We develop techniques to treat massive Kaluza-Klein modes to arbitrary order in perturbation theory. The Higgs mechanism that renders the higher Kaluza-Klein modes massive is displayed. To this end we give an algorithm in perturbation theory that yields new fields with the following characteristics: they are gauge invariant under all higher-mode gauge transformations, which are broken, but they transform covariantly under the zero-mode gauge transformations, which are unbroken. We employ the formulation of field theory in terms of $\textit{L}$ algebras together with their $\textit{homotopy transfer}$, which here maps the gauge redundant fields of gravity to gauge invariant fields. We illustrate these results, as a proof of concept, for Kaluza-Klein theory on a torus. In an accompanying paper these results will be applied to a large class of generalized Scherk-Schwarz backgrounds in exceptional field theory.

France

Camille Eloy

Germany

Olaf Hohm

Camilla Lavino

Henning Samtleben

Yehudi Simon

Homotopy transfer for massive Kaluza-Klein modes

In Kaluza-Klein theory, gauge fields on $\textit{M}$ arise as components of a higher-dimensional metric defined on $\textit{M}$ × $\textit{K}$. The traditional expectation is that all the gauge fields of the Standard Model are linked to exact Killing vector fields on the internal space. This paper questions that assumption and investigates the properties of 4D gauge fields linked to non-Killing fields on $\textit{K}$. It is shown that they have massive yet arbitrarily light bosons; they can mix fermions with different masses; and they can have asymmetric couplings to left- and right-handed fermions. None of these properties is easily satisfied by gauge fields linked to internal isometries. Thus, backgrounds encoding such massive gauge fields circumvent traditional no-go arguments and offer a geometric source of chiral interactions with fermions. This may help to model the weak force within the Kaluza-Klein framework. Technically, the paper uses the language of spin geometry and Riemannian submersions. It studies the higher-dimensional Dirac operator with non-trivial background metrics. The results are derived for a general $\textit{K}$. They are illustrated explicitly in the simpler cases where $\textit{K}$ is the two-sphere and the two-torus.

Portugal

João Baptista

Chiral interactions of fermions and massive gauge fields in Kaluza-Klein models

We perform a global analysis of deep-inelastic $\textit{e}$ + $\textit{p}$ scattering data from HERA and transverse energy distributions in $\textit{p}$ + $\textit{p}$ and $\textit{p}$ + Pb collisions, alongside charged hadron multiplicities in Pb+Pb collisions at $$ \sqrt{s_{\textrm{NN}}}=5.02 $$ TeV from ALICE. Using a saturation-based initial state model grounded in high-energy QCD, we determine the early-time non-equilibrium shear viscosity to entropy density ratio $\textit{η/s}$ of the quark-gluon plasma. Our results provide new insights into the early-time transport properties of nuclear matter under extreme conditions.

Anton Andronic

Nicolas Borghini

Spain

Xiaojian Du

Christian Klein-Bösing

Renata Krupczak

United States

Hendrik Roch

Sören Schlichting

Constraining hot and cold nuclear matter properties from heavy-ion collisions and deep-inelastic scattering

We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong steplike electric potential in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions. First, for a constant (eternal) potential, we calculate the current for different Fock space ground states corresponding to distinct mode bases. While one basis yields a zero current, another produces the standard nonzero value. We then consider a potential that is rapidly switched on, recovering the standard current in the asymptotic future. This result is generalized to potentials that interpolate between different constant values at spatial infinity. Finally, we analyze a potential acting for a finite duration and again reproduce the standard current. A physical interpretation of these results is provided.

Russia

E.T. Akhmedov

D.V. Diakonov

V.I. Lapushkin

D.I. Sadekov

Lessons from the Klein paradox

In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the “length of time” <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> as the evolution direction of the system. In our novel construction, some additional modes beyond the plane wave modes are crucial in the canonical quantization and the later derivation of the Lehmann-Symanzik-Zimmermann reduction formula. We also derive the free two-point function by using Wick contraction in the canonical quantization formalism. Moreover, we introduce the path-integral formalism in which we can redefine the vacuum states and rederive the correlation functions. We show that all the results in the Klein space derived in our novel approach match those obtained via analytical continuation from the Minkowski spacetime.

China

Bin Chen

Zezhou Hu

Xin-Cheng Mao

QFT in Klein space

We explore a higher-dimensional universe that is a product of Minkowski space and the nonorientable Klein bottle. The topology explicitly breaks important symmetries, such as translational invariance and (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> invariance. Somewhat surprisingly, the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>p</mi></math> of the Minkowski space can also be broken by the Klein bottle, both explicitly and in the presence of a brane. The topology enforces a background of fermion correlations that amounts to a condensate wall localized in the Klein bottle. The wall acts as an order parameter for the broken symmetries. If a brane passes through the wall, brane fermions that couple to the condensate are produced as quantified by the Bogoliubov coefficients for a time-dependent mass. The scenario meets the conditions, including <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mi>p</mi></math> violation, to potentially generate the matter-antimatter asymmetry of the universe.

Brian Greene

Daniel Kabat

Janna Levin

Massimo Porrati

Klein bottle cosmology

Two photons from the ground state para-positronium annihilation are emitted in a maximally entangled singlet state of orthogonal polarizations. In case of the Compton scattering of both photons the phenomenon of quantum entanglement leads to a measurable increase in the azimuthal correlations of scattered photons, as opposed to a classical description treating the two scattering events as independent. The probability of the scattering of the system of entangled photons is described by the Pryce-Ward cross section dependent on a difference of the azimuthal scattering angles in the fixed coordinate frame, while the independent scattering of single photons is described by the Klein-Nishina cross section dependent on the azimuthal angle relative to each photon’s initial polarization. Since the singlet state of orthogonal polarizations is rotationally invariant, it does not carry any physical information on the initial polarizations of the single annihilation photons. In such bipartite state the angular origin for the Klein-Nishina cross section is undefined, making the Pryce-Ward and Klein-Nishina descriptions mutually exclusive. However, semi-classical simulations of the joint Compton scattering of entangled photons – implementing the Pryce-Ward cross section, but still treating the two photons as separate entities – can reconcile the Pryce-Ward correlations with the Klein-Nishina statistics for single photons by implementing a modified version of a scattering cross section presented in this work.

Croatia

Petar Žugec

Eric Andreas Vivoda

Mihael Makek

Ivica Friščić

A reconciliation of the Pryce-Ward and Klein-Nishina statistics for semi-classical simulations of annihilation photons correlations

We propose an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations and implement it in the supergravity limit of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> supersymmetric Yang-Mills theory. By incorporating this mechanism into Mellin space bootstrap, together with an observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry under <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">↔</mo><mi mathvariant="normal">S</mi></mrow></math>, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo>×</mo><mi mathvariant="normal">S</mi></mrow></math> bootstrap method is directly applicable to generic multipoint computation at tree level.

Bruno Fernandes

Vasco Gonçalves

Zhongjie Huang

Yichao Tang

United Kingdom

Joao Vilas Boas

Ellis Ye Yuan

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>AdS</mi><mo stretchy="false">×</mo><mi mathvariant="normal">S</mi></mrow></math> Mellin Bootstrap, Hidden 10D Symmetry and Five-Point Kaluza-Klein Functions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> Supersymmetric Yang-Mills Theory

We present a derivation of the first curvature correction to the AdS Veneziano amplitude for arbitrary Kaluza-Klein (KK) modes, using a bootstrap approach based on the world-sheet representation and AdS × S formalism. Our results establish a universal formula for the first order curvature correction without considering any low-lying KK configurations. We give new predictions for Wilson coefficients in the low-energy expansion. In the high-energy regime, the amplitude exhibits a universal exponent independent of the external KK charges, providing a coherent picture of AdS stringy amplitudes in different backgrounds.

Bo Wang

Bootstrap AdS Veneziano amplitude with arbitrary Kaluza-Klein modes

We investigate the response of the Kaluza–Klein (KK) mass spectrum to various deformations of the rugby-ball background in 6D supergravity. We derived the mode equations that contain the 3D scale factor and the lapse function. By solving these, we numerically evaluate the KK masses for a bulk scalar and a spinor when the background has a nontrivial dependence on the position in the compact space. We clarify some qualitative features of the spectrum deformation for some perturbations of the rugby-ball background. For perturbations of a supersymmetric background, we find that the mass-splitting between bosonic and fermionic modes is much smaller than the deviation from the values of the supersymmetric mass eigenvalues.

Japan

Hajime Otsuka

Yutaka Sakamura

Response of Kaluza–Klein Mass Spectrum to Deformations of Rugby-Ball Compact Space