We study Higher-Spin Gravity in 4-dimensional (Anti-)de Sitter space, at leading order in the interactions (cubic vertices), in the AdS lightcone formalism developed by Metsaev. Using the vertices’ chiral structure, we extend the formalism into a broader class of lightcone frames, which allows for lightcones of bulk points. This enables us to write the lightcone theory in de Sitter space, where only these more general frames are available. It also allows us to formulate and verify (for the first time!) some causal properties of massless higher-spin interactions, involving lightcone foliations that share a lightray. These causal properties serve to both motivate and enable the computation of “static-patch scattering amplitudes” — the evolution of fields between the two horizons of the maximal observable region in de Sitter space. We present a computation scheme for such “amplitudes” in coordinate space, and in momentum space with spinor-helicity variables.

Japan

Jin Kozaki

Julian Lang

Yasha Neiman

Causality of higher-spin interactions on the (A)dS lightcone, with application to the static patch

The Standard Model prediction of the muon $$g-2$$ increasingly depends on lattice QCD computations of the hadronic vacuum polarization (HVP), where the isospin-breaking (IB) effects remain a significant source of uncertainty. To complement the lattice QCD evaluations, the data-driven approach to HVP has been used to assess some of the electromagnetic IB effects, in particular from the channels with a photon in the final state, e.g., $$e^+e^-\rightarrow \pi ^0 \gamma $$ . Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $$\pi ^+ \pi ^-$$ , $$\pi ^+ \pi ^- \pi ^0$$ , etc. We identify these leading corrections by performing a field-theoretic calculation in a vector-meson dominance model, thereby reconciling the timelike and spacelike approaches to electromagnetic effects. Although these virtual corrections are more difficult to extract in a systematic manner, addressing them is essential for the data-driven method to consistently complement the lattice QCD program.

Germany

France

Volodymyr Biloshytskyi

Dominik Erb

Switzerland

Harvey Meyer

Julian Parrino

Vladimir Pascalutsa

Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $$(g-2)_\mu $$

We develop a systematic approach to the computation of gauge invariant quartic interactions between reducible massive and massless higher spin fields. Extending the BRST formulation of existing cubic results, we obtain a single constraint for each off-shell quartic vertex that ensures both the gauge invariance of the Lagrangian and formal closure of the gauge algebra at quartic order. A solution to these equations is presented. The general equation is then reduced to an on-shell version to reduce complexity. We find example solutions for the off-shell and on-shell quartic vertices in low spin examples relevant to the problem of black hole scattering.

Mirian Tsulaia

BRST methods for constructing quartic actions for spinning black holes

Wilson loops are essential objects in QCD and have been pivotal in scale setting and demonstrating confinement. Various generalizations are crucial for computations needed in effective field theories. In lattice gauge theory, Wilson loop calculations face challenges, including excited-state contamination at short times and the signal-to-noise ratio issue at longer times. To address these problems, we develop a new method by using neural networks to parametrize interpolators for the static quark-antiquark pair. We construct gauge-equivariant layers for the network and train it to find the ground state of the system. The trained network itself is then treated as our new observable for the inference. Our results demonstrate a significant improvement in the signal compared to traditional Wilson loops, performing as well as Coulomb-gauge Wilson-line correlators while maintaining gauge invariance. Additionally, we present an example where the optimized ground state is used to measure the static force directly, as well as another example combining this method with the multilevel algorithm. Finally, we extend the formalism to find excited-state interpolators for static quark-antiquark systems. To our knowledge, this work is the first study of neural networks with a physically motivated loss function for Wilson loops.

United States

Verena Bellscheidt

Nora Brambilla

Andreas S. Kronfeld

Julian Mayer-Steudte

Wilson loops with neural networks

We provide an extended lattice study of the SU(2) gauge theory coupled to one Dirac fermion flavor (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math>) transforming in the adjoint representation as the continuum limit is approached. This investigation is supplemented by results obtained for the SU(2) gauge theory with two Dirac fermion flavors (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math>) transforming in the adjoint representation, for which we perform numerical investigations at three values of the lattice spacing. The purpose of our study is to advance the characterization of the infrared properties of both theories, which previous investigations have concluded to be in the conformal window. For both, we determine the mass spectrum and the anomalous dimension of the fermion condensate using finite-size hyperscaling of the spectrum, mode number analysis of the Dirac operator (for which we improve on our previous proposal) and the ratio of masses of the lightest spin-2 particle over the lightest scalar. All methods provide a consistent picture, with the anomalous dimension of the condensate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub></math> decreasing significantly as one approaches the continuum limit for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>1</mn></math> theory towards a value consistent with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.170</mn><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo></math>, while for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi mathvariant="normal">f</mi></msub><mo>=</mo><mn>2</mn></math> the anomalous dimension converges more rapidly with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math> to a value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>γ</mi><mo>*</mo></msub><mo>=</mo><mn>0.291</mn><mo stretchy="false">(</mo><mn>9</mn><mo stretchy="false">)</mo></math>. A chiral perturbation theory analysis shows that the infrared behavior of both theories is incompatible with the breaking of chiral symmetry.

Cyprus

Andreas Athenodorou

United Kingdom

Ed Bennett

Georg Bergner

Spain

Denmark

Pietro Butti

Julian Lenz

Biagio Lucini

SU(2) gauge theory with one and two adjoint fermions toward the continuum limit

The long-distance contribution of QED corrections to the hadronic vacuum polarization is particularly challenging to compute in lattice <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>QCD</mi><mo>+</mo><mi>QED</mi></mrow></math>. Currently, it is one of the limiting factors toward matching the precision of the recent result by the Fermilab E989 experiment for the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>. In this work, we present a method for obtaining high-precision results for this contribution by reconstructing exclusive finite-volume state contributions. We find relations between the pion-photon contributions of individual diagrams and demonstrate the reconstruction method with lattice <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>QCD</mi><mo>+</mo><mi>QED</mi></mrow></math> data at a single lattice spacing of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>a</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>≈</mo><mn>1.73</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>≈</mo><mn>275</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

C. Lehner

J. Parrino

A. Völklein

Long-distance reconstruction of QED corrections to the hadronic vacuum polarization for the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

The period geometry of Calabi-Yau $\textit{n}$-folds — characterised by their variations of Hodge structure governed by Griffiths transversality, a graded Frobenius algebra, an integral monodromy and an intriguing arithmetic structure — is analysed for applications in string compactifications and to Feynman integrals. In particular, we consider type IIB flux compactifications on Calabi-Yau three-folds and elliptically fibred four-folds. After constructing suitable three-parameter three-folds, we examine the relation between symmetries of their moduli spaces and flux configurations. Although the fixed point loci of these symmetries are projective special Kähler, we show that a simultaneous stabilisation of multiple moduli on the intersection of these loci need not be guaranteed without the existence of symmetries between them. We furthermore consider F-theory vacua along conifolds and use mirror symmetry to perform a complete analysis of the two-parameter moduli space of an elliptic Calabi-Yau four-fold fibred over ℙ . We use the relation between Calabi-Yau period geometries in various dimensions and, in particular, the fact that the antisymmetric products of one-parameter Calabi-Yau three-fold operators yield four-fold operators to establish pairs of flux vacua on the moduli spaces of the three- and four-fold compactifications. We give a splitting of the period matrix into a semisimple and nilpotent part by utilising the Frobenius structure. This helps bringing $\textit{ϵ}$-dimensional regulated integration by parts relations between Feynman integrals into $\textit{ϵ}$-factorised form and solve them by iterated integrals of the periods.

Janis Dücker

Albrecht Klemm

Julian Piribauer

Calabi-Yau period geometry and restricted moduli in Type II compactifications

In order to reach a precision of 0$\textit{.}$2% on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, ($\textit{g}$ – 2) , such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($\textit{α}$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a (−0.89 ± 0.18)% correction to the leading-order HVP contribution to ($\textit{g}$ – 2) . To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O($\textit{α}$)-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

En-Hung Chao

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon ($\textit{g}$ − 2) from lattice QCD

In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers and for arbitrary global physical states), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the ‘observers’ considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [1] is equivalent to the Page-Wootters formalism, leading to the informal slogan “PW = CLPW”. It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.

Julian Vuyst

Stefan Eccles

Philipp Höhn

Canada

Josh Kirklin

Gravitational entropy is observer-dependent

It has been known for some time that generalised geometry provides a particularly elegant rewriting of the action and symmetries of 10-dimensional supergravity theories, up to the lowest nontrivial order in fermions. By exhibiting the full symmetry calculations in the second-order formalism, we show in the $$ \mathcal{N} $$ = 1 case that this analysis can be upgraded to all orders in fermions and we obtain a strikingly simple form of the action as well as of the supersymmetry transformations, featuring overall only five higher-fermionic terms. Surprisingly, even after expressing the action in terms of classical (non-generalised geometric) variables one obtains a simplification of the usual formulae. This in particular confirms that generalised geometry provides the natural set of variables for studying (the massless level of) string theory. We also show how this new reformulation implies the compatibility of the Poisson-Lie T-duality with the equations of motion of the full supergravity theory.

Julian Kupka

Charles Strickland-Constable

Fridrich Valach

Direct derivation of $$ \mathcal{N} $$ = 1 supergravity in ten dimensions to all orders in fermions