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Norton Lee

Publications and source records attributed to Norton Lee.

At least 19 recordsLinked to original sources

TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma

TokaMind is a multi-modal transformer (MMT) foundation model pre-trained on tokamak plasma diagnostics data from MAST, where it was shown to outperform CNN-based approaches on fusion benchmarks. We investigate whether its learned representations generalize to physically distinct but structurally analogous domains. Through systematic experimentation across four domains-industrial bearing degradation, NASA CMAPSS turbofan degradation, and two independent power grid PMU datasets-we identify four transfer-favoring characteristics that help explain where TokaMind's pretrained representations are most effective. Power grid synchrophasor data matches this target-domain profile most directly, while industrial degradation datasets demonstrate that TokaMind can still yield useful performance under partial alignment, especially when task design and feature construction expose physically meaningful degradation structure. On the GESL/PNNL 500-event benchmark with provider-aware evaluation, TokaMind achieves test $\text{F1} = 0.837 \pm 0.040$ (3~seeds) for severe event classification. Our central finding, however, is not the aggregate score: classification difficulty is structurally determined by provider-level grid topology, not model capacity. In the single-window early-warning regime, TokaMind outperforms a CNN baseline (F1~0.889 vs.~0.878)--a reversal that disappears as more event windows are provided. Furthermore, Critical Slowing Down (CSD) indicators, used as a confidence gate rather than a classification label, improve F1 from 0.696 to 0.750 at 63% coverage-outperforming the CNN baseline (0.636) at any coverage level. These results establish the first cross-domain validation of TokaMind outside nuclear fusion and propose a transferability framework and revised evaluation protocol for multi-source PMU datasets.

physics.plasm-ph

Integrable Systems for Generalized Toric Polygons and Higgsed 5d N=1 Theories

The interplay between toric Calabi-Yau 3-folds, dimer integrable systems, and 5-dimensional quantum field theories has proved fruitful. We extend this framework to generalized toric polygons (GTPs) and show that their integrable systems arise from refined birational transformations of known dimer integrable systems acting on the Casimirs and Hamiltonians as well as the Poisson structure and spectral curves. We argue that these transformations are realized as Hanany-Witten transitions producing (p,q) 5-brane webs dual to GTPs. We show that the resulting 5d N=1 theory is obtained by Higgsing a higher-rank theory whose associated toric Calabi-Yau has a toric diagram of the same shape as the GTP.

hep-th

Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons

Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d N=1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds. We present a complete classification of dimer integrable systems corresponding to the 30 brane tilings whose toric Calabi-Yau 3-folds are given by the 16 reflexive polygons in 2 dimensions. For each dimer integrable system associated to a reflexive polygon, we present the Casimirs, the single Hamiltonian built from 1-loops, the spectral curve, and the Poisson commutation relations. We also identify all birational equivalences between dimer integrable systems in this classification by presenting the birational transformations that match the Casimirs and the Hamiltonians as well as the spectral curves and Poisson structures between equivalent dimer integrable systems. In total, we identify 16 pairs of birationally equivalent dimer integrable systems which combined with Seiberg duality between the corresponding brane tilings form 5 distinct equivalence classes. Echoing phenomena observed for brane brick models realizing a family of 2d (0,2) supersymmetric gauge theories corresponding to toric Calabi-Yau 4-folds, we illustrate that deformations of brane tilings, including mass deformations, correspond to the birational transformations we discover in this work, and leave invariant the number of generators of the mesonic moduli space as well as the corresponding U(1)R-refined Hilbert series.

hep-th

Dimers for Relativistic Toda Models with Reflective Boundaries

We construct dimer graphs for relativistic Toda chains associated with classical untwisted Lie algebras of A, B, C$_0$, C$_\pi$, D types and twisted A, D types. We show that the Seiberg-Witten curve of 5d $\mathcal{N}=1$ pure supersymmetric gauge theory of gauge group $G$ is a spectral curve of the relativistic Toda chain of the dual group $G^\vee$.

hep-th

$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

We study the quantization of the moduli space of multiplicative Higgs bundles through the lens of five-dimensional $\mathcal{N}=1$ supersymmetric gauge theories in $\Omega$-background. We extend the 4d $\mathcal{N}=2$ gauge theoretical construction of key geometric and representation-theoretic structures, established in earlier works, to the five-dimensional uplift. We construct and analyze the $Q$-operators and $q$-opers associated with the canonical codimension-two defect: the $Q$-operators are defined via the insertion of the defect, while the $q$-opers arise as the $q$-difference chiral ring equations in its presence. The $q$-oper difference equations are further identified with the Baxter TQ equations for XXZ spin chains constructed from tensor products of bi-infinite evaluation modules over quantum affine algebras of type ${\mathfrak{gl}}(n)$. We define a $q$-difference module structure on the space of monodromy codimension-two defect partition functions and show that the eigenstates of the $Q$-operators, constructed from monodromy defects, simultaneously diagonalize the quantum Hamiltonians of the XXZ spin chain. A Fourier transformation exchanges the $Q$-operators associated with two XXZ spin chains bispectral dual to each other. Finally, we relate these constructions to the quantum cluster algebra arising from the BPS quiver of the 5d theory, and re-express the R-matrices in terms of the cluster variables.

hep-th

Birational Transformations on Dimer Integrable Systems

We show that when two toric Calabi-Yau 3-folds and their corresponding toric varieties are related by a birational transformation, they are associated with a pair of dimer models on the 2-torus that define dimer integrable systems, which themselves become birationally equivalent. These integrable systems defined by dimer models were first introduced by Goncharov and Kenyon. We illustrate this equivalence explicitly using a pair of dimer integrable systems corresponding to the abelian orbifolds of the form C^3/Z_4 x Z_2 with orbifold action (1,0,3)(0,1,1) and C/Z_2 x Z_2 with action (1,0,0,1)(0,1,1,0), whose spectral curves and Hamiltonians are shown to be related by a birational transformation.

hep-th

Defects and type D relativistic Toda lattice for some 5d gauge theories

We perform folding on the ADHM construction of the instanton moduli space from $SU$ to $SO$ group. A Young diagram description for the $SO$ instanton is obtained after modifying the real and complex moment maps of the ADHM data. We study the Bethe gauge correspondence between type D relativistic Toda lattice and 5d $\mathcal{N}=1$ folded theory. In particular we prove that the regular monodromy defect in the folded gauge theory is the stationary wavefunction of the type D relativistic Toda lattice.

hep-th

Dimers for Type D Relativistic Toda Model

We construct dimer graphs for type D relativistic Toda models by introducing impurities to the $Y^{2N,0}$ square dimer graphs. By properly placing the impurities and change of canonical variables assigned to the 1-loops on the dimer graph, we introduce the "folding" of the graphs and get the type D relativistic Toda lattice Hamiltonian and monodromy matrix.

hep-th

Generalized Calogero-Moser system and supergroup gauge origami

We study the integrability and the Bethe/Gauge correspondence of the Generalized Calogero-Moser system proposed by Berntson, Langmann and Lenells which we call the elliptic quadruple Calogero-Moser system (eqCM). We write down the Dunkl operators which give commuting Hamiltonians of the quantum integrable system. We identify the gauge theory in correspondence is a supergroup version of the gauge origami, from which we construct the transfer matrix of the eqCM system.

hep-th

di-Langlands correspondence and extended observables

We explore the $\textit{difference Langlands correspondence}$ using the four dimensional ${\mathcal{N}}=2$ super-QCD. Surface defects and surface observables play the crucial role. As an application, we give the first construction of the full set of quantum integrals, i.e. commuting differential operators, such that the partition function of the so-called regular monodromy surface defect is their joint eigenvectors in an evaluation module over the Yangian $Y(\mathfrak{gl}(2))$, making it the wavefunction of a $N$-site $\mathfrak{gl}(2)$ spin chain with bi-infinite spin modules. We construct the $\mathbf{Q}$- and $\tilde{\mathbf{Q}}$-surface observables which are believed to be the $Q$-operators on the bi-infinite module over the Yangian $Y(\mathfrak{gl}(2))$, and compute their eigenvalues, the $Q$-functions, as vevs of the surface observables.

hep-th

Bispectral duality and separation of variables from surface defect transition

We study two types of surface observables $-$ the $\mathbf{Q}$-observables and the $\mathbf{H}$-observables $-$ of the 4d $\mathcal{N}=2$ $A_1$-quiver $U(N)$ gauge theory obtained by coupling a 2d $\mathcal{N}=(2,2)$ gauged linear sigma model. We demonstrate that the transition between the two surface defects manifests as a Fourier transformation between the surface observables. Utilizing the results from our previous works, which establish that the $\mathbf{Q}$-observables and the $\mathbf{H}$-observables give rise, respectively, to the $Q$-operators on the evaluation module over the Yangian $Y(\mathfrak{gl}(2))$ and the Hecke operators on the twisted $\widehat{\mathfrak{sl}}(N)$-coinvariants, we derive an exact duality between the spectral problems of the $\mathfrak{gl}(2)$ XXX spin chain with $N$ sites and the $\mathfrak{sl}(N)$ Gaudin model with 4 sites, both of which are defined on bi-infinite modules. Moreover, we present a dual description of the monodromy surface defect as coupling a 2d $\mathcal{N}=(2,2)$ gauged linear sigma model. Employing this dual perspective, we demonstrate how the monodromy surface defect undergoes a transition to multiple $\mathbf{Q}$-observables or $\mathbf{H}$-observables, implemented through integral transformations between their surface observables. These transformations provide, respectively, $\hbar$-deformation and a higher-rank generalization of the KZ/BPZ correspondence. In the limit $\varepsilon_2\to 0$, they give rise to the quantum separation of variables for the $\mathfrak{gl}(2)$ XXX spin chain and the $\mathfrak{sl}(N)$ Gaudin model, respectively.

hep-th

New dimer integrable systems and defects in five dimensional gauge theory

We study the relation between the quantum integrable systems derived from the dimer graphs and five dimensional $\mathcal{N}=1$ supersymmetric gauge theories on $S^1 \times \mathbb{R}^4$. We construct integrable systems based on new dimer graphs obtained from modification of hexagon dimer diagram. We study the gauge theories in correspondence to the newly proposed integrable systems. By examining three types of defects -- a line defect, a canonical co-dimensional two defect and a monodromy defect -- in five-dimensional gauge theory with $\mathcal{N}=1$ supersymmetry and $\Omega_{\varepsilon_1,\varepsilon_2}$-background. We identify, in the $\varepsilon_2 \to 0$ limit, the canonical co-dimensional two defect satisfying the Baxter T-Q equation of the generalized $A$-type dimer integrable system, and the monodromy defect as its common eigenstate of the commuting Hamiltonians, with the eigenvalues being the expectation value of the BPS Wilson loop in the anti-symmetric representation of the bulk gauge group.

hep-th

Quantum Spin Systems and Supersymmetric Gauge Theories, I

The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the $N$ site $\mathfrak{sl}_{2}$ $XXX$ spin chain (for infinite dimensional complex spin representations), as well as the $SL_N$ Gaudin system, which reduces, in a limiting case, to that of the $N$-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.

hep-th

Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $\mathcal{N}=2$ supersymmetric $SU(N)$ gauge theory with $2N$ fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the $5$-point conformal block of the $\widehat{\mathfrak{sl}}_N$ current algebra with one of the vertex operators corresponding to the $N$-dimensional $\mathfrak{sl}_N$ representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the $XXX_{\mathfrak{sl}_2}$ spin chain of $N$ Heisenberg-Weyl modules over $Y(\mathfrak{sl}_2)$. We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

hep-th

Parallel surface defects, Hecke operators, and quantum Hitchin system

We examine two types of half-BPS surface defects $-$ regular monodromy surface defect and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal{N}=2$ supersymmetry and $\Omega_{\varepsilon_1,\varepsilon_2}$-background. Mathematically, we investigate integrals over the moduli spaces of parabolic framed sheaves over $\mathbb{P}^2$. Using analytic methods of $\mathcal{N}=2$ theories, we demonstrate that the former gives a twisted $\mathcal{D}$-module on $\text{Bun}_{G_{\mathbb{C}}}$ while the latter acts as a Hecke operator. In the limit $\varepsilon_2 \to 0$, the cluster decomposition implies the Hecke eigensheaf property for the regular monodromy surface defect. The eigenvalues are given by the opers associated to the canonical surface defect. We derive, in our $\mathcal{N}=2$ gauge theoretical framework, that the twisted $\mathcal{D}$-modules assigned to the opers in the geometric Langlands correspondence represent the spectral equations for quantum Hitchin integrable system. A duality to topologically twisted four-dimensional $\mathcal{N}=4$ theory is discussed, in which the two surface defects are mapped to Dirichlet boundary and 't Hooft line defect. This is consistent with earlier works on the $\mathcal{N}=4$ theory approach to the geometric Langlands correspondence.

hep-th

Defect in Gauge Theory and Quantum Hall States

We study the surface defect in $\mathcal{N}=2^*$ $U(N)$ gauge theory in four dimensions and its relation to quantum Hall states in two dimensions. We first prove that the defect partition function becomes the Jack polynomial of the variables describing the brane positions by imposing the Higgsing condition and taking the bulk decoupling limit. Further tuning the adjoint mass parameter, we may obtain various fractional quantum Hall states, including Laughlin, Moore-Read, and Read-Rezayi states, due to the admissible condition of the Jack polynomial.

hep-th

Quantum Integrable Systems from Supergroup Gauge Theories

In this note, we establish several interesting connections between the supergroup gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras. In particular, we construct the super-characteristic polynomials of super-Toda lattice and elliptic double Calogero-Moser system by considering certain orbifolded instanton partition functions of their corresponding supergroup gauge theories. We also derive an exotic generalization of sl(2) XXX spin chain arising from the instanton partition function of SQCD with supergauge group, and study its Bethe ansatz equation.

hep-th

Quantum Elliptic Calogero-Moser Systems from Gauge Origami

We systematically study the interesting relations between the quantum elliptic Calogero-Moser system (eCM) and its generalization, and their corresponding supersymmetric gauge theories. In particular, we construct the suitable characteristic polynomial for the eCM system by considering certain orbifolded instanton partition function of the corresponding gauge theory. This is equivalent to the introduction of certain co-dimension two defects. We next generalize our construction to the folded instanton partition function obtained through the so-called "gauge origami" construction and precisely obtain the corresponding characteristic polynomial for the doubled version, named the elliptic double Calogero-Moser (edCM) system.

hep-th