An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz method. We identify the boundary bound states and determine the ground state phase diagram. By analyzing the impurity contributions to the magnetization density and magnetic susceptibility, we demonstrate that a local moment is formed at the impurity site and is screened by the host electrons, consistent with Kondo physics.

China

Renjie Song

Mingchen Zheng

Junpeng Cao

Yupeng Wang

An integrable Anderson-impurity problem embedded in the one-dimensional Hubbard model

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

In this work we investigate 5-dimensional theories obtained from M-theory on genus one fibered threefolds which exhibit twisted algebras in their fibers. We provide a base-independent algebraic description of the threefolds and compute light 5D BPS states charged under finite sub-algebras of the twisted algebras. We further construct the Jacobian fibrations that are associated to 6-dimensional F-theory lifts, where the twisted algebra is absent. These 6/5-dimensional theories are compared via twisted circle reductions of F-theory to M-theory. In the 5-dimensional theories we discuss several geometric transitions that connect twisted with untwisted fibrations. We present detailed discussions of   <math> <msubsup> <mi>e</mi> <mn>6</mn> <mfenced> <mn>2</mn> </mfenced> </msubsup> </math>  $$ {\mathfrak{e}}_6^{(2)} $$ ,   <math> <msubsup> <mi>so</mi> <mn>8</mn> <mfenced> <mn>3</mn> </mfenced> </msubsup> </math>  $$ {\mathfrak{so}}_8^{(3)} $$  and   <math> <msubsup> <mi>su</mi> <mn>3</mn> <mfenced> <mn>2</mn> </mfenced> </msubsup> </math>  $$ {\mathfrak{su}}_3^{(2)} $$  twisted fibers and provide several explicit example threefolds via toric constructions. Finally, limits are considered in which gravity is decoupled, including Little String Theories for which we match 2-group symmetries across twisted T-dual theories.

United States

Lara Anderson

James Gray

Paul-Konstantin Oehlmann

Twisted Fibrations in M/F-theory

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.

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

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.

Andrei Alexandru

Czechia

Ivan Horváth

Anderson metal-to-critical transition in QCD

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

Sweden

Magdalena Larfors

Matthew Magill

Robin Schneider

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in ℙ4.

Mathis Gerdes

Sven Krippendorf

Nikhil Raghuram

United Kingdom

CERN

Fabian Ruehle

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification geometry. These effects are crucial for a number of key features of the theory, including vacuum stability and moduli stabilization. Despite their importance, few tools exist in the literature to compute such effects in a given heterotic vacuum. In this work we present new techniques to explicitly determine holomorphic Chern-Simons invariants in heterotic string compactifications. The key technical ingredient in our computations are real bundle morphisms between the gauge and tangent bundles. We find that there are large classes of examples, beyond the standard embedding, where the Chern-Simons superpotential vanishes. We also provide explicit examples for non-flat bundles where it is non-vanishing and non-integer quantized, generalizing previous results for Wilson lines.

Andre Lukas

Juntao Wang

Chern-Simons invariants and heterotic superpotentials