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A. Yung

Publications and source records attributed to A. Yung.

At least 37 records · Page 2Linked to original sources
arXiv2016

Non-Abelian Vortex in Four Dimensions as a Critical Superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N=2 supersymmetric QCD with the U(2) gauge group, N_f=4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a two-dimensional sigma model with the target space {R}^4\times Y_6 where Y_6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N=2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole-monopole baryon of the 4D theory (at strong coupling).

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arXiv2016

Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions

Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP(2,2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."

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arXiv2016

Heterotic Non-Abelian String of a Finite Length

We consider non-Abelian strings in N=2 supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N=2 supersymmetry down to N=1. Dynamics of orientational zero modes on the string world sheet are described then by CP$(N-1)$ model with N=(0,2) supersymmetry. We study the string of a finite length $L$ assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-$N$ approximation. We find a rich phase structure in the $(L, \,u)$ plane where $u$ is a deformation parameter. At large $L$ and intermediate $u$ we find a phase with broken $Z_{2N}$ symmetry, $N$ vacua and a mass gap. At large values of $L$ and $u$ still larger we have the $Z_{2N}$-symmetric phase with a single vacuum and massless fermions. In both phases N=(0,2) supersymmetry is spontaneously broken. We also observe a phase with broken SU$(N)\;$ symmetry at small $L$. In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading $1/N$ approximation. However, we expect that $1/N$ corrections will break N=(0,2) supersymmetry. We also discuss how this rich phase structure matches the N=(2,2) limit in which the world-sheet theory has a single phase with the mass gap independent of $L$.

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arXiv2015

Critical String from Non-Abelian Vortex in Four Dimensions

In a class of non-Abelian solitonic vortex strings supported in certain N=2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U(2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP(2,2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.

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arXiv2014

Lessons from supersymmetry: "Instead-of-Confinement" Mechanism

We review physical scenarios in different vacua of N=2 supersymmetric QCD deformed by the mass term μfor the adjoint matter. This deformation breaks supersymmetry down to N=1 and, at large μ, the theory flows to N=1 SQCD. We focus on dynamical scenarios which can serve as prototypes of what we observe in real-world QCD. The so-called r=N vacuum is especially promising in this perspective. In this vacuum an "instead-of-confinement" phase was identified previously, which is qualitatively close to the conventional QCD confinement: the quarks and gauge bosons screened at weak coupling, at strong coupling evolve into monopole-antimonopole pairs confined by non-Abelian strings. We review genesis of this picture.

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arXiv2014

Two-Dimensional Sigma Models Related to Non-Abelian Strings in Super-Yang-Mills

We review diverse two-dimensional models emerging on the world sheet of non-Abelian strings in the low-energy limit. Non-Abelian strings are supported in a class of four-dimensional bulk theories with or without supersymmetry. In supersymmetric bulk theories we are mostly interested in BPS-saturated strings. Some of these two-dimensional models, in particular, heterotic models, were scarcely studied in the past, if at all. Our main emphasis is on the heterotic N=(0,2) models. We describe their large-N solution. We briefly comment on N=(0,1) models although so far they are not obtained on the the world sheet of non-Abelian strings.

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arXiv2014

N=1 Duality in the Chiral Limit from N=2 Duality

We study a deformation of N=2 supersymmetric QCD with U(N) gauge group and N_f quark flavors induced by the mass term μfor the adjoint matter which breaks supersymmetry down to N=1 QCD. Recently this deformation was shown to lead to a weakly coupled dual theory only in two particular sets of vacua: the r=N vacuum and the so-called zero vacua which can be found at r< N_f-N, where r is the number of condensed quarks. For small quark masses and intermediate values of μthe gauge group of the dual theory is U(N_f-N)\times U(1)^{2N-N_f} where the Abelian sector is heavy and can be integrated out. However, at larger values of μthe Abelian sector enters the strong coupling regime. We show that the 't Hooft matching conditions in the chiral limit require the Seiberg neutral meson field M from this sector to become light. In the r=N vacuum M is constructed of a monopole and antimonopole connected by a confining magnetic strings while in the zero vacua it is built of a quark and antiquark connected by a confining electric strings.

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arXiv2014

More on the Abrikosov Strings with Non-Abelian Moduli

We continue explorations of deformed Abrikosov-Nielsen-Olesen (ANO) strings, with non-Abelian moduli on the world sheet. In a simple model with an extra field we find classically stable ANO and non-Abelian strings. The tension of the latter is a few percent lower than the tension of the ANO string. Then we calculate the interpolating field configuration. Once the kink mass $M_k$ and the difference of tensions $ΔT$ are found we calculate the decay rate of the ANO string with a higher tension ("false vacuum") into the non-Abelian string with the lower tension ("genuine vacuum") through the "bubble" formation in the quasiclassical approximation.

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arXiv2014

Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence

We explore non-Abelian strings in the r=N-1 vacuum of N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of quarks (N_f\geq N), where r is the number of condensed quarks. N=2 supersymmetry is broken down to N=1 by a small mass term for the adjoint matter. We discover that the low-energy two-dimensional theory on the string world-sheet receives nonperturbative corrections from the bulk, through the bulk gaugino condensate. This is in contradistinction with the r=N vacuum situation, in which nonperturbative effects on the world sheet are determined by internal dynamics of the world-sheet theory. The 2D-4D correspondence (the coincidence of spectra of two-dimensional kinks and four-dimensional monopoles) remains valid in the BPS sector. Nonperturbative bulk effects deforming the weighted CP model on the world sheet are found by virtue of the method of resolvents suggested by Gaiotto, Gukov and Seiberg for surface defects. In the r=N vacuum the gaugino condensate in the bulk vanishes, and there are no "outside" nonperturbative corrections on the world sheet.

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arXiv2013

Revisiting the Faddeev-Skyrme Model and Hopf Solitons

We observe that the Faddeev-Skyrme model emerges as a low-energy limit of scalar QED with two charged scalar fields and a selfinteraction potential of a special form (inspired by supersymmetric QCD). Then we discuss possible Hopf solitons of the "twisted-toroidal" type.

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arXiv2013

Abrikosov-Nielsen-Olesen string with Non-Abelian Moduli and "Spin-Orbit" Interaction

It is generally believed that the spontaneous breaking of the Poincaré group by flux tubes (strings) generate only two zero modes localized on the string and associated with the spontaneous breaking of translational invariance (the so-called Low-Manohar argument). Being perfectly true in many instances it is nevertheless nonuniversal, and have to be amended in the case of order parameters carrying spatial indices. We show that under certain circumstances additional zero (or quasizero) modes can appear due to spin symmetry.

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arXiv2013

Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2

Starting from the Seiberg-Witten solution of N=2 SQCD with the U(N) gauge group and N_f quark flavors we construct the so-called μ-dual N=1 theory in the r vacua in the regime analogous to that existing to the left of the left edge of the Seiberg conformal window (here r is the number of condensed quarks). The strong-weak coupling duality is shown to exist in the so-called zero vacua which can be found at r< N_f-N. We show that the μ-dual theory matches the Seiberg dual in the zero vacua.

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arXiv2013

Hybrid r-Vacua in N=2 Supersymmetric QCD: Universal Condensate Formula

We derive an exact unified formula for all condensates (quark and monopole) in the hybrid r vacua in N=2 supersymmetric QCD slightly deformed by a μA^2 term. The gauge group is assumed to be U(N) and the number of the quark flavors N_f subject to the condition N< N_f < 2N. In the r vacua r quarks and N-r-1 monopoles from non-overlapping subgroups of U(N) develop vacuum expectation values (r<N). We then briefly review possible dynamical regimes (confinement, screening, and "instead of confinement") in the hybrid r vacua in μ-deformed N=2 SQCD (the small-μlimit).

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arXiv2012

r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD

We consider N=2 SQCD with the U(N) gauge group and N_f flavors (N_f>N) perturbed by an N=2 breaking deformation - a small mass term μfor the adjoint matter. We study r-vacua, with the constraint $2N_f/3 < r \le N. At large values of the parameter ξ\simμm (m is a typical value of the quark masses) r quark flavors condense, by construction. The effective low-energy theory with the gauge group U(r)\times U(1)^{N-r} is at weak coupling. Upon reducing ξthe original theory undergoes a crossover transition from weak to strong coupling. As the original theory becomes strongly coupled, at low energies it is described by a weakly coupled infrared-free dual theory with the gauge group U(N_f-r)\times U(1)^{N-N_f+r} and N_f light dyon flavors. These dyons condense triggering formation of non-Abelian strings which still confine monopoles, rather than quarks, contrary to naive duality arguments. "Instead-of-confinement" mechanism for quarks and gauge bosons of the original theory takes place: screened quarks and gauge bosons of the original theory decay, on curves of the marginal stability (CMS), into confined monopole-antimonopole pairs that form stringy mesons. Next, we increase the deformation parameter μthus decoupling the adjoint fields. Then our theory flows to N=1 SQCD. The gauge group of the dual theory becomes U(N_f-r). We show that the dual theory is weakly coupled if we are sufficiently close to the Argyres-Douglas point. The "instead-of-confinement" mechanism for quarks and gauge bosons survives in the limit of large μ. It determines low-energy non-Abelian dynamics in the r-vacua of N=1 SQCD.

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arXiv2012

Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD

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 decreases ξone hits a a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of-confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3) N_f$.

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arXiv2011

Description of the Heterotic String Solutions in U(N) SQCD

We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained [1] in a particular U(2) gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Here we generalize the previous results to U(N) gauge theories. As was suggested by Edalati and Tong [2], the string world sheet theory is 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) world sheet model directly from the U(N) bulk theory. Parameters of the bulk theory are related to those of the world sheet theory. Qualitatively this relation turns out to be the same as in the U(2) case.

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arXiv2011

Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD

We consider non-Abelian semilocal strings (vortices, or vortex-strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+Ñ matter hypermultiplets in the fundamental representation (quarks), and a Fayet-Iliopoulos term ξ. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both, orientational and size zero modes. Our derivation is complete in the limit, ln(L)\rightarrow \infty, where L is an infrared (IR) regulator in the transverse plane. In this limit the world-sheet theory is obtained exactly. It is presented by a so far unknown N=2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(Nf-1) model conjectured by Hanany and Tong, through D-branes, as the world-sheet theory for the non-Abelian semilocal strings. The Hanany-Tong set-up has no parallel for the field-theoretic IR parameter and metrics of the weighted CP(Nf-1) model and zn model are different. Still their quasiclassical excitation spectra coincide.

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