−1 with $f_\mathrm{EDE} = 0.1179_{-0.022}^{+0.025}$ (Gaussian priors) and $H_0=72.03_{-0.87}^{+0.82}$ km s−1 Mpc−1 with $f_\mathrm{EDE} = 0.1399_{-0.022}^{+0.023}$ (Jeffreys prior). Although the Hubble tension is mitigated compared to ΛCDM, the inclusion of eBOSS data amplifies the tension within EDE from 2σ to 3σ, in contrast to the full shape analysis of BOSS data with Planck, external BAO, PantheonPlus, and SH0ES. This highlights the significance of incorporating additional large-scale structure data in discussions concerning models aiming to resolve the Hubble tension.

Holographic Weyl anomalies for 4d defects in 6d SCFTs

In this note, we study 1/4- and 1/2-BPS co-dimension two superconformal defects in the 6d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (2, 0) AN−1 SCFT at large N using their holographic descriptions as solutions of 11d supergravity. In this regime, we are able to compute the defect contribution to the sphere entanglement entropy and the change in the stress-energy tensor one-point function due to the presence of the defect using holography. From these quantities, we are then able to unambiguously compute the values for two of the twenty-nine total Weyl anomaly coefficients that characterize 4d conformal defects in six and higher dimensions. We are able to demonstrate the consistency of the supergravity description of the defect theories with the average null energy condition on the field theory side. For each class of defects that we consider, we also show that the A-type Weyl anomaly coefficient is non-negative. Lastly, we uncover and resolve a discrepancy between the on-shell action of the 7d 1/4-BPS domain wall solutions and that of their 11d uplift.