Low-energy Theory Research Articles

Criterion of perturbativity with the mass-dependent beta function in extended Higgs models

In order to realize an electroweak first-order phase transition, a category of extended Higgs models with relatively large self-coupling constants is often considered. In such a scenario, the running coupling constants can blow up at an energy scale much below the Planck scale. To clarify the allowed parameter space of the model, it is important to evaluate the scale where perturbative calculation breaks down. In the renormalization group equation analysis using the mass-independent renormalization scheme, we need a matching condition to connect the low energy theory and the high energy theory. Consequently, the analysis depends on the details of the matching condition. On the other hand, an analysis with the mass-dependent beta function can be performed in a simpler way because the threshold effect is automatically included in the beta function. In this paper, using the mass-dependent beta function, we discuss the application limit of perturbative calculations at the one-loop level. First, we explain the essence of our method and compare our results with those based on the mass-independent beta function in a toy model with two complex scalar fields. We then apply our method to a more realistic model, i.e., the inert doublet model. We find that, in our method, in which the threshold effect is automatically included, the energy scale where the perturbative calculation breaks down can be higher than the one using the mass-independent beta function, especially when the blowup scale is relatively low. Published by the American Physical Society 2024

Numerical Study on the Summer High-Temperature Climate Adaptation of Traditional Dwellings in the Western Plains of Sichuan, China

Ongoing global climate change, marked by sustained warming and extreme weather events, poses a severe threat to both the Earth’s ecosystems and human communities. Traditional settlements that underwent natural selection and evolution developed a unique set of features to adapt to and regulate the local climate. A comprehensive exploration of the spatial patterns and mechanisms of the adaptation of these traditional settlements is crucial for investigating low-energy climate adaptation theories and methods as well as enhancing the comfort of future human habitats. This study used numerical simulations and field measurements to investigate the air temperature, relative humidity, wind speed, wind direction, and thermal comfort of traditional settlements in Western Sichuan Plain, China, and uncovered their climate suitability characteristics to determine the impact mechanisms of landscape element configurations (building height, building density, tree coverage, and tree position) and spatial patterns on microclimates within these settlements. The results revealed the structural and layout strategies adopted by traditional settlements to adapt to different climatic conditions, providing valuable insights for future rural protection and planning and enhancing climate resilience through natural means. These findings not only contribute to understanding the climate adaptability of Earth’s ecosystems and traditional settlements but also offer new theories and methods to address the challenges posed by climate change.

Phonon-mediated unconventional superconductivity in rhombohedral stacked multilayer graphene

Understanding the origin of superconductivity in correlated two-dimensional materials is a key step in leveraging material engineering techniques for next-generation nanoscale devices. While it is widely accepted that phonons fluctuations only mediate conventional (s-wave) superconductivity, the common phenomenology of superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well as in a large family of graphene-based moiré systems, suggests a common superconducting mechanism across these platforms. In particular, in all these platforms some superconducting regions violate the Pauli limit, indicating unconventional superconductivity, naively ruling out conventional phonon-mediated pairing as the underlying mechanism. Here we combine first principles simulations with effective low-energy theories to investigate the superconducting mechanism and pairing symmetry in rhombohedral stacked graphene multilayers. We find that phonon-mediated superconductivity explains the main experimental findings, namely the displacement field and doping level dependence of the critical temperature, and the presence of two superconducting regions with different pairing symmetries that depend on the parent normal state. In particular, we find that intra-valley phonon scattering favors a triplet f-wave pairing when combined with electronic correlations stabilizing a spin- and valley-polarized normal state. We also propose a so far unexplored superconducting region at higher hole doping densities nh ≈ 4 × 1012 cm−2, and demonstrate how this highly hole-doped regime can be reached in heterostructures consisting of monolayer α-RuCl3 and rhombohedral trilayer graphene. Our findings promote phonon-mediated pairing as a strong contender to explain superconductivity across a wide range of graphene platforms, and demonstrate that phonons can, in fact, stabilize unconventional superconducting orders.

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Dimensionally reducing generalized symmetries from (3+1)-dimensions

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible symmetries, in four dimensions. In this paper we shall examine what happens to this structure when the 4d theory is compactified to lower dimensions, specifically to 3d and 2d, where we shall be mainly interested in generalized symmetry structures whose origin can be linked to mixed flavor-gauge anomalies. We discuss several aspects of the compactification, and in particular argue that under certain conditions the discussed generalized symmetry structure may trivialize in the infrared. Nevertheless, we show that even when this happens the presence of the 4d generalized symmetry structure may still leave an imprint on the low-energy theory in terms of additional ’t Hooft anomalies or by breaking part of the symmetry. We apply and illustrate this using known examples of compactifications from four dimensions, particularly, the reduction of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 U(Nc) SQCD on a circle to 3d and on a sphere to 2d.

Candidate phases for SU(2) adjoint QCD$_4$ with two flavors from $\mathcal{N}=2$ supersymmetric Yang-Mills theory

We study four-dimensional adjoint QCD with gauge group SU(2)SU(2) and two Weyl fermion flavors, which has an SU(2)_RSU(2)R chiral symmetry. The infrared behavior of this theory is not firmly established. We explore candidate infrared phases by embedding adjoint QCD into {\mathcal N}=2𝒩=2 supersymmetric Yang-Mills theory deformed by a supersymmetry-breaking scalar mass MM that preserves all global symmetries and ’t Hooft anomalies. This includes ’t Hooft anomalies that are only visible when the theory is placed on manifolds that do not admit a spin structure. The consistency of this procedure is guaranteed by a nonabelian spin-charge relation involving the SU(2)_RSU(2)R symmetry that is familiar from topologically twisted {\mathcal N}=2𝒩=2 theories. Since every vacuum on the Coulomb branch of the {\mathcal N}=2𝒩=2 theory necessarily matches all ’t Hooft anomalies, we can generate candidate phases for adjoint QCD by deforming the theories in these vacua while preserving all symmetries and ’t Hooft anomalies. One such deformation is the supersymmetry-breaking scalar mass MM itself, which can be reliably analyzed when MM is small. In this regime it gives rise to an exotic Coulomb phase without chiral symmetry breaking. By contrast, the theory near the monopole and dyon points can be deformed to realize a candidate phase with monopole-induced confinement and chiral symmetry breaking. The low-energy theory consists of two copies of a \mathbb{CP}^1ℂℙ1 sigma model, which we analyze in detail. Certain topological couplings that are likely to be present in this \mathbb{CP}^1ℂℙ1 model turn the confining solitonic string of the model into a topological insulator. We also examine the behavior of various candidate phases under fermion mass deformations. We speculate on the possible large-MM behavior of the deformed {\mathcal N}=2𝒩=2 theory and conjecture that the \mathbb{CP}^1ℂℙ1 phase eventually becomes dominant.

Moiré band renormalization due to lattice mismatch in bilayer graphene

We investigated the band renormalization caused by the compressive-strain-induced lattice mismatch in parallel AA stacked bilayer graphene using two complementary methods: the tight-binding approach and the low-energy continuum theory. While a large mismatch does not alter the low-energy bands, a small one reduces the bandwidth of the low-energy bands along with a decrease in the Fermi velocity. In the tiny-mismatch regime, the low-energy continuum theory reveals that the long-period moiré pattern extensively renormalizes the low-energy bands, resulting in a significant reduction of bandwidth. Meanwhile, the Fermi velocity exhibits an oscillatory behavior and approaches zero at specific mismatches. However, the resulting low-energy bands are not perfectly isolated flat, as seen in twisted bilayer graphene at magic angles. These findings provide a deeper understanding of moiré physics and offer valuable guidance for related experimental studies in creating moiré superlattices using two-dimensional van der Waals heterostructures.

AutoEFT: Automated operator construction for effective field theories

The program AutoEFT is described. It allows one to generate Effective Field Theories (EFTs) from a given set of fields and symmetries. Allowed fields include scalars, spinors, gauge bosons, and gravitons. The symmetries can be local or global Lie groups based on U(1) and SU(N). The mass dimension of the EFT is limited only by the available computing resources. The operators are stored in a compact, human and machine-readable format. Aside from the program itself, we provide input files for EFTs based on the Standard Model and a number of its extensions. These include additional particles and symmetries, EFTs with minimal flavor violation, and gravitons. Program summaryProgram title:AutoEFTCPC Library link to program files:https://doi.org/10.17632/z8xm2hpbsp.1Developer's repository link:https://gitlab.com/auto_eft/autoeftLicensing provisions: MIT licenseProgramming language:PythonNature of problem: The bottom-up construction of an Effective Field Theory (EFT) which describes physics below a certain energy scale Λ requires obtaining a set of operators, composed of fields with mass m≪Λ, that are invariant under certain symmetries. One is primarily interested in complete sets of independent operators, called operator bases. Their construction for a given mass dimension of the operators is nontrivial due to algebraic and kinematic relations that may render different operators redundant. Except for the lowest mass dimensions, the number of operators is so large that the task of constructing an explicit EFT operator basis requires a high degree of automation on a computer. In addition, an automated approach will allow one to immediately take into account newly postulated or discovered light particles beyond the Standard Model.Solution method: Based on the group theoretical techniques and concepts established in Refs. [1–9] and in particular Refs. [10,11], we developed the program AutoEFT, capable of constructing a non-redundant on-shell operator basis for general EFTs and arbitrary mass dimension. Provided a suitable model file, the respective operator basis is generated explicitly, including contractions of the symmetry group indices, in a fully automated fashion. Due to the generality of the algorithm, it can be applied to a variety of low-energy scenarios. The underlying low-energy theory is encoded in a model file which defines the symmetries and the field content. The fairly simple format enables the user to compose their own model files and to construct the respective operator basis with minimal effort.Additional comments including restrictions and unusual features: In its current form, AutoEFT is restricted to theories including particles with spin 0, 1/2, 1, and 2, where the latter two are considered massless. In addition, AutoEFT only constructs operators that mediate proper interactions, meaning that any operator must be composed of at least three fields. The internal symmetries must be given as factors of U(1) and SU(N) groups. In principle, operator bases can be generated for any mass dimension, which is, however, limited by the available computing resources.

Mott insulator-density ordered superfluid transition and ‘shamrock transition’ in a frustrated triangle lattice

Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z 2 × Z 3. We call the transition a ‘shamrock transition’, due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.

Dynamical t/U Expansion of the Doped Hubbard Model

We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.

One-loop effective action up to dimension eight: Integrating out heavy fermion(s)

We present the universal one-loop effective action up to dimension eight after integrating out heavy fermion(s) using the Heat-Kernel method. We have discussed how the Dirac operator being a weak elliptic operator, the fermionic operator still can be written in the form of a strong elliptic one such that the Heat-Kernel coefficients can be used to compute the fermionic effective action. This action captures the footprint of both the CP conserving as well as violating UV interactions. As it does not rely on the specific forms of either UV or low energy theories, can be applicable for a very generic action. Our result encapsulates the effects of heavy fermion loop through Yukawa couplings only.

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the Kagome and breathing Kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct a consistent lattice Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two apparently novel phenomena: an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing Kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

The inheritance of energy conditions: Revisiting no-go theorems in string compactifications

One of the fundamental challenges in string theory is to derive realistic four-dimensional cosmological backgrounds from it despite strict consistency conditions that constrain its possible low-energy backgrounds. In this work, we focus on energy conditions as covariant and background-independent consistency requirements in order to classify possible backgrounds coming from low-energy string theory in two steps. Firstly, we show how supergravity actions obey many relevant energy conditions under some reasonable assumptions. Remarkably, we find that the energy conditions are satisfied even in the presence of objects which individually violate them due to the tadpole cancellation condition. Thereafter, we list a set of conditions for a higher-dimensional energy condition to imply the corresponding lower-dimensional one, thereby categorizing the allowed low-energy solutions. As for any no-go theorem, our aim is to highlight the assumptions that must be circumvented for deriving four-dimensional spacetimes that necessarily violate these energy conditions, with emphasis on cosmological backgrounds.

Quasi-fractionalization of edge spin in chirality-assisted cluster-based Haldane state on triangular spin tube

Fractionalization of quantum degrees of freedom holds the key to finding new phenomena in physics, e.g., the quark model in hadron physics and the spin-charge separation in strongly-correlated electron systems. A typical example of the fractionalization in quantum spin systems is the spin-1 Haldane state, whose intriguing characteristics are well described by fractionalized virtual spins, delivering two individual spin-1/2 degrees of freedom as edge states. Here we theoretically propose an exotic extension of the Haldane state to the pseudo spin-1 model consisting of the mixture of real spin and spin chirality, resulting in quasi-fractionalization of spin-1/2 magnetization, i.e., an approximately-1/4 spin. Existence of the edge state is confirmed both analytically and numerically in a triangular spin tube, combining a low-energy perturbation theory and variational matrix-product state method. Our study not only proposes an unconventional quantum spin object but paves a way to chop the elementary quantities further.

On/off scale separation

We discuss minimally supersymmetric AdS3 flux vacua of massive type IIA supergravity on G2-orientifolds. We find that configurations with broken scale-separation can be within finite distance from scale-separated ones, while both remain at large volume, weak coupling and have moduli stabilization. The transition is achieved with the use of a D4-brane modulus, which allows the F4 flux to jump, and has an effective potential always accessible to the three-dimensional low-energy theory. Our analysis further allows us to check the distance conjecture quantitatively, as we can track explicitly the masses of the KK modes.

Chronological-safe kind of geometric phase for C60 fullerenes in Gödel space–times

In this paper, we investigate a rotating fullerene molecule with Ih symmetry within the framework of non-inertial space-times. We use a low-energy geometric theory to describe the molecule as a two-dimensional spherical space of Gödel type. Using the well-known fictitious ’t Hooft–Polyakov monopole to decouple the doublet associated with the lattice, we employ the Dirac factor method to derive a geometric phase for the fermions in the system. We also discuss the chronology protection feature of the phase through specific geometric considerations for the system.

Axion effective potentials induced by heavy sterile fermions

A model of (3 + 1)-dimensional leptogenesis, proposed previously by the authors, requires a CPT Violating (CPTV) background of the Kalb–Ramond (KR) axion field. The KR axion is a pseudoscalar, which is dual to the field strength of the spin-one field present in the massless gravitational multiplet in the theory of closed bosonic strings (compactified to four dimensions). Microscopic models for the emergence of such backgrounds are provided both by low-energy string-inspired gravitational theories with torsion (including (primordial) gravitational and axial gauge anomalies) and by Einstein–Cartan gravity, a closely related simpler model. In this work we examine the pseudoscalar quanta of the KR axion in this background using the methods of effective field theory. In our model for leptogenesis there is a single sterile right-handed neutrino (RHN) with mass m_N. At energies lower than m_N, an axion potential is derived by integrating out at one loop the sterile neutrino in the spirit of effective field theory. The stability of this axion potential is important for the viability of our model. The vacuum of this potential is generally metastable. The stability of the vacuum is determined by the ratio of the torsion-induced-axion coupling (which depends on the string mass scale) to m_N, which should be larger or equal to one, for the validity of our effective field theory. The vacuum is metastable only for axion couplings much larger than the sterile neutrino mass (large string mass scales, e.g. comparable to the four-dimensional Planck mass), with a lifetime much larger than the age of the observable Universe. By contrast, if axion couplings are comparable to the RHN mass the false vacuum is highly unstable, with a lifetime much smaller than the age of the observable Universe; in this case the CPTV leptogenesis scenario is not viable.

Bromine Adsorption and Thermal Stability on Rh(111): A Combined XPS, LEED and DFT Study.

This study addresses a fundamental question in surface science: the adsorption of halogens on metal surfaces. Using synchrotron radiation-based high-resolution X-ray photoelectron spectroscopy (XPS), temperature-programmed XPS, low-energy electron diffraction (LEED) and density functional theory (DFT) calculations, we investigated the adsorption and thermal stability of bromine on Rh(111) in detail. The adsorption of elemental bromine on Rh(111) at 170 K was followed in situ by XPS in the Br 3d region, revealing two individual, coverage-dependent species, which we assign to fcc hollow- and bridge-bound atomic bromine. In addition, we find a significant shift in binding energy upon increasing coverage due to adsorbate-adsorbate interactions. Subsequent heating shows a high thermal stability of bromine on Rh(111) up to above 1000 K, indicating strong covalent bonding. To complement the XPS data, LEED was used to study the long-range order of bromine on Rh(111): we observe a (√3×√3)R30° structure for low coverages (≤0.33 ML) and a star-shaped compression structure for higher coverages (0.33-0.43 ML). Combining LEED and DFT calculations, we were able to visualize bromine adsorption on Rh(111) in real space for varying coverages.

Evidence of pseudogravitational distortions of the Fermi surface geometry in the antiferromagnetic metal FeRh

The confluence between high-energy physics and condensed matter has produced groundbreaking results via unexpected connections between the two traditionally disparate areas. In this work, we elucidate additional connectivity between high-energy and condensed matter physics by examining the interplay between spin-orbit interactions and local symmetry-breaking magnetic order in the magnetotransport of thin-film magnetic semimetal FeRh. We show that the change in sign of the normalized longitudinal magnetoresistance observed as a function of increasing in-plane magnetic field results from changes in the Fermi surface morphology. We demonstrate that the geometric distortions in the Fermi surface morphology are more clearly understood via the presence of pseudogravitational fields in the low-energy theory. The pseudogravitational connection provides additional insights into the origins of a ubiquitous phenomenon observed in many common magnetic materials and points to an alternative methodology for understanding phenomena in locally-ordered materials with strong spin-orbit interactions.

Axion-polaritons in the magnetic dual chiral density wave phase of dense QCD

We investigate the propagation of electromagnetic radiation in the magnetic dual chiral density wave (MDCDW) phase of dense quark matter. Considering the theory of low-energy fluctuations in this phase, we show how linearly polarized photons reaching the MDCDW medium couple to the fluctuation field to produce two hybridized modes of propagation that we call in analogy with similar phenomenon in condensed matter physics axion polaritons, one of them being gapless and the other gapped. The gapped mode's gap is proportional to the background magnetic field and inversely proportional to the amplitude of the inhomogeneous condensate. The generation of axion polaritons can be traced back to the presence of the chiral anomaly in the low-energy theory of the fluctuations. Considering the Primakoff effect in the MDCDW medium, we argued that axion polaritons can be generated inside quark stars bombarded by energetic photons coming from gamma-ray bursts and point out that this mechanism could serve to explain the missing pulsar paradox in the galaxy center.