It is well-known that a Lagrangian resembling scalar–tensor gravity naturally emerges from string theory in the low-energy limit. This suggests that a scalar–tensor theory intrinsically inhabits precious information about quantum gravitational effects. With this motivation, we quantize the scalar–tensor theory $$R+ \lambda R\phi ^2$$ in order to unfold the black hole physics in quantum gravity. We are interested in the behavior of the wave function near the interior singularity of a black hole, which would give a pathway to resolving the singularity. Consequently, we employ canonical quantization in a Kantowski–Sachs minisuperspace representation for the black hole interior. The ensuing Wheeler–DeWitt equation turns out to be intricately coupled among the three minisuperspace variables. Upon a suitable transformation, one of the variables could be easily separated – however, the scalar field $$\phi $$ remains coupled intricately and cannot be separated by any obvious transformation. Consequently, we employ a perturbative approach in powers of $$\lambda $$ . As a result, the zeroth order equation is immediately separable, and the first order equation still remains coupled in two variables. We adopt a Green function approach to solve this first order (inhomogeneous) equation. Our detailed calculation reveals that the Green function is well-defined in the vicinity of the black hole singularity, an important result for admitting the DeWitt criterion for singularity resolution. Furthermore, our calculations illustrate that both the zeroth order and first order wave functions are well-defined at the singularity as they are consistent with the DeWitt criterion, paving the way to black hole singularity resolution in scalar–tensor quantum gravity.

India

Harpreet Singh

Malay Nandy

Quantum black holes in scalar–tensor gravity: a Green function approach

The electrical conductivity of hot and dense quark matter is calculated using the 2-flavour gauged Nambu–Jona–Lasinio (NJL) model in the presence of a chiral imbalance quantified in terms of a chiral chemical potential (CCP). To this end, the in-medium spectral function corresponding to the vector current correlator is evaluated employing the real time formulation of finite temperature field theory. Taking the long wavelength limit of the spectral function we extract the electrical conductivity using the Green–Kubo relation. The thermal widths of the quarks/antiquarks that appear in the expression of electrical conductivity are calculated by considering the $$2\rightarrow 2$$ scattering in the NJL model. The scattering amplitudes containing the polarization functions of the mesonic modes in the scalar and pseudoscalar channels are also evaluated by considering finite value of CCP. We find that the ratio of electrical conductivity to temperature has significant dependence on CCP especially in the low temperature region.

Snigdha Ghosh

Nilanjan Chaudhuri

Sourav Sarkar

Pradip Roy

Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green–Kubo method within the 2-flavour gauged NJL model

We study for the first time the production of charmonia in nuclear ultraperipheral and electron-ion collisions based on a rigorous Green function formalism. Such formalism allows to incorporate properly formation effects (color transparency), as well as the quantum coherence inherent in higher-twist shadowing corrections related to the <math><mo>|</mo><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover><mo>⟩</mo></math> Fock component of the photon. The leading twist gluon shadowing associated with multigluon photon fluctuations is also included within the same formalism. The later effect represents the dominant source of shadowing at midrapidities in the LHC kinematic region, while the reduced effect of quark shadowing leads to a significant modification of differential cross sections <math><mi>d</mi><mi>σ</mi><mo>/</mo><mi>d</mi><mi>y</mi></math> at forward and/or backwards rapidities. Model calculations for <math><mi>d</mi><mi>σ</mi><mo>/</mo><mi>d</mi><mi>y</mi></math> are in a good agreement with available ultraperipheral nuclear <math><mrow><mi>P</mi><mi>b</mi><mtext>−</mtext><mi>P</mi><mi>b</mi></mrow></math> collisions data on coherent charmonium production at RHIC and the LHC. In addition, we also perform predictions for nuclear effects in the electroproduction of charmonia, which can be verified by new data from electron-ion colliders.

Czechia

Slovakia

J. Nemchik

J. Óbertová

Coherent photo- and electroproduction of charmonia on nuclear targets revisited: Green function formalism

We perform nonrelativistic expansions of type IIB <math altimg='si1.svg'><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>&#215;</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math> Green-Schwarz (GS) superstrings upto quadratic order in fermionic excitation. We carry out a systematic <math altimg='si2.svg'><mn>1</mn><mo stretchy='false'>/</mo><mi>c</mi></math> expansion both for the bosonic as well as the fermionic sector of the type IIB model and explore the LO theory in detail. We explore various global as well as local symmetries of the nonrelativistic sigma model at LO including the world-sheet supersymmetry. As a special case, we choose the flat gauge and explore the longitudinal T-duality rules for the LO theory. Finally, we comment on the NLO theory and discuss some of its interesting properties including the scale invariance.

Dibakar Roychowdhury

Nonrelativistic expansion of Green-Schwarz strings on <italic>AdS</italic> <inf>5</inf>&#8239;&#215;&#8239; <italic>S</italic> <sup>5</sup>

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple spatially-separated samples from each gauge field; in the extreme case, we arrive at the master-field approach in which a single gauge field is used. Here we develop techniques for studying hadronic observables using position-space correlators, which are more localized, and compare with the standard time-momentum representation. We also adapt methods for estimating the variance of an observable from autocorrelated Monte Carlo samples to the case of correlated spatially-separated samples.

Italy

Mattia Bruno

Switzerland

Marco Cè

Taiwan

Anthony Francis

Ireland

Patrick Fritzsch

Germany

Jeremy Green

United Kingdom

Maxwell Hansen

Denmark

Antonio Rago

Exploiting stochastic locality in lattice QCD: hadronic observables and their uncertainties

Abstract We begin a series of two papers that is devoted to the study of the multi-loop effective potential evolution in φ$^{4}$ theory using the conformal symmetry. In this first part, we introduce and describe in detail the vacuum V$_{z, x}$ operation (“V” stems from “vacuum”; {z, x} imply the corresponding coordinates) that transforms the given Green’s functions to the corresponding vacuum integrations that generate the effective potential. Our operation can be considered as an inverse procedure compared to the Gorishnii–Isaev method. To reach the final goal, it is also necessary to introduce a special treatment of the mass terms as types of “interaction” in an asymptotical expansion of the generating functional.

JINR

I V Anikin

Conformal symmetry and effective potential: I. Vacuum operation for the Green functions

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor g of the muon to deviate from the value of two predicted by Dirac’s theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon (g − 2). Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at  https://github.com/RJHudspith/KQED  .

Nils Asmussen

En-Hung Chao

France

Antoine Gérardin

Renwick Hudspith

Harvey Meyer

Andreas Nyffeler

Hadronic light-by-light scattering contribution to the muon g − 2 from lattice QCD: semi-analytical calculation of the QED kernel

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale Λ ~ 400 MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale Λ, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to γ ∗ γ ∗ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level γ ∗ γ ∗ → e + e  −  cross-section, we predict the expected lattice-QCD integrand resulting from the γ ∗ γ ∗ → π 0 process.

Volodymyr Biloshytskyi

Franziska Hagelstein

Julian Parrino

Vladimir Pascalutsa

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a ’t Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

Markus Dierigl

United States

Paul-Konstantin Oehlmann

Thorsten Schimannek

The discrete Green-Schwarz mechanism in 6D F-theory and elliptic genera of non-critical strings

We express the nonlocal Bondi-Metzner-Sachs (BMS) charges of a free massless Klein-Gordon scalar field in <math><mn>2</mn><mo>+</mo><mn>1</mn></math> in terms of the Green functions of the polyharmonic operators. Using the properties of these Green functions, we are able to discuss the asymptotic behavior of the fields that ensures the existence of the charges and prove that one obtains a realization of the <math><mn>2</mn><mo>+</mo><mn>1</mn></math> BMS algebra in canonical phase space. We also discuss the transformations in configuration space and show that in this case the algebra closes only up to skew-symmetric combinations of the equations of motion. The formulation of the charges in terms of Green functions opens the way to the generalization of the formalism to other dimensions and systems.

Spain

Carles Batlle

Víctor Campello

Joaquim Gomis

Polyharmonic Green functions and nonlocal Bondi-Metzner-Sachs transformations of a free scalar field