arXiv subjects

A. Yung

Publications and source records attributed to A. Yung.

At least 55 records · Page 3Linked to original sources

arXiv2011

Confined Magnetic Monopoles in Dense QCD

Non-Abelian strings exist in the color-flavor locked phase of dense QCD. We show that kinks appearing in the world-sheet theory on these strings, in the form of the kink-antikink bound pairs, are the magnetic monopoles --- descendants of the 't Hooft-Polyakov monopoles surviving in such a special form in dense QCD. Our consideration is heavily based on analogies and inspiration coming from certain supersymmetric non-Abelian theories. This is the first ever analytic demonstration that objects unambiguously identifiable as the magnetic monopoles are "native" to non-Abelian Yang-Mills theories (albeit our analysis extends only to the phase of the monopole confinement and has nothing to say about their condensation). Technically our demonstration becomes possible due to the fact that low-energy dynamics of the non-Abelian strings in dense QCD is that of the orientational zero modes. It is described by an effective two-dimensional CP(2) model on the string world sheet. The kinks in this model representing confined magnetic monopoles are in a highly quantum regime.

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arXiv2010

Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass term μfor the adjoint matter, W=μA^2, assuming that N\leq N_f<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small μ, so that the Z_N strings preserve, in a sense, their BPS nature. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N_f-1) model on the string world sheet. The bulk μ-deformation makes this theory N= (0,2) supersymmetric heterotic weighted CP(N_f-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.

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arXiv2010

N=(0,2) Deformation of the N=(2,2) Wess-Zumino Model in Two Dimensions

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field ζ_R involved in the N=(0,2) deformation plays the role of Goldstino.

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arXiv2010

Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model

We continue explorations of non-Abelian strings, focusing on the solution of a heterotic deformation of the CP(N-1) model with an extra right-handed fermion field and N=(0,2) supersymmetry. This model emerges as a low-energy theory on the worldsheet of the BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by a superpotential of a special type breaking N=2 supersymmetry down to N=1. Using large-N expansion we solve this model to the leading order in 1/N. Our solution exhibits spontaneous supersymmetry breaking for all values of the deformation parameter. We identify the Goldstino field. The discrete Z_{2N} symmetry is shown to be spontaneously broken down to Z_2; therefore, the worldsheet model has N strictly degenerate vacua (with nonvanishing vacuum energy). Thus, the heterotic CP(N-1) model is in the deconfinement phase. We can compare this dynamical pattern, on the one hand, with the N=(2,2) CP(N-1) model which has N degenerate vacua with unbroken supersymmetry, and, on the other hand, with nonsupersymmetric CP(N-1) model with split quasivacua and the Coulomb/confining phase. We determine the mass spectrum of the heterotic CP(N-1) model in the large-N limit.

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arXiv2010

Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings

Recently we observed a crossover transition (in the Fayet-Iliopoulos parameter) from weak to strong coupling in N=2 supersymmetric QCD with the U(N) gauge group and N_f > N quark flavors. At strong coupling this theory can be described by a dual non-Abelian weakly coupled SQCD with the dual gauge group U(N_f-N) and N_f light dyon flavors. Both theories support non-Abelian strings. We continue the study of confinement dynamics in these theories, in particular, metamorphoses of excitation spectra, from a different side. A number of results obtained previously are explained, enhanced and supplemented by analyzing the world-sheet dynamics on the non-Abelian confining strings. The world-sheet theory is the two-dimensional N=(2,2) supersymmetric weighted CP(N_f-1) model. We explore the vacuum structure and kinks on the world sheet, corresponding to confined monopoles in the bulk theory. We show that (in the equal quark mass limit) these kinks fall into the fundamental representation of the unbroken global SU(N)\times SU(N_f-N)\timesU(1) group. This result confirms the presence of "extra" stringy meson states in the adjoint representation of the global group in the bulk theory. The non-Abelian bulk duality is in one-to-one correspondence with a duality taking place in the N=(2,2) supersymmetric weighted CP(N_f-1) model.

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arXiv2009

Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD

We consider N=2 supersymmetric QCD with the gauge group SU(N_c)=SU(N+1) and N_f number of quark matter multiplets, being perturbed by a small mass term for the adjoint matter, so that its Coulomb branch shrinks to a number of isolated vacua. We discuss the vacuum where r=N quarks develop VEV's for N_f\geq 2N=2N_c-2 (in particular, we focus on the N_f= 2N and N_f= 2N+1 cases). In the equal quark mass limit at large masses this vacuum stays at weak coupling, the low-energy theory has U(N) gauge symmetry and one observes the non-Abelian confinement of monopoles. As we reduce the average quark mass and enter the strong coupling regime the quark condensate transforms into the condensate of dyons. We show that the low energy description in the strongly-coupled domain for the original theory is given by U(N) dual gauge theory of N_f\geq 2N light non-Abelian dyons, where the condensed dyons still cause the confinement of monopoles, and not of the quarks, as can be thought by naive duality.

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arXiv2009

Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality

The crossover transition from weak coupling at large ξto strong coupling at small ξis studied in N=2 supersymmetric gauge theory with the U(N) gauge group and N_f>N (here ξis the Fayet--Iliopoulos parameter). We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small ξ. The dual gauge group is U(N_f-N). The dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both theories support non-Abelian strings. In each of these two regimes there are two varieties of physical excitations: elementary fields and nonperturbative composite states bound by confining strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields.

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arXiv2009

Description of the Heterotic String Solutions in the M Model

We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained in U(N) gauge theories: N=2 supersymmetric QCD deformed by superpotential terms μA^2 breaking N=2 supersymmetry down to N=1. In these models one cannot consider the limit μ\to\infty which would eliminate adjoint fields: the bulk theory develops a Higgs branch; the emergence of massless particles in the bulk precludes one from taking the limit μ\to\infty. This drawback is absent in the M model (hep-th/0701040) where the matter sector includes additional "meson" fields M introduced in a special way. We generalize our previous results to the M model, derive the heterotic string (the string world-sheet theory is a heterotic N=(2,0) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion coupled to the fermion fields of the N=(2,2) CP(N-1) model), and then explicitly obtain all relevant zero modes. This allows us to relate parameters of the microscopic M model to those of the world-sheet theory. The limit μ\to\infty is perfectly smooth. Thus, the full-blown and fully analyzed heterotic string emerges, for the first time, in the N=1 theory with no adjoint fields. The fate of the confined monopoles is discussed.

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arXiv2009

Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD

In N=2 supersymmetric QCD with the U(N) gauge group and N_f>N we study the crossover transition from the weak coupling regime at large ξto strong coupling at small ξwhere ξis the Fayet--Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists which describes low-energy physics at small ξ. The dual gauge group is U(N_f-N) and the dual theory has N_f flavors of light dyons, to be compared with N_f quarks in the original U(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N) x SU(N_f-N) x U(1), albeit the physical meaning of the SU(N) and SU(N_f-N) factors is different in the large- and small-ξregimes. Both regimes support non-Abelian semilocal strings. In each of these two regimes particles that are in the adjoint representations with respect to one of the factor groups exist in two varieties: elementary fields and composite states bound by strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields. The bulk duality that we observed translates into a two-dimensional duality on the world sheet of the non-Abelian strings. At large ξthe internal dynamics of the semilocal non-Abelian strings is described by the sigma model of N orientational and (N_f-N) size moduli, while at small ξthe roles of orientational and size moduli interchange. The BPS spectra of two dual sigma models (describing confined monopoles/dyons of the bulk theory) coincide. It would be interesting to trace parallels between the non-Abelian duality we found and string theory constructions.

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arXiv2009

Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations

We consider non-Abelian BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N =(1,1) SUSY is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1) x C rather than CP(N-1). This allowed them to suggest a "heterotic" N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

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arXiv2009

Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD

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 Δm the world-sheet dynamics of the string orientational moduli is described by N=2 two-dimensional CP(N-1) model. We show that as we reduce ξthe theory exhibits a crossover to the Abelian (Seiberg-Witten) regime. Instead of N^2 degrees of freedom of non-Abelian theory now only N degrees of freedom survive in the low-energy spectrum. Dyons with certain quantum numbers condense leading to the formation of the Abelian Z_N strings whose fluxes are fixed inside the Cartan subalgebra of the gauge group. As we increase N this crossover becomes exceedingly sharper becoming a genuine phase transition at N =\infty.

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arXiv2008

Confinement and Localization on Domain Walls

We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.

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arXiv2007

Non-Abelian Strings and the Luscher Term

We calculate the Luscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Luscher term is determined by the number of light degrees of freedom on the string wordsheet. Unlike the standard π/12 we get Nπ/12 for non-Abelian strings in the U(N) gauge theories. Thus, the Luscher coefficient acquires a dependence on the rank of the gauge group. In the models with non-Abelian strings discussed in the literature there are two distinct scales: the string tension ξ(the string thickness \sim ξ^{-1/2}) and the dynamical scale of strong interactions Λ. At weak coupling ξ\ggΛ^2. The Luscher term for non-Abelian strings experiences a jump: at ξ^{-1/2}\ll L\ll Λ^{-1} it is Nπ/12 while at at L\gg Λ^{-1} the orientational moduli are frozen out and the Luscher coefficient approaches its "Luscher" value π/12. We raise the question of possible extra (i.e. non-translational) light moduli on the worldsheet of QCD strings at large N.

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arXiv2007

Composite non-Abelian Flux Tubes in N=2 SQCD

Composite non-Abelian vortices in N=2 supersymmetric U(2) SQCD are investigated. The internal moduli space of an elementary non-Abelian vortex is CP^1. In this paper we find a composite state of two coincident non-Abelian vortices explicitly solving the first order BPS equations. Topology of the internal moduli space T is determined in terms of a discrete quotient CP^2/Z_2. The spectrum of physical strings and confined monopoles is discussed. This gives indirect information about the sigma model with target space T.

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arXiv2007

Confinement in N=1 SQCD: One Step Beyond Seiberg's Duality

We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(N_c) and N_c+N quark flavors. N_c flavors are massless; the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with N_c +N flavors of "dual quark" fields plus a gauge-singlet mesonic field M. The original theory is referred to as "quark theory" while the dual one is termed "monopole theory." The suggested mild deformation of Seiberg's procedure changes the dynamical regime of the monopole theory from infrared free to asymptotically free at large distances. We show that, upon condensation of the "dual quarks," the dual theory supports non-Abelian flux tubes (strings). Seiberg's duality is extended beyond purely massless states to include light states on both sides. Being interpreted in terms of the quark theory, the monopole-theory flux tubes are supposed to carry chromoelectric fields. The string junctions -- confined monopole-theory monopoles -- can be viewed as "constituent quarks" of the original quark theory. We interpret closed strings as glueballs of the original quark theory. Moreover, there are string configurations formed by two junctions connected by a pair of different non-Abelian strings. These can be considered as constituent quark mesons of the quark theory.

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arXiv2007

Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories

In the last decade it became clear that methods and techniques based on supersymmetry provide deep insights in quantum chromodynamics and other supersymmetric and non-supersymmetric gauge theories at strong coupling. In this review we summarize major advances in the critical (Bogomol'nyi-Prasad-Sommerfeld-saturated, BPS for short) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After a brief introduction in the theory of critical solitons (including a historical introduction) we focus on three topics: (i) non-Abelian strings in N=2 and confined monopoles; (ii) reducing the level of supersymmetry; and (iii) domain walls as D brane prototypes.

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arXiv2007

Supersymmetric Quantum Chromodynamics: How Confined Non-Abelian Monopoles Emerge from Quark Condensation

We consider N =1 supersymmetric QCD with the gauge group U(N) and N_f=N quark flavors. To get rid of flat directions we add a meson superfield. The theory has no adjoint fields and, therefore, no 't Hooft-Polyakov monopoles in the quasiclassical limit. We observe a non-Abelian Meissner effect: condensation of color charges (squarks) gives rise to confined monopoles. The very fact of their existence in N =1 supersymmetric QCD without adjoint scalars was not known previously. Our analysis is analytic and is based on the fact that the N =1 theory under consideration can be obtained starting from N =2 SQCD in which the 't Hooft-Polyakov monopoles do exist, through a certain limiting procedure allowing us to track the status of these monopoles at various stages. Monopoles are confined by BPS non-Abelian strings (flux tubes). Dynamics of string orientational zero modes are described by supersymmetric CP(N-1) sigma model on the string world sheet. If a dual of N =1 SQCD with the gauge group U(N) and N_f=N quark flavors could be identified, in this dual theory our demonstration would be equivalent to the proof of the non-Abelian dual Meissner effect.

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arXiv2006

Bulk-Brane Duality in Field Theory

We consider (3+1)-dimensional N=2 supersymmetric QED with two flavors of fundamental hypermultiplets. This theory supports 1/2-BPS domain walls and flux tubes (strings), as well as their 1/4-BPS junctions. The effective (2+1)-dimensional theory on the domain wall is known to be a U(1) gauge theory. Previously, the wall-string junctions were shown to play the role of massive charges in this theory. However, the field theory of the junctions on the wall (for semi-infinite strings) appears to be inconsistent due to infrared problems. All these problems can be eliminated by compactifying one spatial dimension orthogonal to the wall and considering a wall-antiwall system on a cylinder. We argue that for certain values of parameters this set-up provides an example of a controllable bulk-brane duality in field theory. Dynamics of the 4D bulk are mapped onto 3D boundary theory: 3D N=2 SQED with two matter superfields and a weak-strong coupling constant relation in 4D and 3D, respectively. The cylinder radius is seen as a "real mass" in 3D N=2 SQED. We work out (at weak coupling) the quantum version of the world-volume theory on the walls. Integrating out massive matter (strings in the bulk theory) one generates a Chern-Simons term on the wall world volume and an interaction between the wall and antiwall that scales as a power of distance. Vector and scalar (classically) massless excitations on the walls develop a mass gap at the quantum level; the long-range interactions disappear. The above duality implies that the wall and its antiwall partner (at strong coupling in the bulk theory) are stabilized at the opposite sides of the cylinder.

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