arXiv subjects

Nabil Iqbal

Publications and source records attributed to Nabil Iqbal.

At least 19 recordsLinked to original sources

arXiv2026

Information Spreading in Diffusion Models from Effective Field Theory

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

hep-th↗

arXiv2026

Spontaneous symmetry breaking and Goldstone modes for deep information propagation

In physical systems, whenever a continuous symmetry is spontaneously broken, the system possesses excitations called Goldstone modes, which allow coherent information propagation over long distances and times. In this work, we study deep neural networks whose internal layers are equivariant under a continuous symmetry and may therefore support analogous Goldstone-like degrees of freedom. We demonstrate, both analytically and empirically, that these degrees of freedom enable coherent signal propagation across depth and recurrent iterations, providing a mechanism for stable information flow without relying on architectural stabilizers such as residual connections or normalization. In feedforward networks, this results in improved trainability and representational diversity across layers. In recurrent settings, we demonstrate the same mechanism is valuable for long-term memory by propagating information over recurrent iterations, thereby improving performance of RNNs and GRUs on long-sequence modeling tasks.

cs.LG↗

arXiv2025

Phase structure of self-dual lattice gauge theories in 4d

We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their 't~Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of $\mathbb Z_4$ by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.

hep-th↗

arXiv2025

AdS-GNN -- a Conformally Equivariant Graph Neural Network

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

cs.LG↗

arXiv2025

Jena lectures on generalized global symmetries: principles and applications

This is an elementary set of lectures on generalized global symmetries originally given at the Jena TPI School on QFT and Holography, designed to be accessible to the reader with a basic knowledge of quantum field theory. Topics covered include an introduction to higher-form symmetries with selected applications: Abelian and non-Abelian gauge theories in the continuum and on the lattice, statistical mechanical systems, the Adler-Bell-Jackiw anomaly from the point of view of non-invertible symmetry, and magnetohydrodynamics. Mathematical formalism is kept to a minimum and an emphasis is placed on understanding the global symmetry structure present in well-known models.

hep-th↗

arXiv2025

Wilson lines with endpoints in 3d CFT

In Abelian gauge theories with dynamical matter, Wilson lines can end on the insertions of charged fields. We study the endpoints of Wilson lines in large $N$ bosonic QED$_3$. at its critical point. We first study the stability of an infinite Wilson line in the $\mathbb{CP}^{N-1}$ model by computing the appropriate functional determinant at large $N$. We also compute the conformal dimension of the lowest-dimension endpoint of the line to first order in $N^{-1}$. Along the way we calculate the field-strength tensor $F_{\mu\nu}$ in the presence of the line with endpoint and discuss a state-operator correspondence for the endpoints, as well as the existence of an OPE that allows two open-ended Wilson lines to be glued together into a single line.

hep-th↗

arXiv2024

Machine learning and optimization-based approaches to duality in statistical physics

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual Hamiltonian and a map from the original to the dual observables. By using simple neural networks to parameterize these maps and introducing a loss function that penalises the difference between correlation functions in original and dual models, we formulate the process of duality discovery as an optimization problem. We numerically solve this problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model, reconstructing the known mapping of temperatures. We also discuss an alternative approach which uses known features of the mapping of topological lines to reduce the problem to optimizing the couplings in a dual Hamiltonian, and explore next-to-nearest neighbour deformations of the 2d Ising duality. We discuss future directions and prospects for discovering new dualities within this framework.

cond-mat.stat-mech↗

arXiv2024

Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma -- defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD -- remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.

hep-th↗

arXiv2024

Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics

Chiral magnetohydrodynamics is devoted to understanding the late-time and long-distance behavior of a system with an Adler-Bell-Jackiw anomaly at finite temperatures. The non-conservation of the axial charge is determined by the topological density $\vec{E} \cdot \vec{B}$; in a classical hydrodynamic description this decay rate can be suppressed by tuning the background magnetic field to zero. However it is in principle possible for thermal fluctuations of $\vec{E} \cdot \vec{B}$ to result in a non-conservation of the charge even at vanishing $B$-field; this would invalidate the classical hydrodynamic effective theory. We investigate this by computing the real-time susceptibility of the topological density at one-loop level in magnetohydrodynamic fluctuations, relating its low-frequency limit to the decay rate of the axial charge. We find that the frequency-dependence of this susceptibility is sufficiently soft as to leave the axial decay rate unaffected, validating the classical hydrodynamic description. We show that the susceptibility contains non-analytic frequency-dependence which is universally determined by hydrodynamic data. We comment briefly on possible connections to the recent formulation of the ABJ anomaly in terms of non-invertible symmetry.

hep-th↗

arXiv2023

2-group global symmetries, hydrodynamics and holography

2-group global symmetries are a particular example of how higher-form and conventional global symmetries can fuse together into a larger structure. We construct a theory of hydrodynamics describing the finite-temperature realization of a 2-group global symmetry composed out of $U(1)$ zero-form and $U(1)$ one-form symmetries. We study aspects of the thermodynamics from a Euclidean partition function and derive constitutive relations for ideal hydrodynamics from various points of view. Novel features of the resulting theory include an analogue of the chiral magnetic effect and a chiral sound mode propagating along magnetic field lines. We also discuss a minimalist holographic description of a theory dual to 2-group global symmetry and verify predictions from hydrodynamic descriptions. Along the way we clarify some aspects of symmetry breaking in higher-form theories at finite temperature.

hep-th↗

arXiv2023

Higher-form symmetries, anomalous magnetohydrodynamics, and holography

In $U(1)$ Abelian gauge theory coupled to fermions, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $F_{μν} \tilde{F}^{μν}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. We construct a holographic dual with this symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields.

hep-th↗

arXiv2022

Towards an effective action for chiral magnetohydrodynamics

We consider chiral magnetohydrodynamics, i.e. a finite-temperature system where an axial $U(1)$ current is not conserved due to an Adler-Bell-Jackiw anomaly saturated by the dynamical operator $F_{μν} \tilde{F}^{μν}$. We express this anomaly in terms of the 1-form symmetry associated with magnetic flux conservation and study its realization at finite temperature. We present Euclidean generating functional and dissipative action approaches to the dynamics and reproduce some aspects of chiral MHD phenomenology from an effective theory viewpoint, including the chiral separation and magnetic effects. We also discuss the construction of non-invertible axial symmetry defect operators in our formalism.

hep-th↗

arXiv2022

A Goldstone theorem for continuous non-invertible symmetries

We study systems with an Adler-Bell-Jackiw anomaly in terms of non-invertible symmetry. We present a new kind of non-invertible charge defect where a key role is played by a local current operator localized on the defect. The charge defects are now labeled by elements of a continuous $U(1)$. We use this construction to prove an analogue of Goldstone's theorem for such non-invertible symmetries. We comment on possible applications to string theory.

hep-th↗

arXiv2022

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field -- defined on the space of closed loops -- that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

hep-th↗

arXiv2021

Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge coupling. There exists a self-dual value of the gauge coupling where one may study the model as a function of the remaining matter coupling. Using Monte Carlo simulations based on a worldline/worldsheet representation of the system we evaluate order parameters for spontaneous breaking of self-duality. We find that in some interval of the matter coupling self-duality becomes broken spontaneously. We determine the endpoints of this interval and study the nature of the corresponding critical points. Finally we explore the system away from the self-dual gauge coupling and show that when crossing the self-dual point a first order jump is seen in the order parameters.

hep-lat↗

arXiv2021

Towards traversable wormholes from force-free plasmas

The near-horizon region of magnetically charged black holes can have very strong magnetic fields. A useful low-energy effective theory for fluctuations of the fields, coupled to electrically charged particles, is force-free electrodynamics. The low energy collective excitations include a large number of Alfven wave modes, which have a massless dispersion relation along the field worldlines. We attempt to construct traversable wormhole solutions using the negative Casimir energy of the Alfven wave modes, analogously to the recent construction using charged massless fermions. The behaviour of massless scalars in the near-horizon region implies that the size of the wormholes is strongly restricted and cannot be made large, even though the force free description is valid in a larger regime.

hep-th↗

arXiv2021

Higher-form symmetry breaking and holographic flavour

We study the realisation of higher-form symmetries in the holographic dual of gauge theories coupled to probe matter in the fundamental. We particularly focus on the dual of U(N) gauge theory coupled to fundamental matter. We demonstrate the existence of a continuous 1-form symmetry associated with the conservation of magnetic flux and show that this symmetry is spontaneously broken in the IR when the flavour degrees of freedom are gapped. We numerically compute the spectral function of the 2-form current and demonstrate the existence of the associated Goldstone mode. We compare to expectations at weak-coupling.

hep-th↗

arXiv2020

Generalized global symmetries and holography

We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous. Such higher-form global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a non-conformal field theory with a marginally running double-trace coupling. We explore its hydrodynamic behavior at finite temperature and make contact with recent symmetry-based formulations of magnetohydrodynamics. We also argue that discrete global symmetries on the boundary are dual to discrete gauge theories in the bulk. Such gauge theories have a bulk Chern-Simons description: we clarify the conventional 0-form case and work out the 1-form case. Depending on boundary conditions, such discrete symmetries may be embedded in continuous higher-form symmetries that are spontaneously broken. We study the resulting boundary Goldstone mode, which in the 1-form case may be thought of as a boundary photon. Our results clarify how the global form of the field theory gauge group is encoded in holography. Finally, we study the interplay of Maxwell and Chern-Simons terms put together. We work out the operator content and demonstrate the existence of new backreacted anisotropic scaling solutions that carry higher-form charge.

hep-th↗