In this paper we investigate the loop-level geometry of ABJM theory from the perspective of lightcone geometries in dual space. This geometry admits a natural fibration, where one of the loop variables can be naturally interpreted as living in a $\textit{fiber}$ for each fixed point of a lower-loop geometry. When varying the latter, this leads us to the definition of $\textit{L}$-loop $\textit{half-chambers}$, defined such that ‘half’ of the ($\textit{L}$ + 1)-loop fiber remains unchanged. We provide a full classification of these half-chambers, and demonstrate a surprising bijection between $\textit{n}$-point $\textit{L}$-loop half-chambers and $\textit{L}$-loop Feynman diagrams for a cubic scalar theory with $\textit{n}$/2 particles. Consequently, the sum over $\textit{L}$-loop half-chambers that computes the $\textit{n}$-point ABJM amplitude is in direct correspondence with the sum over $\textit{L}$-loop Feynman diagrams that computes the ($\textit{n}$/2)-point amplitude of Tr($\textit{ϕ}$ ) theory. These Feynman diagrams are also realised geometrically in the structure of the loop fibers. Furthermore, we argue that the half-chamber expansion is equivalent to the loop-level BCFW recursion for ABJM, which arises naturally from our geometric construction. Finally, we will illustrate how $\textit{L}$-loop $\textit{chambers}$ emerge as the intersection of two $\textit{L}$-loop half-chambers, and we provide concrete examples of this construction.

United Kingdom

Livia Ferro

Ross Glew

Tomasz Łukowski

Czechia

Jonah Stalknecht

The geometry of BCFW for ABJM loop integrands

We establish a connection between the superconformal index of $$ \mathcal{N} $$ = 4 $\textit{U}$ ($\textit{N}$) SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $\textit{B}$ ($\textit{p}$, $\textit{q}$, $\textit{t}$) and normalization constants $$ {\mathcal{N}}_{\lambda}\left(p,q,t\right) $$ . By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $\textit{p}$, a systematic expansion of the index in powers of $\textit{p}$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $\textit{N}$ limit, our formalism reduces to previously known results.

China

Gao-fu Ren

Min-xin Huang

Superconformal index for $$ \mathcal{N} $$ = 4 super Yang-Mills and elliptic Macdonald polynomials

We develop an operator-algebraic framework for modular self-duality, symmetrized relative entropy, and Bogoliubov-Kubo-Mori (BKM) susceptibility of local states in quantum field theory. In finite dimensions, modular self-duality singles out fixed points at which a state coincides with its modularly reflected partner. At such points, the natural comparison functional is the symmetrized Umegaki relative entropy. It vanishes at coincidence, and its Hessian is governed by the BKM quantum Fisher information along the reflected tangent direction. We then extend this fixed-point construction to the local type III von Neumann algebras that arise in quantum field theory. Here, a local state is compared with the modular pullback of its commutant restriction, and the intrinsic comparison functional is the symmetrized Araki relative entropy. For sufficiently regular state deformations, the fixed-localization Hessian at the self-dual point defines a type III BKM susceptibility. This coefficient is obtained by evaluating the BKM bilinear form on the tangent selected by the modular pairing. Exact coherent-state realizations are obtained for the free scalar field on wedge algebras and for the chiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> current on half-line algebras. In both examples, the comparison functional is exactly quadratic in the deformation parameter, and the susceptibility coefficients admit explicit boost-energy, stress-tensor, or half-line integral representations. We also apply the construction to a ball-shaped boundary region in the vacuum state of a conformal field theory with a semiclassical anti–de Sitter (AdS) gravitational dual. For linear bulk coherent excitations in an exact complementary-recovery model of this sector, bulk-boundary modular intertwining identifies the modular partner with the AdS-Rindler-reflected coherent state, and the symmetrized relative entropy is exactly quadratic. Its Hessian is twice the bulk canonical energy of the reflected-difference perturbation.

United States

Rupak Chatterjee

Modular self-duality, symmetrized relative entropy, and Bogoliubov-Kubo-Mori susceptibility in quantum field theory

The local physics of light scalar fields in de Sitter space is well described by classical random walks, as expressed through the framework of stochastic inflation. Recent work has clarified how this formalism arises from quantum field theory and the renormalization group (RG), allowing for corrections to this formalism to be determined order by order. Yet, this description is incomplete. For example, the quantum dynamics of these fields are expected to become important when determining the tail of the probability distribution for the fluctuations. In this paper, we develop the understanding of fields in de Sitter as a quantum walk in order to bridge the gap between the classical and quantum description. We use the framework of exact RG to calculate the evolution equation for the reduced density matrix of the long wavelength fields. This master equation provides the direct map from light fields to models of quantum walks. We show how to reduce the master equation to stochastic inflation, and provide a new understanding of how the higher-order corrections arise. In the process, we demonstrate that divergences and secular growth in de Sitter, for both light and heavy fields, can be absorbed by (dynamical) renormalization.

Daniel Green

Kshitij Gupta

Quantum walks and exact RG in de Sitter space

We present a constituent two-gluon description of the lowest-lying glueball states in pure Yang-Mills theory, calibrated against quenched lattice results. The framework incorporates an instanton-induced dynamical gluon mass, Casimir-scaled adjoint confinement, the short-distance adjoint Coulomb interaction, and instanton-induced central and tensor forces. The scalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></mrow></math> glueball is found to be exceptionally compact, with a radius of order the instanton size, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>ρ</mi><mo>∼</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math>, consistent with lattice indications. By contrast, the tensor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> state remains spatially extended due to the centrifugal barrier. We also discuss the role of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>–</mi><mi>D</mi></math> mixing. A semiclassical analysis further supports Regge behavior for excited states, in agreement with lattice results.

Edward Shuryak

Ismail Zahed

Glueballs, constituent gluons, and instantons

Previous studies have shown that cascade production in the thick target of the Search for Hidden Particles (SHiP) experiment may substantially enhance the number of light long-lived particles (LLPs) decaying in the fiducial volume. However, cascade-produced LLPs are typically soft, so daughter-level acceptance and reconstruction effects can strongly suppress the observable event rate. We quantify this suppression for two representative cases: photophilic axionlike particles (ALPs) produced in electromagnetic cascades and heavy neutral leptons (HNLs) produced in decays of secondary kaons. We combine a semianalytic event-rate calculation with a detector-level study of ALP reconstruction in the electromagnetic calorimeter. For the nominal SHiP detector design, cascade ALPs give at most a moderate enhancement over primary production and only at the lightest masses; at higher masses, the cascade contribution becomes subdominant or negligible. For HNLs from secondary kaons, the cascade contribution is already subdominant after imposing daughter-level geometric acceptance. We also identify possible ways to recover part of the cascade event rate, including relaxed event-selection criteria and an active decay-volume subdetector.

Belgium

Matei Climescu

Ukraine

Yehor Kyselov

CERN

Maksym Ovchynnikov

Detector performance at SHiP for cascade-produced long-lived particles

The new measurement of the $$K^+\rightarrow \pi ^+\nu \bar{\nu }$$ branching ratio by the NA62 collaboration represents an important milestone in precision flavour physics. Under different flavour assumptions on beyond the standard model physics, this decay mode can be related to many other observables with underlying flavour-changing currents, such as $$B\rightarrow K\nu \bar{\nu }$$ or $$B_s\rightarrow \mu \mu $$ , effectively providing an additional handle in our exploration of flavour-violating new physics effects. We study the impact of this new result, under the hypotheses that deviations from the standard model arise from modified $\textit{Z}$ couplings, or from effects in semileptonic interactions. Finally, we review the implications of our scenarios for the yet to be measured partner mode $$K_L\rightarrow \pi ^0\nu \bar{\nu }$$ .

Germany

Lukas Allwicher

Marzia Bordone

Implications of $$K\rightarrow \pi \nu \bar{\nu }$$ for new physics in $\textit{B}$ decays

The penguin loop-suppressed $\textit{B}$ → $\textit{ϕK}$ decays are highly sensitive to contributions of hypothetical heavy new particles. Particularly interesting probes for testing the Standard Model and revealing such phenomena are provided by CP violation in the $${B}_{d}^{0}\to \phi {K}_{S}$$ decay. Standard-Model estimates for the corresponding CP-violating observables are theoretically limited by doubly Cabibbo-suppressed penguin contributions. We study these effects using a factorization approach, and provide predictions for CP asymmetries, to be contrasted with future measurements. To gain additional insight into these hadronic effects, we propose the $${B}_{s}^{0}\to \phi {K}_{S}$$ decay as a new channel. We predict the observables for this decay for which currently no measurements exist. By comparing $${B}_{d}^{0}\to \phi {K}_{S}$$ and $\textit{B}$ → $\textit{ϕK}$ , we further derive state-of-the-art constraints on isospin observables within the Standard Model. The same framework enables probing of possible New-Physics contributions, including general effects and those with non-trivial isospin structure. Interesting prospects arise for the high-precision era of flavour physics ahead.

Netherlands

Robert Fleischer

Jelle Groot

K. Vos

CP violation in $\textit{B}$ ($\textit{s}$) $\textit{→ ϕK}$ decays: Standard Model benchmarks and isospin-breaking New Physics

We present a comprehensive study of the current-phase relation of the Josephson junction in a holographic superfluid ring, realized from the stochastic and non-equilibrium dynamics according to the Kibble-Zurek mechanism. By employing a spatially modulated charge density to engineer a weak link, the current-phase relation is investigated in a range of geometric and thermodynamic parameters. The seminal sinusoidal relation between the current and the phase emerges periodically due to the compact shape of the geometry. We also identify the relations between the critical current and the geometric parameters of the junction: the width, steepness and depth. Furthermore, we demonstrate that the critical current exhibits a characteristic exponential decaying against the final temperature, reflecting the thermal degradation of the order parameter in a strong-coupling regime. Our results establish a robust framework for holographic Josephson devices, offering experimentally testable predictions for the non-equilibrium dynamics of high-$\textit{T}$ superconductors.

Zhi-Hong Li

Huai-Fan Li

Hai-Qing Zhang

Kibble-Zurek mechanism and current-phase relation in a holographic Josephson junction

In this note we show how the consistent truncations on half-supersymmetric branes of Leung and Stelle and Lin, Skrzypek and Stelle fit into the general exceptional generalised geometry analysis of Cassani et al. Each solution defines a torsion-free Spin($\textit{n}$) structure in the Spin($\textit{n, n}$) × ℝ generalised geometry introduced by Strickland–Constable, where $\textit{n}$ is the dimension of the space transverse to the brane. Embedding this into the appropriate exceptional generalised geometry then defines the truncation. As a by-product we derive a new consistent truncation on the IIA NS5-brane to six-dimensional 𝒩 = (2$\textit{,}$ 0) supergravity coupled to a tensor multiplet, and new consistent truncations on the D6- and D7-branes to seven- and eight-dimensional pure half-maximal supergravity respectively.

Jieming Lin

K. Stelle

Daniel Waldram

Spin($\textit{n, n}$) $\textit{×}$ ℝ+ generalised geometry and consistent truncations on branes