Minoru Eto, Koji Hashimoto, Seiji Terashima
We construct a classical vortex string solution in a Seiberg-dual theory of N=1 supersymmetric SO(N_c) QCD which flows to a confining phase. We claim that this vortex string is a QCD string, as previouly argued by M.Strassler. In SO(N_c) QCD, it is known that stable QCD strings exist even in the presence of dynamical quarks. We show that our vortex strings are stable in the Seiberg-dual theory.
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The Seiberg--Witten equations, when dimensionally reduced to $\bf R^{2}\mit$, naturally yield the Liouville equation, whose solutions are parametrized by an arbitrary analytic function $g(z)$. The magnetic flux $Φ$ is the integral of a singular Kaehler form involving $g(z)$; for an appropriate choice of $g(z)$ , $N$ coaxial or separated vortex configurations with $Φ=\frac{2πN}{e}$ are obtained when the integral is regularized. The regularized connection in the $\bf R^{1}\mit$ case coincides with the kink solution of $φ^{4}$ theory.
We propose an embedding of $U(N_c)$ QCD$_3$ with a Chern-Simons term in string theory. The UV gauge theory lives on the worldvolume of a Hanany-Witten brane configuration in type 0B string theory in the presence of Sagnotti's O$'3$ orientifold. We use the brane configuration to propose a magnetic Seiberg dual. We identify various phases of the magnetic theory with conjectured phases of QCD$_3$. In particular the symmetry breaking and bosonization phases are both associated with condensation of the dual squark field. We also discuss the abelian theory without Chern-Simons term and argue that fl…
We consider a non-supersymmetric USp Yang-Mills Chern-Simons gauge theory coupled to fundamental flavours. The theory is realised in type IIB string theory via an embedding in a Hanany-Witten brane configuration which includes an orientifold and anti-branes. We argue that the theory admits a magnetic Seiberg dual. Using the magnetic dual we identify dynamics in field theory and brane physics that correspond to various phases, obtaining a better understanding of 3d bosonization and dynamical breaking of flavour symmetry in USp QCD$_3$ theory. In field theory both phases correspond to magnetic '…
In this note, we consider so-called "Higgs Branch Localization" for four dimensional N=2 field theories on 4d ellipsoid. We find a new set of saddle point equations arising from additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton-vortex mixed configurations. By evaluating the contour integral, we also demonstrate the ellipsoid partition almost factorizes into purely b and 1/b dependent parts, using SQCD as an explicit example. We identify various factorized parts with the ellipsoid partition function of two dimensional N=(2,2) SQCDA, which is p…
We study $N = 2$ 3-d theories with two adjoints and fundamental flavors along with D-type superpotential. For superpotential $W_{D_{n+2}} = \mathrm{Tr} \left(X^{n+1}+X Y^2\right)$ with $n$ odd, we propose the 3d dualities, which we motivate from the dimensional reduction of the related 4-d theory. We consider the factorization of the superconformal index and match precisely the vortex partition function of the dual pairs. In the language of the Higgs branch localization, the nonzero contribution of the vortex partition function comes from the discrete Higgs vacua of the massively deformed theo…
The instanton-induced effective vertex is derived for N=2 supersymmetric QCD (SQCD) with arbitrary mass matter hypermultiplets for the case of SU(2). The leading term of the low energy effective lagrangian obtained from this vertex agrees with one-instanton effective term of the Seiberg-Witten result.
Certain exact results in supersymmetric gauge theories are generated by non-perturbative effects different from instantons. In supersymmetric QCD with N colours and Nf fundamental flavours we examine the Affleck-Dine-Seiberg (ADS) superpotential using controlled semi-classical analysis. We show how for Nf < N-1 the ADS superpotential arises from monopole contributions to the path integral of the supersymmetric gauge theory compactified on R^3*S^1. These are the monopole effects leading to gaugino condensation and confinement of the low-energy SU(N-Nf) supersymmetric gauge theory.
We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f invariant, and has common features with Seiberg duality in N=1 SQCD with SU or SO/Sp gauge group. At large N the duality holds due to planar equivalence with N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes and orientifolds in a non-supersymmetric, but tachyo…
We try to identify the light hadron world as the magnetic picture of QCD. We take both phenomenological and theoretical approaches to this hypothesis, and find that the interpretation seems to show interesting consistencies. In particular, one can identify the rho and omega mesons as the magnetic gauge bosons, and the Higgs mechanism for them provides a dual picture of the color confinement.
Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the interval 2N_f/3 < r \le N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term μfor the adjoint matter, eventually decoupling the adjoint matter in the limit of large μ. If one starts from a large value of the parameter ξ\simμm, where the original theory is at weak coupling, and d…
The exact solution of N=2 supersymmetric QCD found by Seiberg and Witten includes a prediction for all multi-instanton contributions to the low-energy dynamics. In the case where the matter hypermultiplets are massless, the leading non-perturbative contribution at weak coupling comes from the two-instanton sector. We calculate this contribution from first principles using the exact two-instanton solution of the self-dual Yang-Mills equation found by Atiyah, Drinfeld, Hitchin and Manin. We find exact agreement with the predictions of Seiberg and Witten for all numbers of flavours. We also confi…
We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply connected simple type Riemann manifold with $b_2^+ \geq 3$. As the corollaries, we determine the topological correlation functions of the theory without the bare mass and those of the theory without coupling to the hypermultiplet. This includes a concrete field theoretic proof of the relation between the Donaldson and the Seiberg-Witten invariants.
We present an explicit non-perturbative solution of N=2 supersymmetric SU(N_c) gauge theory with N_f \le 2N_c flavors generalizing results of Seiberg and Witten for N_c=2.
We consider type IIA brane configurations, similar to those that realize SO(2N) supersymmetric QCD, that include orientifold planes and anti-branes. Such brane configurations lead to Sp(2N) field theories that become supersymmetric in the large-N limit and break supersymmetry upon the inclusion of 1/N corrections. We argue that this class of field theories admit Seiberg duality and interpret the potential between branes and orientifolds as field theory phenomena. In particular we find in the magnetic theory a meson potential that leads to dynamical symmetry breaking and a meson condensate simi…
The confinement scenario in N=2 supersymmetric gauge theory at the monopole point is reviewed. Basic features of this U(1) confinement are contrasted with those we expect in QCD. In particular, extra states in the hadron spectrum and non-linear Regge trajectories are discussed. Then another confinement scenario arising on Higgs branches of the theory with fundamental matter is also reviewed. Peculiar properties of the Abrikosov-Nielsen-Olesen string on the Higgs branch lead to a new confining regime with the logarithmic suppression of the linear rising potential. Motivations for a search for t…
We interpret the dynamics of Supersymmetric QCD (SQCD) in terms of ideas familiar from the hadronic world. Some mysterious properties of the supersymmetric theory, such as the emergent magnetic gauge symmetry, are shown to have analogs in QCD. On the other hand, several phenomenological concepts, such as "hidden local symmetry" and "vector meson dominance," are shown to be rigorously realized in SQCD. These considerations suggest a relation between the flavor symmetry group and the emergent gauge fields in theories with a weakly coupled dual description.
The AGT relations allow one to convert the Zamolodchikov asymptotic formula for the conformal block into the instanton expansion of the Seiberg-Witten prepotential for theory with two colors and four fundamental flavors. This provides an explicit formula for the instanton corrections in this model, resolving in this way an old problem in Seiberg-Witten theory. The answer is especially elegant for vanishing matter masses, then the bare charge of gauge theory 16q_0 = 16e^{iπτ_0} plays the role of a branch point on the spectral torus. The exact prepotential at this point is F a^2\log q with q\neq…
We construct an anomaly-preserving compactification of 4d gauge theories, including $SU(N)$ Yang-Mills theory, $\mathcal{N}=1$ supersymmetric Yang-Mills theory, and QCD, down to 2d by turning on 't Hooft flux through $T^2$. It provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and multi-branch structure of vacua. We give the semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly matching condition with the original $4$d gauge theory. We conjecture that the weak-co…
We study ${\cal N}=2$ SU(2) supersymmetric QCD with massive hypermultiplets deformed in the Nekrasov-Shatashvili limit of the Omega-background. The prepotential of the low-energy effective theory is determined by the WKB solution of the quantum Seiberg-Witten curve. We calculate the deformed Seiberg-Witten periods around the massless monoplole point explicitly up to the fourth order in the deformation parameter.
The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^{N-1} sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in…
We construct examples of single-sector supersymmetry breaking based on simple deformations of supersymmetric QCD with (weakly) gauged flavor group. These theories are calculable in a weakly coupled Seiberg dual description. In these models, some of the particles in the first two generations of quarks and leptons are composites of the same strong dynamics which leads to dynamical supersymmetry breaking. Such models can explain the hierarchies of Yukawa couplings in the Standard Model, in a way that predictively correlates with the spectrum of SUSY-breaking soft terms.
It is very plausible that confinement in QCD comes from linking of Wilson loops to finite-thickness vortices with magnetic fluxes corresponding to the center of the gauge group. The vortices are solitons of a gauge-invariant QCD action representing the generation of gluon mass. There are a number of other solitonic states of this action. We discuss here what we call nexus solitons, in which for gauge group SU(N), up to N vortices meet a a center, or nexus, provided that the total flux of the vortices adds to zero (mod N). There are fundamentally two kinds of nexuses: Quasi-Abelian, which can b…
Confinement in QCD: A Hybrid String Model with Vortex Corrections and Entanglement Entropy
本文在SU(3)规范理论中提出结合色电通量管与Z3中心涡旋的混合有效弦模型，推导了Wilson loop期望值与修正禁闭势，并解析证明禁闭增加受限夸克对的纠缠熵，揭示了QCD禁闭的量子结构。
We use the dual description proposed by Seiberg to calculate the pressure in the low temperature confined phase of $N=1$ supersymmetric QCD using perturbation theory to $O(g^3_m)$, where $g_m$ is the gauge coupling in the dual theory. Combining this result with the usual high temperature expansion based on asymptotic freedom, we study how the physics in the intermediate temperature regime depends on the relative size of the scale parameters in the two descriptions. In particular we explore the possibility of having a temperature range where both perturbation expansions are valid.
We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation $(STS^{-1}T)^{2n+1}=1$. Thus, the groups are not subgroups of $SL(2,Z)$. We also construct automorphic functions that map the fundamental region of the group generated by $T$ and $STS$ to the Riemann sphere. These automorphic functions faithfully represent the duality symmetry in the Seiberg-Witten curve.
We consider field theory side of new multiple Seiberg dualities conjectured within superconformal index matching approach. We study the case of SU(2) supersymmetric QCD and find that the numerous conjectured duals are different faces of handful of master theories. These different faces are inequivalent to each other in a very peculiar sense. Some master theories are fully known; we construct superpotentials for others. We confirm that all index identities correspond to theories flowing to one and the same theory in the infrared, thus supporting the conjecture of index matching for Seiberg dual…
The low-energy limit of the 6D non-critical string theory with $N=1$ SUSY and $E_8$ chiral current algebra compactified on $T^2$ is generically an $N=2$ $U(1)$ vector multiplet. We study the analog of the Seiberg-Witten solution for the low-energy effective action as a function of $E_8$ Wilson lines on the compactified torus and the complex modulus of that torus. The moduli space includes regions where the Seiberg-Witten curves for $SU(2)$ QCD are recovered as well as regions where the newly discovered 4D theories with enhanced $E_{6,7,8}$ global symmetries appear.
Chiral non-Abelian vortex molecules in dense QCD
本文研究稠密QCD中无Ansatz的涡旋解，发现轴向对称性破坏导致手征非阿贝尔涡旋分子及畴壁受限构型。
We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry breaking terms. In this way, we recover the standard vacuum of QCD with $N_f$ flavors and $N_c$ colors when $N_f < N_c$. However, for $N_f \geq N_c$, we find new exotic states---new vacua with spontaneously broken baryon number for $N_f = N_c$, and a vacuum state with unbroken chiral symmetry for $N_f > N_c$. These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg's electric-magnetic d…
We study Seiberg duality for N=1 supersymmetric QCD with soft supersymmetry-breaking terms. We generate the soft terms through gauge mediation by coupling two theories related by Seiberg duality to the same supersymmetry-breaking sector. In this way, we know what a supersymmetry-breaking perturbation in one theory maps into in its ``dual''. Assuming a canonical Kahler potential we calculate the soft terms induced in the magnetic theory and find that some of the scalars acquire negative masses squared. If duality is still good for small supersymmetry breaking, this may imply some specific symme…
Starting from Seiberg's electric-magnetic duality for supersymmetric QCD, we construct dual pairs of non-supersymmetric gauge theories. This is accomplished by first taking the large N limit of supersymmetric QCD and its dual partner and then performing a special ``orbifold projection'' recently introduced by Kachru and Silverstein. We argue that in the large N limit the two projected theories remain dual. The non-supersymmetric gauge theories which can be studied in this fashion have non-supersymmetric field content, chiral fermions and exactly massless scalar matter.
Magnetic axion vortex and very light QCD axions
本文提出在轴子均匀介质中存在携带恒定磁通量的稳定涡旋孤子，并由此约束轴子-光子耦合须小于$10^{-17}\,{\ m GeV^{-1}}$，否则轴子无法作为星系暗物质。
Quark matter at high density may exhibit color superconductivity. As magnetic flux tubes in metallic superconductors, color magnetic flux tubes as non-Abelian vortices appear in the color-flavor locked phase of high density QCD. ${\mathbb C}P^2$ Nambu-Goldstone bosons and Majorana fermions belonging to the triplet representation are known to be localized around a non-Abelian vortex. In this paper, we determine the coupling of these bosonic and fermionic modes by using the nonlinear realization method.
Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high-density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the ${\mathbb C}P^2$ model [ arXiv:0908.4470 , arXiv:0912.1352 ]. Here, we reconstruct the effective theory in a regular gauge without taking a singular gauge, confirming the previous results in t…
We present a general analysis of all the possible soft breakings of N=2 supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all the couplings of the spurion fields in terms of properties of the Seiberg-Witten periods, which we express in terms of elementary elliptic functions by uniformizing the elliptic curves associated to each number of flavors. We analyze in detail the monodromy properties of the softly broken theory, and obtain them by a particular embedding into a pure gauge theory with high…
Baryonic Vortex Phase and Magnetic Field Generation in QCD with Isospin and Baryon Chemical Potentials
该研究在含有限重子与同位旋化学势的低能致密QCD中提出重子涡旋相，证明其携重子数且高密下负张力可自发形成，为理解QCD相图和中子星磁场提供新思路。
We address the problem of non-Abelian super-QCD, with a Fayet-Iliopoulos term, as seen from the vortex worldsheet perspective. Together with the FI term $ξ$, also a mass $μ$ for the adjoint superfield $Φ$ enters in the game. This mass allows the interpolation between $\N=2$ and $\N=1$ super-QCD. While the phenomenology of the $\N=2$ case ($μ=0$) is pretty much understood, much remains to be clarified for the finite-$μ$ case. We distinguish, inside the parameter space spanned by the FI term and the mass $μ$, four different corners where some quantitative statements can be made. These are the re…
We study the low-energy quantum dynamics of vortex strings in the Higgs phase of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is shown to coincide with the BPS spectrum of the four-dimensional parent gauge theory. Perturbative string excitations correspond to bound W-bosons and quarks while the monopoles appear as kinks on the vortex string. This provides a physical explanation for an observation by N. Dorey relating the quantum spectra of theories in two and four dimensions.
We show that QCD$_2$ on 2D pseudo-manifolds is consistent with the Gross-Taylor string picture. It allows us to introduce a model describing the one-dimensional evolution of the QCD$_2$ string (in the sense that QCD$_2$ itself is regarded as a zero-dimensional system). The model is shown to possess the third order phase transition associated with the $c=1$ Bose string below which it becomes equivalent to the vortex-free sector of the 1-dimensional matrix model. We argue that it could serve as a toy model for the glueball-threshold behavior of multicolor QCD.
Numerical indication that center vortices drive dynamical mass generation in QCD
本研究通过格点QCD数值计算，证实中心涡旋是QCD中动力学质量产生、手征对称性破缺及夸克禁闭的核心驱动因素。
Centre vortex evidence for a second finite-temperature QCD transition
本研究通过分析FASTSUM合作组的格点QCD系综，利用中心涡旋的逾渗行为、团簇特征等十项统计指标，证实QCD存在手征相变和约2倍手征温度处的退禁闭相变，并精确测得退禁闭温度为321(6)MeV。
Color magnetic flux tubes appear in the color-flavor locked phase of high density QCD, which exhibits color superconductivity as well as superfluidity. They are non-Abelian superfluid vortices and are accompanied by orientational zero modes in the internal space associated with the color-flavor locked symmetry spontaneously broken in the presence of the vortex. We show that those zero modes are localized around the vortex in spite of the logarithmic divergence of its tension, and derive the low-energy effective theory of them on the world-sheet of the vortex-string.
As was shown recently, non-Abelian vortex strings supported in four-dimensional ${\cal N}=2$ supersymmetric QCD with the U(2) gauge group and $N_f=4$ quark multiplets (flavors) become critical superstrings. In addition to the translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau non-compact threefold, namely, the conifold. We study closed string sta…
We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the Color-Flavor-Locked phase whose symmetry SU(3)_{c+L+R} is further broken to SU(2)_{c+L+R} x U(1)_{c+L+R} at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes (B-dG) equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the B-dG equation by treating the diquark gap having the vortex configuration as a background fi…
In this lecture I will explain the established pictures of the QCD vacuum and, in particular, the underlying confinement mechanism. These are: the magnetic monopole condensation (dual Meißner effect), the center vortex picture and the Gribov--Zwanziger picture. I will start by giving a survey of the common order and disorder parameters of confinement: the temporal and spatial Wilson loop, the Polyakov loop and the 't Hooft loop. Next the dual Meißner effect, which assumes a condensate of magnetic monopoles, will be explained as a picture of confinement. I will also show how magnetic monopoles …
Seiberg and Witten's proposed solution of N=2 SQCD with N_c=2 and N_F=4 is known to conflict with instanton calculations in three distinct ways. Here we show how to resolve all three discrepancies, simply by reparametrizing the elliptic curve in terms of quantities $τ^0_{eff}$ and $\tilde{u}$ rather than $τ$ and $u = < Tr A^2 > $. SL(2,Z) invariance of the curve is preserved. However, there is now an infinite ambiguity in the relation between $τ^0_{eff}$ and $τ$ and between $\tilde{u}$ and $u$, corresponding to an infinite number of unknown coefficients in the instanton expansion. Thus the rei…
Baryons as linked vortices in QCD matter with isospin asymmetry
利用手征微扰理论，研究发现当重子化学势超过临界值时，ANO涡旋与全局涡旋线形成拓扑链接，其链接数对应重子数，从而提出一种无需Skyrme项的稳定Skyrmion型重子物质新相。
Emergent Conformal Symmetry on Superfluid Vortices in Two-Color QCD and Pseudoreal Gauge Theories
该研究发现在双色QCD及伪实规范理论的超流体涡旋上，体WZW项诱导量子化模式，使涡旋理论在红外流向中心荷c=1的SU(2)_1共形场论，从而在非共形背景中涌现强耦合共形对称性。
We study deformations of dualities in finite N=2 supersymmetric QCD. Adding mass terms for some quarks and the adjoint matter to the finite N=2 theory, which is known to have dual descriptions, the correspondence of gauge invariant operators between the original and dual theory is deformed. As a result, we naturally obtain N.Seiberg's N=1 duality. Furthermore, we discuss the origin of the meson and superpotential in the dual theory. This approach can be applied to SU(N), SO(N), and USp(2N) gauge theories, and we analyze all these cases.
The classical massless SU(2) field theory has an infinite number of gauge equivalent representations of the vacuum. We show that among these there exists a non-perturbative center vortex representation with some similarity to the quantum vacuum of the same theory. This classical SU(2) vacuum consists of a lattice of center vortex pairs combining to triviality. However, this triviality can be broken by perturbations, for example by adding a mass term, or by considering the electroweak theory where the Higgs field does the breaking, or by quantum fluctuations like in QCD.
We analytically show that mesonic bound states of confined monopoles appear inside a non-Abelian vortex-string in massless three-flavor QCD at large quark chemical potential mu. The orientational modes CP^2 in the internal space of a vortex is described by the low-energy effective world-sheet theory. Mesons of confined monopoles are dynamically generated as bound states of kinks by the quantum effects in the effective theory. The mass of monopoles is shown to be an exponentially soft scale Delta*exp[-c*(mu/Delta)^2], with the color superconducting gap Delta and some constant c. A possible quar…
We consider large-N confining gauge theories with a Hagedorn density of states. In such theories the potential between a pair of colour-singlet sources may diverge at a critical distance r_c = 1/ T_H. We consider, in particular, pure N=1 super Yang-Mills theory and argue that when a domain-wall and an anti domain-wall are brought to a distance near r_c the interaction potential is better described by an ``open QCD-string channel''. We interpret the divergence of the potential in terms of a tachyonic mode and relate its mass to the Hagedorn temperature. Finally we relate our result to a theorem…
We propose an axionic QCD string scenario based on the original flux-tube model by Kogut and Susskind, and then incorporate it into a gauged Nambu-Jona-Lasinio (NJL) model. Axial anomaly is studied by a new topological coupling from the string side, and by the 't Hooft vortex from the NJL side, respectively. The nontrivial phase distribution of the quark condensate plays an important role in this scenario.
Magnetically charged vortex defects are shown to arise in canonically quantised modified axial gauge QCD_{3+1} on a torus. This gauge -- being an Abelian projection -- keeps only the eigenphases as dynamical variables of the Wilson line in x_3-direction. A mismatch between the identification of large gauge transformations before and after gauge fixing is indicated.
Hall Droplet Sheets in Holographic QCD
本文提出单味全息QCD中重子“片”的弦理论描述，基于Witten-Sakai-Sugimoto模型揭示其由D6-branes核心与D8-brane介子壳构成，并精确计算了片与涡旋弦的张力、厚度及四维有效作用量。
In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs. phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N_f=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term ξtriggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: ξand the quark mass difference Δm. We obtain the phase diagram on the (ξ, Δm) plane. At large ξand small …
We construct a non Abelian model for SU(2) QCD in Euclidean three-dimensional spacetime and study its different phases. The model contains a center vortex sector coupled to a dual effective field encoding information about how the vortices are paired in the ensemble. The possible phases in parameter space are interpreted in terms of the proliferation of either closed center vortices or closed chains, where the endpoints of open vortices are attached in pairs to monopole-like defects.
Different types of non-Abelian vortex-strings appear in dense or hot QCD, both of which possess non-Abelian internal orientation zero modes. We calculate the interaction between them and find the universal repulsion for dense QCD (color superconductivity) and the dependence on the orientations for hot QCD (chirally broken phase). This is a review article based on our papers arXiv:0708.4092 and arXiv:0708.4096.
We review lattice evidence showing that center-vortex condensation is a serious candidate for the mechanism of colour confinement in quantum chromodynamics.
I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector a vacuum wave functional is used which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170 MeV and 198 MeV,…
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