Recently, we used methods of arithmetic geometry to study the anomaly-free irreducible representations of an arbitrary gauge Lie algebra. Here we generalize to the case of products of irreducible representations, where it is again possible to give a complete description. A key result is that the projective variety corresponding to $\textit{m}$-fold product representations of the Lie algebra $$ {\mathfrak{su}}_n $$ is a rational variety for every $\textit{m}$ and $\textit{n}$. We study the simplest case of $$ {\mathfrak{su}}_3 $$ (corresponding to the strong interaction) in detail. We also describe the implications of a number-theoretic conjecture of Manin (and related theorems) for the number of chiral representations of bounded size $\textit{B}$ (measured roughly by the Dynkin labels) compared to non-chiral ones, giving a precise meaning to the sense in which the former (which are those most relevant for phenomenology) are rare compared to the latter. As examples, we show that, for both irreducible representations of $$ {\mathfrak{su}}_5 $$ and once-reducible product representations of $$ {\mathfrak{su}}_3 $$ that are non-anomalous, the number of chiral representations is asymptotically between $\textit{B}$(log $\textit{B}$) and $$ {B}^{\frac{4}{3}} $$ , while the number of non-chiral representations is asymptotically $\textit{B}$ . Despite this rarity of chiral, anomaly-free, product representations, we show that there are examples relevant for phenomenology, including one that gives an asymptotically-free gauge theory with Lie algebra $$ {\mathfrak{su}}_7 $$ .

United Kingdom

Ben Gripaios

Khoi Le Nguyen Nguyen

More varieties of 4-d gauge theories: product representations

The differential representation of AdS correlators offers a framework to express exchange Witten diagrams as functions of non-local differential operators applied to contact Witten diagrams. In this paper, we develop the differential representation for scalar Carrollian correlators. We first construct this representation using the recently formulated Carrollian limit of AdS Witten diagrams. We then provide an alternate intrinsic analysis that leverages the properties of the Carrollian bulk-to-boundary propagator. Using the differential representation, we also obtain differential Bern-Carrasco-Johansson (BCJ) relations for Carrollian correlators.

India

Shankhadeep Chakrabortty

Germany

Subramanya Hegde

Arpit Maurya

Differential representation for Carrollian correlators

We establish a precise correspondence between the giant graviton expansion of the superconformal index of field theories in $\textit{D}$ ≤ 4, and the master volume formalism of Gauntlett, Martelli and Sparks (GMS) which determines the near horizon geometries of certain BPS black holes and black strings in supergravity. We focus on 4d $$ \mathcal{N} $$ = 1 superconformal field theories arising on the world volume of $\textit{N}$ D3 branes placed at the tip of a cone over a toric Sasaki-Einstein manifold SE , the simplest example of which is $\textit{S}$ , corresponding to $$ \mathcal{N} $$ = 4 super-Yang-Mills. The giant graviton expansion realises the superconformal index as the sum of contributions from wrapped D3 branes in the dual AdS × SE . We argue that, for large wrapping numbers, the asymptotics of each such contribution is governed by the $\textit{master volume}$ of a particular metric deformation of SE (suitably fibred over $\textit{S}$ ). In particular, the wrapping numbers of a generic giant graviton configuration are identified with Kähler moduli of the corresponding metric. We further show that at large $\textit{N}$ the entropy function of the relevant AdS × SE BPS rotating black hole is recovered by extremising over these moduli. Our results suggest that the complex Euclidean geometries corresponding to rotating BPS black holes in AdS are determined by a close analogue of GMS volume minimisation, and that conversely, the off-shell geometries considered in such minimisation procedures should be understood as the near-horizon geometries of back-reacted giant gravitons. We present analogous results for 3d $$ \mathcal{N} $$ = 2 theories holographically dual to M-theory on AdS × SE .

Taiwan

Japan

Heng-Yu Chen

Nick Dorey

Sanefumi Moriyama

Rishi Mouland

Czechia

Canberk Şanlı

Giant gravitons and volume minimisation

We study the supersymmetric structure of the spin current in four dimensional $$ \mathcal{N} $$ = 1 supersymmetric theories. By coupling the stress tensor multiplet to a vierbein multiplet we identify a spin current with the Hodge dual of the bottom component of the stress tensor multiplet in a wide range of theories. This implies that in holographic theories the Hodge dual of the $\textit{R}$ current may serve as a spin current, paving the way for holographic studies of theories with background torsion.

Netherlands

Casey Cartwright

Mexico

Domingo Gallegos

Umut Gürsoy

Israel

Roi Klein

Amos Yarom

A supersymmetric spin current

Braneworlds inside an AdS black hole provide simple models where a closed cosmology can be encoded in a dual field theory. Previous studies have focused on pure-tension branes, where the only matter in the cosmology is that dual to the holographic bulk. We consider models with additional explicit matter fields on the brane. Both for perfect fluid matter and for an axion field on the brane, we show that this can avoid a self-intersection problem in the Euclidean construction of such geometries in higher dimensions.

Spain

José Barbón

Ayan Patra

Juan Pedraza

Simon Ross

Cosmology inside a black hole: adding matter on the brane

In this work, we investigate the quantum Brownian motion of a point charge arising as a consequence of two fluctuating point-like boundaries. The study considers Dirichlet, Neumann, and mixed boundary conditions imposed on a real massless scalar field. Additionally, we analyze the effects of a fluctuating compactification length on the random motion of the point charge, induced by the imposition of a quasi-periodic condition on the scalar field. By associating a wave function with the length scale of each system, we demonstrate that typical divergences, which commonly appear in scenarios with fixed boundaries and compactification size, are effectively smoothed out. This approach generalizes and extends previous results found in the literature, offering new insights into the regularization of divergences appearing in idealized systems.

Brazil

Eliza Guedes

Herondy Mota

Quantum Brownian motion induced by fluctuating boundaries and compactification

We calculate the NNLO QED corrections to the $\textit{C}$-even part of differential cross section of $\textit{e}$ $\textit{e}$ → $\textit{μ}$ $\textit{μ}$ process. We neglect power corrections in the electron mass and obtain the result in terms of Goncharov’s polylogarithms.

Russia

Roman Gerasimov

Petr Krachkov

Roman Lee

Electron-positron annihilation into heavy leptons at two loops

We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of providing an effective dark energy density expression. Assuming a state close to vacuum, here defined by the vanishing product of the Einstein coupling constant and the Universe’s energy density, we perform a Taylor expansion of the theory and hence extend it to the whole domain. In this framework, the (renormalized) vacuum energy problem is studied, and an additional constant pressure term, which induces a Chaplygin-like contribution to the dark energy sector, arises in the late-time dynamics. The correction to the late-time Hubble parameter is investigated by comparing theoretical predictions with the late Universe observational data. Our findings indicate that the current value of the stated vacuum energy is consistent with zero within 1 $$\sigma $$ . Implications of the modified $$\Lambda $$ CDM model with respect to the Hubble tension are also discussed.

Italy

Giovanni Montani

Giulia Maniccia

Elisa Fazzari

Alessandro Melchiorri

Running Einstein constant and a possible vacuum state of the universe

We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the $$ {\overline{\partial}}_A $$ operator on a two dimensional torus coupled to an SU($\textit{N}$) gauge field. Despite the absence of a characteristic class such as $\textit{c}$ relevant for the quantum Hall effect, we show that there are topological invariants associated with the zero modes occuring in a family of Hamiltonians. The flatbands in the spectrum of the effective Hamiltonian are associated with Yang-Mills connections, studied by M. Atiyah and R. Bott long time ago. The emergent U(1) magnetic field with nonzero flux is presumably responsible for the observed Hall effect in the absence of (external) magnetic field. We provide a numeric algorithm transforming the original single-particle Hamiltonian to the direct sum of $$ {\overline{\partial}}_A $$ operators coupled to abelian gauge fields with non-zero $\textit{c}$ ’s. Our gradient flow perspective gives a simple bound for magic angles: if the gauge field $\textit{A}$($\textit{α}$) is such that the YM energy $$ {\int}_{{\mathbbm{T}}^2} $$ tr $$ {F}_{A\left(\alpha \right)}^2 $$ is smaller than that of U(1) magnetic flux embedded into SU(2), then $\textit{α}$ is not magic.

United States

Vasilii Iugov

Nikita Nekrasov

Yang-Mills flows for multilayered graphene

Marginal operators in a $\textit{d}$-dimensional conformal field theory (CFT), those with conformal dimension ∆ = $\textit{d}$, give us information about the space of related theories. This can be incredibly useful when trying to develop an intrinsic definition of a holographic CFT. Recent work has established that in the case of celestial CFTs, those dual to asymptotically flat spacetimes, marginal operators can be constructed as shadow transforms of soft scalars. In this work, rather than starting from a bulk theory of scalars, we start with Yang-Mills and construct marginal operators from soft gluons via light transforms. We obtain the local metric and connections for the associated conformal manifold by studying the two- and three-point functions of these marginal operators. We then discuss the implications of this for broadening our understanding of operator product expansions of soft operators in celestial CFTs.

Canada

Sruthi Narayanan

Marginality from leading soft gluons