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Dan Xie

Publications and source records attributed to Dan Xie.

At least 55 records · Page 3Linked to original sources

A search for minimal 4d N=1 SCFT

We discuss a candidate for a minimal interacting 4-dimensional N=1 superconformal field theory (SCFT). The model contains a chiral primary operator u satisfying the chiral ring relation u^2=0, and its scaling dimension is Δ(u)=1.5. The model is derived by turning on a N=1 preserving deformation of N=2 A2 Argyres-Douglas theory. The central charges are given by (a,c)=(263/768, 271/768) ~ (0.342,0.353). There is no moduli space of vacua, no flavor symmetry, and the chiral ring is finite.

hep-th↗

K stability and stability of chiral ring

We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing a three-fold singularity X, and show that the K stability which implies the existence of Ricci-flat conic metric on X is equivalent to the stability of chiral ring of the corresponding field theory.

hep-th↗

Modeling and Inferring Human Intents and Latent Functional Objects for Trajectory Prediction

This paper is about detecting functional objects and inferring human intentions in surveillance videos of public spaces. People in the videos are expected to intentionally take shortest paths toward functional objects subject to obstacles, where people can satisfy certain needs (e.g., a vending machine can quench thirst), by following one of three possible intent behaviors: reach a single functional object and stop, or sequentially visit several functional objects, or initially start moving toward one goal but then change the intent to move toward another. Since detecting functional objects in low-resolution surveillance videos is typically unreliable, we call them "dark matter" characterized by the functionality to attract people. We formulate the Agent-based Lagrangian Mechanics wherein human trajectories are probabilistically modeled as motions of agents in many layers of "dark-energy" fields, where each agent can select a particular force field to affect its motions, and thus define the minimum-energy Dijkstra path toward the corresponding source "dark matter". For evaluation, we compiled and annotated a new dataset. The results demonstrate our effectiveness in predicting human intent behaviors and trajectories, and localizing functional objects, as well as discovering distinct functional classes of objects by clustering human motion behavior in the vicinity of functional objects.

cs.CV↗

4d N=2 SCFT from Complete Intersection Singularity

Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most of our theories have exactly marginal deformations and we identify the weakly coupled gauge theory descriptions for many of them, which involve (affine) D and E shaped quiver gauge theories and theories formed from Argyres-Douglas matters. These investigations provide strong evidence for the singularity approach in classifying 4d N=2 SCFTs.

hep-th↗

4d N=2 SCFT and singularity theory Part II: Complete intersection

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine the mini-versal deformation of these singularities, and therefore solve the Coulomb branch spectrum and Seiberg-Witten solution.

hep-th↗

Chiral algebra of Argyres-Douglas theory from M5 brane

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d $(2,0)$ type $J$ theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of $J$ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of $J$ type. We can obtain the Schur index of these theories by computing the vacua character of the corresponding chiral algebra.

hep-th↗

New N = 2 dualities

We consider N = 2 superconformal field theory with following properties: a) Coulomb branch operators have fractional scaling dimensions, b) there are exact marginal deformations . The weakly coupled gauge theory descriptions are found by decomposing 3d mirror into different components, and different decompositions correspond to different duality frames. The gauge theory is formed by gauging Argyres-Douglas matter, and we write down all duality frames for several classes with infinite sequence of theories.

hep-th↗

Multivariate Functional Regression Models for Epistasis Analysis

To date, most genetic analyses of phenotypes have focused on analyzing single traits or, analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power, and hold the key to understanding the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two gens in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large scale simulations to calculate its type I error rates for testing interaction between two genes with multiple phenotypes and to compare its power with multivariate pair-wise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate its performance, the MFRG for epistasis analysis is applied to five phenotypes and exome sequence data from the NHLBI Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 136 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has much higher power to detect interaction than the interaction analysis of single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.

q-bio.GN↗

Semicontinuity of 4d N=2 spectrum under renormalization group flow

We study renormalization group flow of four dimensional N=2 SCFTs defined by isolated hypersurface three-fold singularities. We define the spectrum of N=2 theory as the set of scaling dimensions of the parameters on the Coulomb branch, which include Coulomb branch moduli, mass parameters and coupling constants. We prove that the spectrum of those theories is semicontinous under the RG flow on the Coulomb branch using the mathematical result about the singularity spectra under deformation. The semicontinuity behavior of N=2 spectrum implies a theorem under relevant and Coulomb branch moduli deformation, the absence of dangerous irrelevant deformations and can be taken as the necessary condition for the ending point of a RG flow. This behavior is also true for (c,c) ring deformation of two dimensional Landau-Ginzburg model with (2,2) supersymmetry.

hep-th↗

4d N=2 SCFT and singularity theory Part I: Classification

This is the first of a series of papers in which we systematically use singularity theory to study four dimensional N=2 superconformal field theories. Our main focus in this paper is to identify what kind of singularity is needed to define a SCFT. The constraint for a hypersurface singularity has been found by Sharpere and Vafa, and here the complete set of solutions are listed using a related mathematical result of Stephen S. T. Yau and Yu. We also study other type of singularities such as the complete intersection, quotient of hypersurface singularity by a finite group and non-isolated singularity. We finally conjecture that any three dimensional rational Gorenstein graded isolated singularity should define a N=2 SCFT. We explain how to extract various interesting physical quantities such as Seiberg-Witten geometry, central charges, exact marginal deformations, BPS quiver, RG flow trajectory, etc from the properties of singularity.

hep-th↗

Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2

We study compactification of 6 dimensional (1,0) theories on T^2. We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N=2 geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of the T^2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2 CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S with punctures from toroidal compactification of (1,0) SCFTs where the curve of the class S theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S theories with no punctures on arbitrary genus Riemann surface.

hep-th↗

Joint Inference of Groups, Events and Human Roles in Aerial Videos

With the advent of drones, aerial video analysis becomes increasingly important; yet, it has received scant attention in the literature. This paper addresses a new problem of parsing low-resolution aerial videos of large spatial areas, in terms of 1) grouping, 2) recognizing events and 3) assigning roles to people engaged in events. We propose a novel framework aimed at conducting joint inference of the above tasks, as reasoning about each in isolation typically fails in our setting. Given noisy tracklets of people and detections of large objects and scene surfaces (e.g., building, grass), we use a spatiotemporal AND-OR graph to drive our joint inference, using Markov Chain Monte Carlo and dynamic programming. We also introduce a new formalism of spatiotemporal templates characterizing latent sub-events. For evaluation, we have collected and released a new aerial videos dataset using a hex-rotor flying over picnic areas rich with group events. Our results demonstrate that we successfully address above inference tasks under challenging conditions.

cs.CV↗

N=1 Curve

N=1 curve is defined for four dimensional class S theory using Cayley-Hamilton theorem for two commuting matrices. The curve consists of three ingredients: 1: A set of N+1 degree N equations defining a curve; 2: a set of constraints relating the coefficients in the curve; 3: a canonically defined differential. We then extract from spectral curve various physical information such as the space of moduli fields, chiral ring relations, full moduli space, etc. Many examples are discussed, and the curve recovers the intricate vacua structure which often involves highly non-trivial field theory dynamics such as monopole condensation, dynamical generated superpotential, Seiberg duality, etc.

hep-th↗

The moduli space of vacua of N=2 class S theories

We develop a systematic method to describe the moduli space of vacua of four dimensional $\mathcal{N}=2$ class ${\cal S}$ theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed branch roots, and the dimensions of the Coulomb and Higgs components of mixed branches. They are derived by using generalized Hitchin's equations obtained from twisted compactification of 5d maximal Super-Yang-Mills, with local degrees of freedom at punctures given by (nilpotent) orbits. The crucial thing is the holomorphic factorization of the Seiberg-Witten curve and reduction of singularity at punctures. We illustrate our method by many examples including ${\mathcal N}=2$ SQCD, $T_N$ theory and Argyres-Douglas theories.

hep-th↗

The Positive orthogonal Grassmannian and loop amplitudes of ABJM

In this paper we study the combinatorics associated with the positive orthogonal Grassmannian OG_k and its connection to ABJM scattering amplitudes. We present a canonical embedding of OG_k into the Grassmannian Gr(k,2k), from which we deduce the canonical volume form that is invariant under equivalence moves. Remarkably the canonical forms of all reducible graphs can be converted into irreducible ones with products of dLog forms. Unlike N=4 super Yang-Mills, here the Jacobian plays a crucial role to ensure the dLog form of the reduced representation. Furthermore, we identify the functional map that arises from the triangle equivalence move as a 3-string scattering S-matrix which satisfies the tetrahedron equations by Zamolodchikov, implying (2+1)-dimensional integrability. We study the solution to the BCFW recursion relation for loop amplitudes, and demonstrate the presence of all physical singularities as well as the absence of all spurious ones. The on-shell diagram solution to the loop recursion relation exhibits manifest two-site cyclic symmetry and reveals that, to all loop, four and six-point amplitudes only have logarithmic singularities.

hep-th↗

Generalized Hitchin system, Spectral curve and N=1 dynamics

A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional N=1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized Hitchin equations, and extract interesting N=1 dynamics out of it, such as deformed modui space, chiral ring relation, SUSY breaking, etc. Holomorphy plays a crucial role in our construction.

hep-th↗

Aspects of line operators of class S theories

Geometric picture of line operators of N=2 class S theories was found by imposing closure condition on operator product expansion (OPE) of line operators. In this paper, we first identify the geometric representation of ordinary Wilson-'t Hooft line operators of field theory, and study duality action on them. We further define a Dirac product between line operators and classify the allowed set of line operators by requiring: a: closure of OPE; b: mutual locality; c: maximality. Using above classifications, we find many distinct gauge theories associated with a single duality frame, and show explicitly that new possibilities correspond to the choice of global form of gauge group and discrete theta angles. We also study S and T duality actions relating those theories. In particular, we find very interesting duality webs for Maldacena-Nunez theory.

hep-th↗

Three dimensional Seiberg-like duality and tropical cluster algebra

Seiberg-like duality of three dimensional N=2 Chern-Simons-Matter quiver gauge theory is shown to have a chiral double tropical cluster algebra structure. We use cluster algebra results to study combinatorial aspects of these theories such as classification, supersymmetry breaking, etc.

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