arXiv subjects

Dan Xie

Publications and source records attributed to Dan Xie.

At least 19 recordsLinked to original sources

arXiv2026

Seiberg dualities for quiver gauge theories

We study Seiberg duality for quiver gauge theories with fundamental, bifundamental, and rank-two tensor matter. The existence of a Seiberg dual description places strong constraints on the spectrum of undressed mesons, which is naturally encoded in a factorization equation for the matrix Hilbert series. We derive this factorization from a closed-form large-$N$ superconformal index for general quiver gauge theories with these matter contents. We apply the method to two-node quivers and recover known $SU$--$SU$ and $SO$--$USp$ product-group dualities. We also discuss finite-$N$ consistency conditions from anomaly and operator-spectrum matching.

hep-th↗

arXiv2026

On the Representation Theory of Non-Admissible $W$-Algebras: Part I

Motivated by the mirror symmetry for circle compactified 4d $N=2$ theories, we propose a geometric framework for studying the representation theory of non-admissible $W$-algebras $W^{k}(\mathfrak g,f)$ at levels $k=-h^\vee+\frac{1}{n}\frac{m}{u}$, using the geometry of generalized affine Springer fibers $Sp_{\nu}(\tilde{g},f)$ with slope $\nu=u/m$. The central proposal is that each non-empty $C^*$-fixed locus, labeled by a double coset $\tilde w\in W_\nu\backslash\tilde{W}/W_f$, gives rise to simple modules whose highest weight is determined by the map $\tilde w\mapsto\tilde w(k\Lambda_0+\tilde\rho)-\tilde\rho$, while the dimension of the fixed variety encodes additional non-semisimple structure (logarithmic modules). We verify this correspondence in numerous examples, including $D_4$, $E_6$, $E_8$, and twisted theories of type $^3D_4$ and $^2A_3$, where our geometric counting reproduces known results for both admissible and non-admissible $W$-algebras.

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arXiv2025

Information-Dense Reasoning for Efficient and Auditable Security Alert Triage

Security Operations Centers face massive, heterogeneous alert streams under minute-level service windows, creating the Alert Triage Latency Paradox: verbose reasoning chains ensure accuracy and compliance but incur prohibitive latency and token costs, while minimal chains sacrifice transparency and auditability. Existing solutions fail: signature systems are brittle, anomaly methods lack actionability, and fully cloud-hosted LLMs raise latency, cost, and privacy concerns. We propose AIDR, a hybrid cloud-edge framework that addresses this trade-off through constrained information-density optimization. The core innovation is gradient-based compression of reasoning chains to retain only decision-critical steps--minimal evidence sufficient to justify predictions while respecting token and latency budgets. We demonstrate that this approach preserves decision-relevant information while minimizing complexity. We construct compact datasets by distilling alerts into 3-5 high-information bullets (68% token reduction), train domain-specialized experts via LoRA, and deploy a cloud-edge architecture: a cloud LLM routes alerts to on-premises experts generating SOAR-ready JSON. Experiments demonstrate AIDR achieves higher accuracy and 40.6% latency reduction versus Chain-of-Thought, with robustness to data corruption and out-of-distribution generalization, enabling auditable and efficient SOC triage with full data residency compliance.

cs.CR↗

arXiv2025

A Clinical-grade Universal Foundation Model for Intraoperative Pathology

Intraoperative pathology is pivotal to precision surgery, yet its clinical impact is constrained by diagnostic complexity and the limited availability of high-quality frozen-section data. While computational pathology has made significant strides, the lack of large-scale, prospective validation has impeded its routine adoption in surgical workflows. Here, we introduce CRISP, a clinical-grade foundation model developed on over 100,000 frozen sections from eight medical centers, specifically designed to provide Clinical-grade Robust Intraoperative Support for Pathology (CRISP). CRISP was comprehensively evaluated on more than 15,000 intraoperative slides across nearly 100 retrospective diagnostic tasks, including benign-malignant discrimination, key intraoperative decision-making, and pan-cancer detection, etc. The model demonstrated robust generalization across diverse institutions, tumor types, and anatomical sites-including previously unseen sites and rare cancers. In a prospective cohort of over 2,000 patients, CRISP sustained high diagnostic accuracy under real-world conditions, directly informing surgical decisions in 92.6% of cases. Human-AI collaboration further reduced diagnostic workload by 35%, avoided 105 ancillary tests and enhanced detection of micrometastases with 87.5% accuracy. Together, these findings position CRISP as a clinical-grade paradigm for AI-driven intraoperative pathology, bridging computational advances with surgical precision and accelerating the translation of artificial intelligence into routine clinical practice.

cs.LG↗

arXiv2025

Bigraded Polynomials for the Cohomology of Wild Hitchin Systems

We introduce a bi-graded polynomial that encodes the cohomology groups of the wild Hitchin system of type~$A_{n-1}$, constructed using an irregular singularity (determined by an integer~$m$) and an arbitrary regular singularity~$f$. When the regular singularity is of the form~$f = [1, \ldots, 1]$, the bi-graded polynomial~$C_{m,n}(q,t)$ coincides with the bigraded rational parking function defined combinatorially, admitting a Schur expansion~$C_{m,n}(q,t) = \sum_\lambda f_\lambda(q,t) s_\lambda(x)$. For general~$f$, the polynomial takes the form~$C^f_{m,n}(q,t) = \sum_\lambda f_\lambda(q,t) K_{\lambda f}$, where~$K_{\lambda f}$ denotes the Kostka number. We conjecture that this bi-graded polynomial agrees with the one arising from the perverse filtration of the Hitchin fibration, or equivalently, from the weight filtration of the mixed Hodge structure from the character variety. We also give a description by using the geometry of affine Springer fiber.}

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arXiv2025

On classification of rank two theories with eight supercharges Part III: Seiberg-Witten geometry

We study Seiberg-Witten (SW) geometries for rank-two theories, encompassing 4D field theories as well as 5D and 6D Kaluza-Klein (KK) theories. The singular model for each SW geometry is derived from a one-parameter family of algebraic curves $y^2 = f(x,t)$, where $t$ parametrizes one dimension of Coulomb branch moduli space. The functional form of $f(x,t)$ is systematically determined through analysis of singular fibers at $t=\infty$. Two powerful computational methods enable this determination: a): Liu's algorithm for determining singular fibers from local equation; b): The canonical resolution method for fiber degeneration. Our construction provides not only a complete description of known solutions but also establishes a robust framework for generating new theories. This methodology proves particularly valuable for the systematic exploration of 5D and 6D theories.

hep-th↗

arXiv2024

Modularity for $\mathcal{W}$-algebras and affine Springer fibres

We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual affine Lie algebra $\mathfrak{g}^\vee$. Using this bijection, we relate the modularity of the characters of admissible representations to Cherednik's Verlinde algebra construction coming from double affine Hecke algebras. Finally, we show that the expected behaviors of simple modules under quantized Drinfeld-Sokolov reductions are compatible with the reductions from affine Springer fibres to affine Spaltenstein varieties. This yields (modulo some conjectures) a similar bijection for irreducible representations of $\mathcal{W}$-algebras, as well as an interpretation for their modularity properties.

math.RT↗

arXiv2024

On duality of four dimensional $\mathcal{N}=1$ gauge theory

We show that Seiberg-like duality of $\mathcal{N}=1$ gauge theory coupled with tensor chiral fields and fundamental chiral fields works if the meson spectrum built from the tensor fields takes particular form: a) It should be truncated; b) The $R$ charges of tensor fields $\{R_a\}$ and the truncated mesons $\{R_j\}$ take very special values. The meson spectrum so that the duality works is encoded elegantly in the factorization of the polynomial $y^n-1=\Phi_{+}\Phi_{-}$. Our consideration covers many known $\mathcal{N}=1$ dualities and generates a large class of new examples.

hep-th↗

arXiv2023

On rank two theories with eight supercharges part II: Lefschetz pencils

The global Seiberg-Witten (SW) geometries for rank two theories with eight supercharges are studied. The theory is deformed generically so that there are only simplest $I_1$ or $\tilde{I}_1$ singularities on the Coulomb branch, which then geometrically gives the so-called Lefchetz pencils, The local singularity was shown to be determined by the conjugacy class of mapping class group (MCG); The global study is then reduced to the questions about MCG: a) Find the factorization of the MCG element of the singular fiber into positive products of Dehn twists (which gives the $I_1$ singularity or $\tilde{I}_1$ singularity); b) Find the factorization of identity element in terms of Dehn twists. We solved above two MCG problems for most rank two theories.The results are very helpful in determining IR physics for all vacua of 4d SCFTs. Our approach is combinatorial and many aspects can be straightforwardly generalized to the study of higher rank theory.

hep-th↗

arXiv2023

Three dimensional quotient singularity and 4d $\mathcal{N}=1$ AdS/CFT correspondence

We systematically study the AdS/CFT correspondence induced by D3 branes probing three dimensional Gorenstein quotient singularity $\mathbb{C}^3/G$. The field theory is given by the McKay quiver, which has a vanishing NSVZ beta function assuming that all the chiral fields have the $U(1)_R$ charge $\frac{2}{3}$. Various physical quantities such as quiver Hilbert series, superconformal index, central charges, etc are computed, which match exactly with those computed using the singularity. We also study the relevant deformation of those theories and find the dual geometry, therefore generate many new interesting AdS/CFT pairs. The quiver gauge theory defined using finite subgroups of $SO(3)$ group has some interesting features, for example, its Seiberg duality behavior is quite interesting.

hep-th↗

arXiv2023

Hyperelliptic families and 4d $\mathcal{N}=2$ SCFT

We classify four dimensional $\mathcal{N}=2$ SCFTs whose Seiberg-Witten (SW) geometries can be written as hyperelliptic families. By using special Kähler condition of SW geometry, we reduce the problem to one parameter quasi-homogeneous hyperelliptic families $y^2=f(x,t)$. The classification is given by further demanding that the complex algebraic surface defined by $y^2=f(x,t)$ has an isolated singularity. We then write down the full SW geometry by looking at mini-versal deformations of the one parameter family, and the SW differential is also written down. The detailed physical data for these theories are found by matching the theory with other known construction. Our solutions recover the known rank one and rank two results, and give some infinite sequences valid at arbitrary ranks. We also studied $Z_2$ quotient of above hyperelliptic families which give rise to $B$ type and $D$ type conformal gauge theory, and further generalizations.

hep-th↗

arXiv2023

Mirror symmetry for circle compactified 4d $\mathcal{N}=2$ SCFTs

We propose a mirror symmetry for 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator algebra (VOA) describing the Schur sector (containing Higgs branch) of 4d theory, and the Coulomb branch of the effective 3d theory. The basic feature of the mirror symmetry is that many representational properties of VOA are matched with geometric properties of the Coulomb branch moduli space. Our proposal is verified for a large class of Argyres-Douglas (AD) theories engineered from M5 branes, whose VOAs are W-algebras, and Coulomb branches are the Hitchin moduli spaces. VOA data such as simple modules, Zhu's algebra, and modular properties are matched with geometric properties like $\mathbb{C}^*$-fixed varieties in Hitchin fibers, cohomologies, and some DAHA representations. We also mention relationships to 3d symplectic duality.

hep-th↗

arXiv2023

Superconformal indices of $\mathcal{N}=4$ Chern-Simons matter theories

Gaiotto and Witten found that one can construct 3d $\mathcal{N}=4$ Chern-Simons matter theories by using $\mathcal{N}=4$ SCFT whose momentum map of global symmetries satisfy special condition. Usually, one uses free hypermultiplet and twisted hypermultiplet, and more recently it was found that strongly coupled theory such as 3d version of $T_N$ theory and Argyres-Douglas matter can also be used. In this paper, we compute superconformal index of these $\mathcal{N}=4$ theories and derive the Coulomb/Higgs limit. Our results determine the moduli space of vacua, which is used to check various interesting mirror symmetry involving CSM theory and usual $\mathcal{N}=4$ gauge theory.

hep-th↗

arXiv2023

Pseudo-periodic map and classification of theories with eight supercharges

The classification of one parameter local Coulomb branch solution of theories with eight supercharges is given by assuming that it is given by a genus $g$ fiberation of Riemann surfaces. The crucial point is the fact that certain conjugacy class (so-called pseudo-periodic map of negative type) in mapping class group determines the topological type of the degeneration. The classification of conjugacy class has a simple combinatorial description. Each such conjugacy class gives rise to a dual graph and a 3d mirror quiver gauge theory can be derived, which is then used to identify the low energy theory (assuming generic deformation). Some global Seiberg-Witten geometries are given by using the topological data of the degeneration. The geometric setup unifies 4d $\mathcal{N}=2$ SCFTs (such as $T_n$ theory and Argyres-Douglas theory), 5d $\mathcal{N}=1$ SCFTs, 6d $(1,0)$ SCFTs, 4d IR free theories, and 4d asymptotical free theories in a single combinatorial framework.

hep-th↗

arXiv2023

On low rank 4d $\mathcal{N}=2$ SCFTs

There are two major ways of constructing 4d $\mathcal{N}=2$ superconformal field theories (SCFTs): the first one is putting a 6d $(2,0)$ theory on a punctured Riemann surface (class-S theory), and the second one is putting type IIB string theory on a 3d canonical singularity. As there are interests on low rank theories, we search all the possibilities from above two constructions. Most of those theories are engineered by class-S theory with irregular singularities, and we find a universal formula for the rank of theory so that a complete search is possible. We then compute various physical quantities of those theories, such as the central charges, flavor symmetry, associated vertex operator algebra and Higgs branch, etc. One of interesting consequence of our results are the prediction of many new isomorphism of 2d vertex operator algebra.

hep-th↗

arXiv2022

A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring

One can derive a large class of new $\mathcal{N}=1$ SCFTs by turning on $\mathcal{N}=1$ preserving deformations for $\mathcal{N}=2$ Argyres-Dougals theories. In this work, we use $\mathcal{N}=2$ superconformal indices to get indices of $\mathcal{N}=1$ SCFTs, then use these indices to derive chiral rings of $\mathcal{N}=1$ SCFTs. For a large class of $\mathcal{N}=2$ theories, we find that the IR theory contains only free chirals if we deform the parent $\mathcal{N}=2$ theory using the Coulomb branch operator with smallest scaling dimension. Our results provide interesting lessons on studies of $\mathcal{N}=1$ theories, such as $a$-maximization, accidental symmetries, chiral ring, etc.

hep-th↗

arXiv2022

On rank two theories with eight supercharges part I: local singularities

A complete study of local singularities of rank two $\mathcal{N}=2$ Coulomb branch geometry is given. Low energy theory associated with the local singularity is identified: it can be superconformal field theory (SCFT), or IR free gauge theory, or the combination of them. Various invariants for local singularity are also listed which are essential for the study of global Coulomb branch. As a first application, global Coulomb branch with only simplest local singularities in the bulk are given for 4d theories (including SCFTs and asymptotical free theories), 5d KK theories, and 6d KK theories; those examples appear to cover all the findings in the literature and suggest there are more possibilities. More general global Coulomb branch geometry would be discussed in the sequel of this paper.

hep-th↗

arXiv2022

Classification of rank one 5d $\mathcal{N}=1$ and 6d $(1,0)$ SCFTs

This paper gives a classification of rank one 5d $\mathcal{N}=1$ and 6d $(1,0)$ SCFTs. The idea is to compactify 5d theory on $S^1$ and 6d theory on $T^2$ to get effective 4d $\mathcal{N}=2$ theory. These compactified theories all have a 4d $\mathcal{N}=2$ Coulomb branch whose solution can be described by mixed Hodge module (MHM). In the rank one case every Coulomb branch solution is related to rational elliptic surface with a section, whose classification is complete. So the classification is then reduced to pick up a subset from the data base of rational elliptic surface by imposing various physical constraints. The crucial new input is that the singular fiber at infinity determines which dimension the UV theory lives. Various physical properties such as flavor symmetry, one form symmetry, BPS quiver and BPS spectrum, and RG flow are studied. D7 brane configurations for those theories are found which are very useful in studying them. The generalizations to higher rank theories will also be highlighted.

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