Publications

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Vinberg's T-algebras: From exceptional periodicity to black hole entropy

Alessio Marrani

SciPost Phys. Proc. 14, 035 (2023) · published 24 November 2023 | · pdf

We introduce the so-called Magic Star (MS) projection within the root lattice of finite-dimensional exceptional Lie algebras, and relate it to rank-3 simple and semi-simple Jordan algebras. By relying on the Bott periodicity of reality and conjugacy properties of spinor representations, we present the so-called Exceptional Periodicity (EP) algebras, which are finite-dimensional algebras, violating the Jacobi identity, and providing an alternative with respect to Kac-Moody infinite-dimensional Lie algebras. Remarkably, also EP algebras can be characterized in terms of a MS projection, exploiting special Vinberg T-algebras, a class of generalized Hermitian matrix algebras introduced by Vinberg in the '60s within his theory of homogeneous convex cones. As physical applications, we highlight the role of the invariant norm of special Vinberg T-algebras in Maxwell-Einstein-scalar theories in 5 space-time dimensions, in which the Bekenstein-Hawking entropy of extremal black strings can be expressed in terms of the cubic polynomial norm of the T-algebras.
SO(1,3) Yang-Mills solutions on Minkowski space via cosets

Kaushlendra Kumar

SciPost Phys. Proc. 14, 033 (2023) · published 24 November 2023 | · pdf

We present a novel family of Yang-Mills solutions, with gauge group SO(1,3), on Minkowski space that are geometrically distinguished into two classes, viz. interior and exterior of the lightcone. We achieve this by foliating the former with SO(1,3)/SO(3) cosets and the latter with SO(1,3)/SO(1,2) cosets and analytically solving the Yang-Mills equation of an SO(1,3)-invariant gauge field. The resulting fields and their stress-energy tensor, when translated to the Minkowski space, diverge at the lightcone, but we demonstrate how this stress-energy tensor could be regularised due to its unique algebraic structure.
Group invariants for Feynman diagrams

Idrish Huet, Michel Rausch de Traubenberg, Christian Schubert

SciPost Phys. Proc. 14, 031 (2023) · published 24 November 2023 | · pdf

It is well-known that the symmetry group of a Feynman diagram can give important information on possible strategies for its evaluation, and the mathematical objects that will be involved. Motivated by ongoing work on multi-loop multi-photon amplitudes in quantum electrodynamics, here I will discuss the usefulness of introducing a polynomial basis of invariants of the symmetry group of a diagram in Feynman-Schwinger parameter space.
New perspectives in gravity-mediated supersymmetry breaking

Robin Ducrocq

SciPost Phys. Proc. 14, 027 (2023) · published 24 November 2023 | · pdf

New solutions in supersymmetry breaking through gravity mediation have been recently discovered. Such solutions have interesting properties regarding renormalisation and introduce new contributions in the scalar potential that may help to resolve some issues of the Standard Model. The purpose of this article is to investigate the consequences of these new structures. We construct a model related to these new solutions, the S2MSSM, and present some preliminary results on the effects of these new contributions, especially on the Standard Model's Higgs boson mass.
Brane detectors of a dynamical phase transition in a driven CFT

Suchetan Das, Bobby Ezhuthachan, Arnab Kundu, Somnath Porey, Baishali Roy, Krishnendu Sengupta

SciPost Phys. 15, 202 (2023) · published 23 November 2023 | · pdf

We show that a dynamical transition from a non-heating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS$_2$ slices of the pure AdS$_3$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.
BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

David Dudal, Philipe De Fabritiis, Marcelo Santos Guimaraes, Giovani Peruzzo, Silvio Paolo Sorella

SciPost Phys. 15, 201 (2023) · published 23 November 2023 | · pdf

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.
Renormalizable extension of the Abelian Higgs-Kibble model with a dim.6 derivative operator

Daniele Binosi, Andrea Quadri

SciPost Phys. Proc. 14, 019 (2023) · published 23 November 2023 | · pdf

We present a new approach to the consistent subtraction of a non power-counting renormalizable extension of the Abelian Higgs-Kibble (HK) model supplemented by a dim. 6 derivative-dependent operator controlled by the parameter $z$. A field-theoretic representation of the physical Higgs scalar by a gauge-invariant variable is used in order to formulate the theory by exploiting a novel differential equation, controlling the dependence of the quantized theory on $z$. These results pave the way to the consistent subtraction by a finite number of physical parameters of some non-power-counting renormalizable models possibly of direct relevance to the study of the Higgs potential at the LHC.
Jordan meets Freudenthal. A black hole exceptional story

Alessio Marrani

SciPost Phys. Proc. 14, 009 (2023) · published 23 November 2023 | · pdf

Within the extremal black hole attractors arising in ungauged $\mathcal{N}≥ 2$-extended Maxwell Einstein supergravity theories in $3+1$ space-time dimensions, we provide an overview of the stratification of the electric-magnetic charge representation space into "large" orbits and related "moduli spaces", under the action of the (continuous limit of the) non-compact $U$-duality Lie group. While each "large" orbit of the $U$-duality supports a class of attractors, the corresponding " moduli space" is the proper subspace of the scalar manifold spanned by those scalar fields on which the Attractor Mechanism is inactive. We present the case study concerning $\mathcal{N}=2$ supergravity theories with symmetric vector multiplets' scalar manifold, which in all cases (with the exception of the minimally coupled models) have the electric-magnetic charge representation of $U$-duality fitting into a reduced Freudenthal triple system over a cubic (simple or semi-simple) Jordan algebra.
Integrability for Feynman integrals

Florian Loebbert

SciPost Phys. Proc. 14, 008 (2023) · published 23 November 2023 | · pdf

We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT. We discuss the resulting Yangian differential equations for massless fishnets in four dimensions as well as generalizations to massive propagators and generic dimensions. We also comment on the relation to momentum space conformal symmetry and on examples in dimensional regularization. Finally we sketch the recent application to fishnet integrals in two spacetime dimensions and the curious identification of Yangian invariants with period integrals of Calabi-Yau geometries.
The 34th International Colloquium on Group Theoretical Methods in Physics

Rutwig Campoamor-Stursberg, Marc de Montigny, Michel Rausch de Traubenberg, Mauricio Valenzuela

SciPost Phys. Proc. 14, 001 (2023) · published 23 November 2023 | · pdf

Introduction to the proceedings of the 34th International Colloquium on Group Theoretical Methods in Physics.

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