arXiv subjects

Dan Xie

Publications and source records attributed to Dan Xie.

At least 73 records · Page 4Linked to original sources

arXiv2013

M5 brane and four dimensional N=1 theories I

Four dimensional N=1 theories are engineered by compactifying six dimensional (2,0) theory on a Riemann surface with regular punctures. A generalized Hitchin's equation involving two Higgs fields is proposed as the BPS equation for N=1 compactification. The puncture is interpreted as the singular boundary condition of this equation, and regular puncture is shown to be labeled by a nilpotent commuting pair. In this paper, we focus on a subset of regular puncture which is described by rotating branes representing N=2 puncture. As an application, we show that the Seiberg duality of SU(N) SQCD with Nf=2N and certain superpotential term is realized as different degeneration limits of the same punctured Riemann surface, and also find four more dual theories.

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arXiv2013

String Theory Origin of Bipartite SCFTs

We provide a string theory embedding for N = 1 superconformal field theories defined by bipartite graphs inscribed on a disk. We realize these theories by exploiting the close connection with related N = 2 generalized (A_(k-1), A_(n-1)) Argyres-Douglas theories. The N = 1 theory is obtained from spacetime filling D5-branes wrapped on an algebraic curve and NS5-branes wrapped on special Lagrangians of C^2 which intersect along the BPS flow lines of the corresponding N = 2 Argyres-Douglas theory. Dualities of the N = 1 field theory follow from geometric deformations of the brane configuration which leave the UV boundary conditions fixed. In particular we show how to recover the classification of IR fixed points from cells of the totally non-negative Grassmannian Gr^(tnn)_(k,n+k). Additionally, we present evidence that in the 3D theory obtained from dimensional reduction on a circle, VEVs of line operators given by D3-branes wrapped over faces of the bipartite graph specify a coordinate system for Gr^(tnn)_(k,n+k).

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arXiv2013

Higher laminations, webs and N=2 line operators

A detailed study of half-BPS line operators of higher rank 4d N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a bordered Riemann surface with full marked points is performed. Geometrically, each 4d UV line operator is represented by an irreducible bipartite web formed by three junctions on Riemann surface, and such web structure is called higher lamination. Algebraically, the space of UV line operators is identified with the integral tropical a coordinates of the corresponding PGL(N,C) local system, and the space of IR line operator is identified with the cluster X coordinates of SL(N.C) local system. The expectation value of UV line operator at Coulomb branch parameterized by X coordinates is calculated, and the result is a positive Laurent polynomial in X. Using the expectation values, we calculate the operator product expansion (OPE) between the line operators, which is then represented geometrically by higher rank Skein relations. We also calculate the Poisson brackets of these line operators, and Frenchel-Nielson type coordinates are constructed for Higher Teichmuller space, etc.

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arXiv2013

Central charges and RG flow of strongly-coupled N=2 theory

We calculate the central charges a, c and k_G of a large class of four-dimensional N=2 superconformal field theories arising from compactifying the six-dimensional N=(2,0) theory on a Riemann surface with regular and irregular punctures. We also study the renormalization group flows between the general Argyres-Douglas theories, which all agree with the a-theorem.

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arXiv2012

BPS spectrum, wall crossing and quantum dilogarithm identity

BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is interpreted as the quantum dilogarithm identity. Various methods including quiver representation theory, maximal green mutation, and cluster algebra are used extensively. The spectral generator and its refined version for the higher rank theory are written down using the explicit spectrum information. The finite chamber has an interesting N^3 behavior in the large N limit.

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arXiv2012

Network and Seiberg Duality

We define and study a new class of 4d N=1 superconformal quiver gauge theories associated with a planar bipartite network. While UV description is not unique due to Seiberg duality, we can classify the IR fixed points of the theory by a permutation, or equivalently a cell of the totally non-negative Grassmannian. The story is similar to a bipartite network on the torus classified by a Newton polygon. We then generalize the network to a general bordered Riemann surface and define IR SCFT from the geometric data of a Riemann surface. We also comment on IR R-charges and superconformal indices of our theories.

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arXiv2012

Network, cluster coordinates and N = 2 theory II: Irregular singularity

Cluster coordinates for a large class of Argyres-Douglas and asymptotical free theories are constructed using network on bordered Riemann surface. Such N = 2 theories are engineered using six dimensional (2, 0) theory on Riemann surface with irregular and regular singularities. The Stokes phenomenon plays an important role in our construction. Our results are expected to be very useful in studying BPS spectrum, wall crossing, and line operators of these theories, etc. In particular, we conjecture that the quiver from the network is the BPS quiver. Moreover, our construction provides a simple way to build the minimal network for cells of positive Grassmannia .

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arXiv2012

N=2 Generalized Superconformal Quiver Gauge Theory

Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.

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arXiv2012

Network, Cluster coordinates and N=2 theory I

Combinatorial methods are developed to find the cluster coordinates for moduli space of flat connections which is describing the Coulomb branch of higher rank N=2 theories derived by compactifying six dimensional (2,0) theory on a punctured Riemann surface. The construction starts with a triangulation of the punctured Riemann surface and a further tessellation of all the triangles. The tessellation is used to construct a bipartite network from which a quiver can be read straightforwardly. We prove that the quivers for different triangulations are related by quiver mutations and justify that these are really the cluster coordinates. These coordinates are important in studying BPS wall crossing, line operators, and surface operators of these theories; and they are also useful in exploring three dimensional Chern-Simons theory and the corresponding N=2 gauge theory, two dimensional integrable system, etc.}

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arXiv2011

More Three Dimensional Mirror Pairs

We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One side of these mirror pairs are always the conventional quiver gauge theories. One of our result can also be used to determine the matter content and weakly coupled gauge groups of four dimensional N = 2 generalized quiver gauge theories derived from six dimensional A_N and D_N theory, therefore we explicitly constructed four dimensional S-duality pairs.

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arXiv2010

Mirrors of 3d Sicilian theories

We consider the compactification of the 6d N=(2,0) theories, or equivalently of M-theory 5-branes, on a punctured Riemann surface times a circle. This gives rise to what we call 3d N=4 Sicilian theories, and we find that their mirror theories are star-shaped quiver gauge theories. We also discuss an alternative construction of these 3d theories through 4d N=4 SYM on a graph, which allows us to obtain the 3d mirror via 4d S-duality.

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arXiv2010

Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories

In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.

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arXiv2010

Hitchin Equation, Singularity, and N=2 Superconformal Field Theories

We argue that Hitchin's equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N=2 superconformal field theories when we compactify six dimensional $A_N$ $(0,2)$ theory on a punctured Riemann surface. We study the singular solution to Hitchin's equation and the Higgs field of solutions has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residual is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For the mass-deformed theory the residual of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of the massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin's system. The results are all in agreement with Gaiotto's results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory.

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arXiv2010

Flipped SU(5) X U(1)_X Models from F-Theory

We systematically construct flipped SU(5) X U(1)_X models without and with bulk vector-like particles from F-theory. To realize the decoupling scenario, we introduce sets of vector-like particles in complete SU(5) X U(1) multiplets at the TeV scale, or at the intermediate scale, or at the TeV scale and high scale. To avoid the Landau pole problem for the gauge couplings, we can only introduce five sets of vector-like particles around the TeV scale. These vector-like particles can couple to the Standard Model singlet fields, and obtain suitable masses by Higgs mechanism. We study gauge coupling unification in detail. We show that the U(1)_X flux contributions to the gauge couplings preserve the SU(5) X U(1)_X gauge coupling unification. We calculate the SU(3)_C X SU(2)_L unification scales, and the SU(5) X U(1)_X unification scales and unified couplings. In most of our models, the high-scale or bulk vector-like particles can be considered as string-scale threshold corrections since their masses are close to the string scale. Futhermore, we discuss the phenomenological consequences of our models. In particular, in the models with TeV-scale vector-like particles, the vector-like particles can be observed at the Large Hadron collider, the proton decay is within the reach of the future Hyper-Kamiokande experiment, the lightest CP-even Higgs boson mass can be increased, the hybrid inflation can be naturally realized, and the correct cosmic primodial density fluctuations can be generated.

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arXiv2009

On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory

In this note, we explore the relation between crossing symmetry and modular invariance in conformal field theory and S-duality in gauge theory. It is shown that partition functions of different S dual theories of N=2 SU(2) gauge theory with four fundamentals can be derived from the crossing symmetry of the Liouville four point function. We also show that the partition function of N=4 SU(2) gauge theory can be derived from the Liouville partition function on torus.

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arXiv2009

N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter

We consider the four dimensional scale invariant N=2 SU quiver gauge theories with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We argue that these theories are realized as six dimensional A_{2N-1} (0,2) theories compactified on spheres with punctures. With this realization, we can study various strongly coupled cusps in moduli space and find the S-dual theories. We find a class of isolated superconformal field theories with only odd dimensional operators $D(ϕ)\geq3$ and superconformal field theories with only even dimensional operators $D(ϕ)\geq4$.

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arXiv2009

Time Delays of Strings in D-particle Backgrounds and Vacuum Refractive Indices

Using standard techniques in string/D-brane scattering amplitude computations, we evaluate the scattering of open strings off D-particles in brane world scenarios. The D-particles are viewed as D3 branes wrapped up around three cycles, and their embedding in brane worlds constitutes a case of intersecting branes, among which strings are stretched, representing various types of excitations of the Standard Model (SM) particles in the low-energy limit. Our analysis, reveals interesting and novel selection rules for the resulting causal time delays, proportional to the energy of the incident matter state, from the processes of splitting, capture and re-emission of the latter by the D-particles. In particular, we show that there are relatively large time delays only for excitations that belong to the Cartan subalgebra of the SM gauge group, which notably includes photons. We discuss the possible relevance of these results to the models of space time foam predicting a non-trivial vacuum refractive index for photons and the associated cosmic γ-ray phenomenology. In particular, we demonstrate how low-string-scale models can be falsified already in this context, by current astrophysical observations of cosmic photons, and how such observations serve as a way to discriminate low- from high-string scale models.

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arXiv2009

F-SU(5)

We construct three flipped SU(5) X U(1)_X models from F-theory, and consider two such models from free fermionic string model building. To achieve the decoupling scenario in F-theory models and the string-scale gauge coupling unification in free fermionic models, we introduce vector-like particles at the TeV scale that can be observed at the Large Hadron Collider. We study gauge coupling unification, and find that proton decay is within the reach of the future Hyper-Kamiokande experiment. In these models, the doublet-triplet splitting problem and monopole problem can be solved, the neutrino masses and mixings can be explained via the double seesaw or seesaw mechanism, the observed baryon asymmetry can be obtained through leptogenesis, the hybrid inflation can be realized, and the correct cosmic primodial density fluctuations can be generated.

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