arXiv subjects

Andrea Cappelli

Publications and source records attributed to Andrea Cappelli.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamics of perfect fluids with anomalies from the fermionic path integral

The path integral of the Dirac fermion with vector and axial gauge backgrounds is analyzed near the infrared limit in the presence of residual irrelevant current-current interaction. After integrating out fermions, a semiclassical low-energy effective action is obtained, written in terms of currents. Its expression is found to correspond to the hydrodynamic action previously proposed for perfect barotropic fluids with anomalies at zero temperature. This approach also leads to two further hydrodynamic actions to be associated, respectively, with the Weyl fermion, and the Dirac fermion having independent vector and axial currents. These actions feature four- and five-dimensional bulk-boundary terms, owing to anomaly inflow, which are identified as being the so-called transgression forms. These are generalizations of Chern--Simons forms that involve two gauge fields: the dynamical field and the background field. The path-integral argument provides a ``microscopic'' explanation for several ingredients of the action formulation of hydrodynamics that are necessary to incorporate anomalies. It also clarifies the infrared reduction required to pass from the effective field theory to a local hydrodynamic description. This reduction is implemented by considering restricted variations of the action, familiar from hydrodynamics, which at the same time lead to four-dimensional equations of motion from the five-dimensional transgression terms.

hep-th↗

arXiv2026

Gauging in superconductors and other electronic systems

Ordinary, s-wave superconductors have been recognized as being topological phases of matter, in which the dynamical gauge field implies less understood global features. Using the tools of topological field theories and generalized symmetries, we provide an updated description of these systems. At very low energies, the Higgs model reduces to the BF theory, which exhibits topological order. Furthermore, the gauge field must be a spin$_c$ connection, to describe the spin of fermions forming Cooper pairs. Gauging implies that superconductors are inherently bosonic systems, yet they are endowed with a gravito-magnetic anomaly that is the remnant of their fermionic origin. We recognize that this anomaly is related to the Gaiotto-Kapustin-Thorngren bosonization, achieved via gauging fermion parity $(-1)^F$, now included in the gauge dynamics. This anomaly characterizes gauged electronic matter in great generality in three and four spacetime dimensions, forbidding trivial massive phases at low energy. It holds beyond the validity of the Higgs model, nd in other kinds of superconductors as well. It also appears in the nontrivial massless phase of three-dimensional electrodynamics, recently understood.

hep-th↗

arXiv2025

Bosonizations and dualities in 2+1 dimensions

We discuss two methods for relating bosonic and fermionic relativistic field theories in 2+1 dimensions, the $Z_2^f$ gauging and the flux attachment. The first is primarily a correspondence between topological theories. It amounts to summing over fermionic spin structures, as is familiar in two-dimensional conformal theories. Its inverse map, fermionization, shows how spin structures and $Z_2^f$ fermion parity emerge from a bosonic theory equipped with a dual $Z_2^{(1)}$ generalized symmetry. The second method,flux attachment, gives spin and statistics to charged particles by coupling them to a Chern-Simons theory, and provides the basis for the Abelian dualities. We illustrate the two bosonizations with explicit results in a solvable semiclassical conformal theory, and show their differences and interplays with particle-vortex dualities. We employ the so-called loop model, which can describe general infrared critical points in 2+1 dimensions in the semiclassical limit. We also combine the two bosonizations to obtain further duality relations. By applying $Z_2^f$ gauging to the Dirac-boson and Majorana-boson flux-attachment dualities, we find new relations between bosonic theories.

hep-th↗

arXiv2024

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form $Z_2$ symmetry of the bosonic theory and its gauging, which originates the fermion number $(-1)^F$, the spin sectors and the time reversal symmetry obeying ${\cal T}^2=(-1)^F$. These results are detailed for the effective action and the partition function on the geometry $S^2\times S^1$.

hep-th↗

arXiv2024

Hydrodynamics, anomaly inflow and bosonic effective field theory

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom.

hep-th↗

arXiv2023

Benchmarking the Ising Universality Class in $3 \le d < 4$ dimensions

The Ising critical exponents $η$, $ν$ and $ω$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon-expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

hep-th↗

arXiv2022

Quantum Field Theory Anomalies in Condensed Matter Physics

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary.

cond-mat.str-el↗

arXiv2021

W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge

The description of chiral quantum incompressible fluids by the W-infinity symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

hep-th↗

arXiv2020

Introducing a framework to assess newly created questions with Natural Language Processing

Statistical models such as those derived from Item Response Theory (IRT) enable the assessment of students on a specific subject, which can be useful for several purposes (e.g., learning path customization, drop-out prediction). However, the questions have to be assessed as well and, although it is possible to estimate with IRT the characteristics of questions that have already been answered by several students, this technique cannot be used on newly generated questions. In this paper, we propose a framework to train and evaluate models for estimating the difficulty and discrimination of newly created Multiple Choice Questions by extracting meaningful features from the text of the question and of the possible choices. We implement one model using this framework and test it on a real-world dataset provided by CloudAcademy, showing that it outperforms previously proposed models, reducing by 6.7% the RMSE for difficulty estimation and by 10.8% the RMSE for discrimination estimation. We also present the results of an ablation study performed to support our features choice and to show the effects of different characteristics of the questions' text on difficulty and discrimination.

cs.CL↗

arXiv2020

Quantization of a Self-dual Conformal Theory in (2+1) Dimensions

Compact nonlocal Abelian gauge theory in (2+1) dimensions, also known as loop model, is a massless theory with a critical line that is explicitly covariant under duality transformations. It corresponds to the large N_F limit of self-dual electrodynamics in mixed three-four dimensions. It also provides a bosonic description for surface excitations of three-dimensional topological insulators. Upon mapping the model to a local gauge theory in (3+1) dimensions, we compute the spectrum of electric and magnetic solitonic excitations and the partition function on the three torus T_3. Analogous results for the S^2 x S^1 geometry show that the theory is conformal invariant and determine the manifestly self-dual spectrum of conformal fields, corresponding to order-disorder excitations with fractional statistics.

hep-th↗

arXiv2020

R2DE: a NLP approach to estimating IRT parameters of newly generated questions

The main objective of exams consists in performing an assessment of students' expertise on a specific subject. Such expertise, also referred to as skill or knowledge level, can then be leveraged in different ways (e.g., to assign a grade to the students, to understand whether a student might need some support, etc.). Similarly, the questions appearing in the exams have to be assessed in some way before being used to evaluate students. Standard approaches to questions' assessment are either subjective (e.g., assessment by human experts) or introduce a long delay in the process of question generation (e.g., pretesting with real students). In this work we introduce R2DE (which is a Regressor for Difficulty and Discrimination Estimation), a model capable of assessing newly generated multiple-choice questions by looking at the text of the question and the text of the possible choices. In particular, it can estimate the difficulty and the discrimination of each question, as they are defined in Item Response Theory. We also present the results of extensive experiments we carried out on a real world large scale dataset coming from an e-learning platform, showing that our model can be used to perform an initial assessment of newly created questions and ease some of the problems that arise in question generation.

cs.LG↗

arXiv2018

Critical Ising Model in Varying Dimension by Conformal Bootstrap

The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d=2.2 for matching the Virasoro conformal blocks in the d=2 limit. The decoupling of states at the Ising point is studied for 3>d>2 and the vanishing of one structure constant at d=3 is found to persist till d=2 where it corresponds to a Virasoro null-vector condition.

hep-th↗

arXiv2018

Bulk-Boundary Correspondence in the Quantum Hall Effect

We present a detailed microscopic study of edge excitations for n filled Landau levels. We show that the higher-level wavefunctions possess a non-trivial radial dependence that should be integrated over for properly defining the edge conformal field theory. This analysis let us clarify the role of the electron orbital spin s in the edge theory and to discuss its universality, thus providing a further instance of the bulk-boundary correspondence. We find that the values s_i for each level, i=1,...,n, parameterize a Casimir effect or chemical potential shift that could be experimentally observed. These results are generalized to fractional and hierarchical fillings by exploiting the W-infinity symmetry of incompressible Hall fluids.

hep-th↗

arXiv2016

Three-dimensional Topological Insulators and Bosonization

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

cond-mat.str-el↗

arXiv2015

Multipole Expansion in the Quantum Hall Effect

The effective action for low-energy excitations of Laughlin's states is obtained by systematic expansion in inverse powers of the magnetic field. It is based on the W-infinity symmetry of quantum incompressible fluids and the associated higher-spin fields. Besides reproducing the Wen and Wen-Zee actions and the Hall viscosity, this approach further indicates that the low-energy excitations are extended objects with dipolar and multipolar moments.

cond-mat.str-el↗

arXiv2015

Nanoscale Phase Change Memory with Graphene Ribbon Electrodes

Phase change memory (PCM) devices are known to reduce in power consumption as the bit volume and contact area of their electrodes are scaled down. Here, we demonstrate two types of low-power PCM devices with lateral graphene ribbon electrodes: one in which the graphene is patterned into narrow nanoribbons and the other where the phase change material is patterned into nanoribbons. The sharp graphene "edge" contacts enable switching with threshold voltages as low as ~3 V, low programming currents (<1 μA SET, <10 μA RESET) and ON/OFF ratios >100. Large-scale fabrication with graphene grown by chemical vapor deposition also enables the study of heterogeneous integration and that of variability for such nanomaterials and devices.

cond-mat.mes-hall↗

arXiv2014

Stability of Topological Insulators with Non-Abelian Edge Excitations

Chiral-antichiral pairs of non-Abelian Hall states, like the Pfaffian, Read-Rezayi and NASS states, can be used to model two-dimensional time-reversal invariant topological insulators. Their stability was shown to be associated to the presence of a Z_2 anomaly and characterized by the same Z_2 index introduced for free fermion and Abelian systems. In this work, we continue the stability analysis by providing the form of time-reversal invariant interactions that gap the non-Abelian edge excitations. Our approach is based on the description of non-Abelian states as projections of corresponding "parent" Abelian states.

cond-mat.str-el↗

arXiv2013

Partition Functions and Stability Criteria of Topological Insulators

The non-chiral edge excitations of quantum spin Hall systems and topological insulators are described by means of their partition function. The stability of topological phases protected by time-reversal symmetry is rediscussed in this context and put in relation with the existence of discrete anomalies and the lack of modular invariance of the partition function. The $\Z_2$ characterization of stable topological insulators is extended to systems with interacting and non-Abelian edge excitations.

cond-mat.str-el↗