The nearest-neighbour or local mass terms in theory space among quantum fields, with their generic disordered values, are known to lead to the localisation of mass eigenstates, analogous to Anderson localisation in a one-dimensional lattice. This mechanism can be used to create an exponential hierarchy in the coupling between two fields by placing them at opposite ends of the lattice chain. Extending this mechanism, we show that when copies of such fields are appropriately attached to the lattice chain, it leads to the emergence of multiple massless modes. These vanishing masses are a direct consequence of the locality of interactions in theory space. The latter may break down in an ordered and deterministic manner through quantum effects if additional interactions exist among the chain fields. Such non-locality can induce small masses for the otherwise massless modes without necessarily delocalising the mass eigenstates. We provide examples of interactions that preserve or even enhance localisation. Applications to flavour hierarchies, neutrino mass, and the $\textit{μ}$-problem in supersymmetric theories are discussed.

India

Ketan Patel

Hierarchies from deterministic non-locality in theory space Anderson localisation

In this paper, the dimensional reduction is applied to the Lee-Wick electrodynamics in which the classical sources are confined on a spatial plane. As result, the Lee-Wick pseudoelectrodynamics is achieved as a nonlocal electromagnetism defined in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions. The Abelian Anderson-Higgs mechanism is so introduced in the Lee-Wick pseudo-electrodynamics through a complex scalar sector in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions, breaking spontaneously the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math>-gauge symmetry of the nonlocal theory. As consequence, the pseudo-Lee-Wick field acquires a light mass, beyond the usual heavy Lee-Wick mass, that is a natural mass parameter of the theory. After the spontaneous symmetry breaking takes place, classical features of the theory are discussed, as the pseudo-Proca-Lee-Wick electrodynamics, with the field equations and conservation laws. The introduction of Lee-Wick fermions also is proposed, in which it opens the discussion of a viable pseudo-Proca-Lee-Wick quantum electrodynamics in <math><mn>1</mn><mo>+</mo><mn>2</mn></math> dimensions. The unitarity at the tree level of the Lee-Wick pseudo-electrodynamics is discussed through the optical theorem.

Brazil

M. J. Neves

Classical features, Anderson-Higgs mechanism, and unitarity in Lee-Wick pseudo-electrodynamics

In this work we probe the QCD Anderson transition by studying spectral distributions of the massless overlap operator on gauge configurations created by the twisted mass at finite temperature collaboration (tmfT) with <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math> flavors of dynamical quarks and the Iwasaki gauge action. We assess finite-size and discretization effects by considering two different lattice spacings and several physical volumes, and mimic the approach to the continuum limit through stereographic projection. Fitting the inflection points of the participation ratios of the overlap Dirac eigenmodes, we obtain estimates of the temperature dependence of the mobility edge, below which quark modes are localized. We observe that it is well described by a quadratic polynomial and systematically vanishes at temperatures below the pseudocritical one of the chiral transition. In fact, our best estimates within errors overlap with that of the chiral phase transition temperature of QCD in the chiral limit.

Germany

Robin Kehr

Dominik Smith

Lorenz von Smekal

QCD Anderson transition with overlap valence quarks on a twisted-mass sea

The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field theory is a superfluid with a spontaneously broken U(1) global symmetry. As already observed in the previous literature, a bona fide holographic superconductor can be constructed using mixed boundary conditions for the bulk gauge field. By exploiting this prescription, we study the near-equilibrium collective dynamics in the Higgs phase and reveal the characteristic features of the Anderson-Higgs mechanism. We show that second sound disappears from the spectrum and the gauge field acquires a finite energy gap of the order of the plasma frequency. We observe an overdamped to underdamped crossover for the Higgs mode which acquires a finite energy gap below ≈ T  c  /2, with T  c  the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than 2∆, with ∆ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.

China

Spain

Hyun-Sik Jeong

Matteo Baggioli

South Korea

Keun-Young Kim

Ya-Wen Sun

Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

We present a convolutional autoencoder to denoise pulses from a p-type point contact high-purity germanium detector similar to those used in several rare event searches. While we focus on training procedures that rely on detailed detector physics simulations, we also present implementations requiring only noisy detector pulses to train the model. We validate our autoencoder on both simulated data and calibration data from an  $$^{241}$$  <math> <msup> <mrow></mrow> <mn>241</mn> </msup> </math>  Am source, the latter of which is used to show that the denoised pulses are statistically compatible with data pulses. We demonstrate that our denoising method is able to preserve the underlying shapes of the pulses well, offering improvement over traditional denoising methods. We also show that the shaping time used to calculate energy with a trapezoidal filter can be significantly reduced while maintaining a comparable energy resolution. Under certain circumstances, our denoising method can improve the overall energy resolution. The methods we developed to remove electronic noise are straightforward to extend to other detector technologies. Furthermore, the latent representation from the encoder is also of use in quantifying shape-based characteristics of the signals. Our work has great potential to be used in particle physics experiments and beyond.

Canada

Mark Anderson

Vasundhara Basu

Ryan Martin

Charlotte Reed

Noah Rowe

Kazakhstan

Mehdi Shafiee

Tianai Ye

Performance of a convolutional autoencoder designed to remove electronic noise from p-type point contact germanium detector signals

A picture of thermal QCD phase change based on the analogy with metal-to-insulator transition of Anderson type was proposed in the past. In this picture, a low-T thermal state is akin to a metal with deeply infrared (IR) Dirac modes abundant and extended, while a high-T state is akin to an insulator with IR modes depleted and localized below a mobility edge <math><msub><mrow><mi>λ</mi></mrow><mrow><mtext>A</mtext></mrow></msub><mo>&gt;</mo><mn>0</mn></math>. Here we argue that, while <math><msub><mrow><mi>λ</mi></mrow><mrow><mtext>A</mtext></mrow></msub></math> exists in QCD, a high-T state is not an insulator in such an analogy. Rather, it is a critical state arising due to a new singular mobility edge at <math><msub><mrow><mi>λ</mi></mrow><mrow><mtext>IR</mtext></mrow></msub><mo>=</mo><mn>0</mn></math>. This new mobility edge appears upon the transition into the recently proposed IR phase. As a key part of such a metal-to-critical scenario, we present evidence using pure-glue QCD that deeply infrared Dirac modes in the IR phase extend to arbitrarily long distances. This is consistent with our previous suggestion that the IR phase supports scale invariance in the infrared. We discuss the role of Anderson-like aspects in this thermal regime and emphasize that the combination of gauge field topology and disorder plays a key role in shaping its IR physics. Our conclusions are conveyed by the structure of Dirac spectral non-analyticities.

United States

Andrei Alexandru

Czechia

Ivan Horváth

Anderson metal-to-critical transition in QCD

We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a one-dimensional disordered wire and the localization of mass eigenstates along a local “theory space” with random mass parameters. Mass eigenstates are localized even at arbitrarily weak disorder, with exponentially suppressed couplings to sites in the theory space. The mechanism is quite general and may be used to exponentially localize fields of any spin. We apply the localization mechanism to two hierarchies in standard model parameters—the smallness of neutrino masses and the ordering of quark masses—and comment on the possible relevance to the electroweak hierarchy problem. This raises the compelling possibility that some of the large hierarchies observed in and beyond the standard model may result from disorder, rather than order.

Nathaniel Craig

Dave Sutherland

Exponential Hierarchies from Anderson Localization in Theory Space

We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions, in the temperature range [0.9, 1.9]T c . We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop P L , in the high temperature sea of P L ∼ 1. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.

Japan

Guido Cossu

Shoji Hashimoto

Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes

We study the problems of chiral symmetry breaking and eigenmode localisation in finite-temperature QCD by looking at the lattice Dirac operator as a random Hamiltonian. We recast the staggered Dirac operator into an unconventional three-dimensional Anderson Hamiltonian (“Dirac-Anderson Hamiltonian”) carrying internal degrees of freedom, with disorder provided by the fluctuations of the gauge links. In this framework, we identify the features relevant to chiral symmetry restoration and localisation of the low-lying Dirac eigenmodes in the ordering of the local Polyakov lines, and in the related correlation between spatial links across time slices, thus tying the two phenomena to the deconfinement transition. We then build a toy model based on QCD and on the Dirac-Anderson approach, replacing the Polyakov lines with spin variables and simplifying the dynamics of the spatial gauge links, but preserving the above-mentioned relevant dynamical features. Our toy model successfully reproduces the main features of the QCD spectrum and of the Dirac eigenmodes concerning chiral symmetry breaking and localisation, both in the ordered (deconfined) and disordered (confined) phases. Moreover, it allows us to study separately the roles played in the two phenomena by the diagonal and the off-diagonal terms of the Dirac-Anderson Hamiltonian. Our results support our expectation that chiral symmetry restoration and localisation of the low modes are closely related, and that both are triggered by the deconfinement transition.

Hungary

Matteo Giordano

Tamás Kovács

Ferenc Pittler

An Anderson-like model of the QCD chiral transition

With an explicit example, we show that Jordan frame and the conformally transformed Einstein frames clearly lead to different physics for a non-minimally coupled theory of gravity, namely Brans–Dicke theory, at least at the quantum level. The example taken up is the spatially flat Friedmann cosmology in Brans–Dicke theory.

Narayan Banerjee

Barun Majumder

A question mark on the equivalence of Einstein and Jordan frames