arXiv subjects

A. Yung

Publications and source records attributed to A. Yung.

At least 19 recordsLinked to original sources

arXiv2026

Unified description of color-electric and color-magnetic strings in hybrid vacua of $\mathcal{N}=2$ supersymmetric QCD

We study non-Abelian strings supported in $r$-vacua of 4D $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group $U(N)$ and $N_f$ quark hypermultiplets ($N_f\ge N$), where $r<N$ (scalar) quarks develop vacuum expectation values. At the quantum level, $N-r-1$ monopoles in the orthogonal sector of the gauge group also form a condensate. This leads to the formation of flux tubes (strings) that carry both color-electric and color-magnetic fluxes and confine quarks and monopoles, respectively. We present a unified description of the 2D effective theory living on the world sheet of this non-Abelian string. In particular, we derive the exact twisted superpotential of the world sheet theory, which is deformed by the presence of non-perturbative gaugino condensate in 4D hybrid vacua, using the Gaiotto-Gukov-Seiberg method of resolvents. Next, we extrapolate the 2D-4D correspondence of BPS spectra of the world sheet theory and 4D SQCD (known for quark vacua) to hybrid vacua. Namely, our key result is the precise matching between the masses of the two-dimensional kinks and the four-dimensional confined monopoles or quarks. In addition, we provide a physical picture of the quark/monopole confinement in hybrid vacua.

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arXiv2026

Hadrons in $\mathcal{N}=2$ supersymmetric QCD from non-Abelian string on 2D black hole

We continue the study of non-Abelian vortex string in 4D $\mathcal{N}=2$ supersymmetric QCD as critical superstring, and extend this analysis to $U(N)$ gauge theory with arbitrary even $N$ and $N_f=2N$ number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by the string spectrum on the 2D $\mathcal{N}=2$ supersymmetric black hole. We perform a cross-check by computing the multiplicity of hadronic states of the high-energy part of the spectrum both from string and field theory pictures. We also clarify the spontaneous breaking of the global flavor symmetry by VEV of the massless baryon. We finally claim, that phase diagram of $\mathcal{N}=2$ SQCD with $N_f=2N$ consists of the Higgs phase at weak coupling and string/hadronic phase at strong coupling, separated by phase transition, and is seen as a conifold transition from string theory point of view.

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arXiv2025

Critical Non-Abelian Vortex String and 2D N=2 Black Hole

It has been shown that the non-Abelian vortex string in 4D $\mathcal{N}=2$ SQCD with the U(2) gauge group and $N_f=4$ flavors becomes a critical superstring. Its 10D target space is a product of the flat 4D space and an internal noncompact Calabi-Yau threefold, namely, the conifold. It was also shown that the Coulomb branch of the associated string sigma model, which opens up at strong coupling, can be described by $\mathcal{N}=2$ Liouville theory. We continue here the study of the recently proposed mass deformation of the U(2) theory with $N_f=4$, interpolating to SQCD with the U(4) gauge group and $N_f=8$ quarks, by analyzing the mass-deformed $\mathcal{N}=2$ Liouville theory on the string world sheet, and show that it is always described by the trumpet geometry of the target space, which is $T$-dual to the 2D $\mathcal{N}=2$ supersymmetric black hole. We use this correspondence to find the low-lying hadron spectrum in the deformed SQCD, and explain the expected increase in the number of hadronic states in the theory with more gauge fields and quarks by considering the near-Hagedorn behavior of the 2D black hole.

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arXiv2025

Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String

It has been demonstrated that the non-Abelian solitonic vortex string in four-dimensional (4D) $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group U(2) and $N_f=4$ quark hypermultiplets behaves as a critical superstring. This string propagates in a ten-dimensional space comprising the flat 4D space and an internal Calabi-Yau noncompact threefold, specifically, the conifold. The lowest state of this string is a massless BPS baryon associated with the deformation of the conifold's complex structure modulus, $b$. Previous studies considered deformations of the 10-dimensional background by a nonzero Neveu-Schwarz (NS) 3-form flux, which was interpreted as selecting specific quark masses in 4D SQCD. These deformations and the corresponding back reaction on the metric were analyzed at the leading order at small 3-form flux. In this paper, we first derive the exact potential for the conifold complex structure modulus $b$ generated by the 3-form flux assuming a fixed conifold background. Then we include the back reaction effects and solve the corresponding gravity equations of motion. We show that the resulting potential gives a runaway vacuum. At this runaway vacuum the conifold undergoes degeneration.

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arXiv2024

Flowing Between String Vacua for the Critical Non-Abelian Vortex with Deformation of N=2 Liouville theory

It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N=2 supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f=4$ quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of low lying closed string states was found and interpreted as a spectrum of hadrons in 4D N=2 SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. It was recently shown that the Coulomb branch of the associated string sigma model which opens up at strong coupling can be described by N=2 Liouville theory. Building on these results we switch on quark masses in 4D N=2 SQCD and study the interpolation of the initial U(2) SQCD with $N_f=4$ quarks to the final SQCD with the U(4) gauge group and $N_f=8$ quarks. To find the true string vacuum which arises due to the mass deformation we solve the effective supergravity equations of motion associated with the deformed world sheet Liouville theory. We show that the massless BPS baryon $b$ survives the deformation and that finding of the spectrum of low lying massive hadrons in the final SQCD is linked to the Calogero problem.

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arXiv2023

Large-$N$ Solution and Effective Action of "Twisted-Mass'' Deformed $\mathbb{CP}(N-1)$ Model

We study effective dynamics of the non-supersymmetric two-dimensional $\mathbb{CP}(N-1)$ model in the large $N$ limit. This model is deformed by a mass term $m$ preserving $\mathbb{Z}_N$ symmetry of the Lagrangian. At small $m$ the theory is strongly coupled and resembles the undeformed $\mathbb{CP}(N-1)$ model, while at large $m$ it is in a weakly coupled Higgs phase with spontaneously broken $\mathbb{Z}_N$. We find the phase transition point and discuss the fate of the kink-antikink ``mesons'' at strong coupling. We also resolve an issue of instability that arose in previous studies of this model.

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arXiv2022

NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String

It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f = 4$ quark flavors becomes a critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau noncompact threefold, namely, the conifold. The spectrum of low lying closed string states in the associated type IIA string theory was found and interpreted as a spectrum of hadrons in 4D N = 2 SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. In the previous work the deformation of the 10-dimensional background with nonzero Neveu-Schwarz 3-form flux was considered and interpreted as a switching on a particular choice of quark masses in 4D SQCD. This deformation was studied to the leading order at small 3-form flux. In this paper we study the back reaction of the nonzero 3-form flux on the metric and the dilaton introducing ansatz with several warp factors and solving gravity equations of motion. We show that 3-form flux produces a potential for the conifold complex structure modulus $b$, which leads to the runaway vacuum. At the runaway vacuum warp factors disappear, while the conifold degenerates. In 4D SQCD we relate this to the flow to the U(1) gauge theory upon switching on quark masses and decoupling of two flavors.

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arXiv2021

Critical Non-Abelian Vortex and Holography for Little String Theory

It has been shown that non-Abelian vortex string supported in four dimensional (4D) ${\mathcal N}=2$ supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f = 4$ quark flavors becomes a critical superstring. This string propagates in the ten dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau non-compact threefold, namely, the conifold. The spectrum of closed string states of the associated string theory was obtained using the equivalence between the critical string on the conifold and the non-critical string on the semi-infinite cigar described by SL($2, \mathbb{R}$)/U(1) Wess-Zumino-Novikov-Witten model. This spectrum was identified with the spectrum of hadrons in 4D ${\mathcal N}=2$ SQCD. In order to describe effective interactions of these 4D hadrons in this paper we study correlation functions of normalizable vertex operators localized near the tip of the SL($2, \mathbb{R}$)/U(1) cigar. We also compare our solitonic string approach to the gauge-string duality to the AdS/CFT-type holography for little string theories (LSTs). The latter relates off mass-shell correlation functions on the field theory side to correlation functions of non-normalizable vertex operators on the cigar. We show that in most channels holographic approach works in our theory because normalizable and non-normalizable vertex operators with the same conformal dimension are related due to the reflection from the tip of the cigar. However, we find that holography does not work for lightest hadrons with given baryonic charge.

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arXiv2021

Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses

It has been shown that non-Abelian solitonic vortex strings supported in four-dimensional (4D) ${\mathcal N}=2\;$ supersymmetric QCD (SQCD) with the U($N=2$) gauge group and $N_f=4$ quark flavors behave as critical superstrings. In addition to four translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional 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 $\mathbb{R}^4$ and a Calabi-Yau non-compact threefold $Y_6$, namely, the conifold. The spectrum of low lying closed string states in the associated type IIA string theory was found and interpreted as a spectrum of hadrons in 4D ${\mathcal N}=2\;$ SQCD. In particular, the lowest string state appears to be a massless BPS baryon associated with the deformation of the complex structure modulus $b$ of the conifold. Here we address a problem of switching on quark masses in 4D SQCD, which classically breaks the world sheet conformal invariance in the string sigma model. To avoid this problem we follow a standard string theory approach and use a flux "compactification" to lift the complex structure modulus of the conifold. Namely, we find a solution of supergravity equations of motion with non-zero NS 3-form flux. It produces a potential for the baryon $b$, which leads to the run-away vacuum. Using field theory arguments we interpret 3-form flux in terms of a particular choice of quark masses in 4D SQCD. At the run-away vacuum the conifold degenerates to lower dimensions. We interpret this as a flow from a non-Abelian string to an Abelian one.

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arXiv2020

String "Baryon'' in Four-Dimensional $\mathcal{N} = 2$ Supersymmetric QCD from 2D-4D Correspondence

We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we study the conformal world-sheet theory on the non-Abelian string -- the so called weighted $\mathcal{N} = (2,2)$ supersymmetric $\mathbb{CP}$ model. Its target space is given by the six-dimensional non-compact Calabi-Yau space $Y_6$, the conifold. We use mirror description of the model to study the BPS kink spectrum and its transformations on curves (walls) of marginal stability. Then we use the 2D-4D correspondence to show that the deformation of the complex structure of the conifold is associated with the emergence of a non-perturbative Higgs branch in 4D theory which opens up at strong coupling. The modulus parameter on this Higgs branch is the vacuum expectation value of the massless BPS "baryon" previously found in string theory.

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arXiv2019

Dynamics of non-Abelian strings in the theory interpolating from ${\mathcal N}=2$ to ${\mathcal N}=1$ supersymmetric QCD

We study the dynamics of non-Abelian vortex strings supported in ${\mathcal N}=2$ supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by the mass $μ$ of the adjoint matter. In the limit of large $μ$ the bulk four-dimensional theory flows to ${\mathcal N}=1$ supersymmetric QCD. The dynamics of orientational zero modes of the non-Abelian string is described by the world sheet CP$(N-1)$ model. At $μ=0$ this model has ${\mathcal N}= \left(2,2\right) $ supersymmetry while at large $μ$ it flows to the non-supersymmetric CP$(N-1)$ model. We solve the world sheet model in the large $N$ approximation and find a rich phase structure with respect to the deformation parameter $μ$ and quark mass differences. The phases include two strong coupling phases and two Higgs phases. In particular, the Higgs phase at small $μ$ supports CP$(N-1)$ model kinks representing confined monopoles of the bulk QCD, while in the large-$μ$ Higgs phase monopoles disappear.

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arXiv2019

Quantizing a solitonic string

Quite often the zero mode dynamics on solitonic vortices are described by a non-conformal effective world-sheet sigma model (WSSM). We address the problem of solitonic string quantization in this case. As well-known, only crfitical strings with superconformal WSSMs are self-consistent in ultra-violet (UV) domain. Thus, we look for the appropriate UV completion of the low-energy non-conformal WSSM. We ague that for the solitonic strings supported in well-defined bulk theories the UV complete WSSM has a UV fixed point which can be used for string quantization. As an example, we consider BPS non-Abelian vortices supported by four-dimensional (4D) \ntwo SQCD with the gauge group U$(N)$ and $N_f$ quark multiplets where $N_f\ge N$. In addition to translational moduli the non-Abelian vortex under consideration carries orientational and size moduli. Their low-energy dynamics are described by a two-dimensional \ntwot supersymmetric weighted model, namely, $\mathbb{WCP}(N, N_f-N)$. Given our UV completion of this WSSM we find its UV fixed point. The latter defines a superconformal WSSM. We observe two cases in which this conformal WSSM, combined with the free theory for four translational moduli, has ten-dimensional target space required for superstrings to be critical.

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arXiv2018

What Becomes of Semilocal non-Abelian Strings in ${\mathcal N}=1$ Supersymmetric QCD

We study non-Abelian vortex strings in ${\mathcal N}=2$ supersymmetric QCD with the gauge group U$(N)$ deformed by the mass $μ$ of the adjoint matter. This deformation breaks ${\mathcal N}=2$ supersymmetry down to ${\mathcal N}=1$ and in the limit of large $μ$ the theory flows to ${\mathcal N}=1$ QCD. Non-Abelian strings in addition to translational zero modes have orientation moduli. In the ${\mathcal N}=2$ limit of small $μ$ the dynamics of orientational moduli is described by the two dimensional $CP(N-1)$ model for QCD with $N_f=N$ flavors of quark hypermultiplets. For the case of $N_f>N$ the non-Abelian string becomes semilocal developing additional size moduli which modify the effective two dimensional $σ$-model on the string making its target space non-compact. In this paper we consider the $μ$-deformed theory with $N_f>N$ eventually making $μ$ large. We show that size moduli develop a potential that forces the string transverse size to shrink. Eventually in the large $μ$ limit size moduli decouple and the effective theory on the string reduces to the $CP(N-1)$ model. We also comment on physics of confined monopoles.

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arXiv2018

Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory

It was recently shown that non-Abelian vortex strings supported in a version of four-dimensional N=2 supersymmetric QCD (SQCD) become critical superstrings. In addition to four translational moduli, non-Abelian strings under consideration have six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical, namely, the product of the flat four-dimensional space and conifold -- a non-compact Calabi-Yau threefold. In this paper we report on further studies of low-lying closed string states which emerge in four dimensions and identify them as hadrons of our four-dimensional N=2 SQCD. We use the approach based on "little string theory," describing critical string on the conifold as a non-critical $c=1$ string with the Liouville field and a compact scalar at the self-dual radius. In addition to massless hypermultiplet found earlier we observe several massive vector multiplets and a massive spin-2 multiplet, all belonging to the long (non-BPS) representations of N=2 supersymmetry in four dimensions. All the above states are interpreted as baryons formed by a closed string with confined monopoles attached. Our construction presents an example of a "reverse holography."

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arXiv2017

Index Theorem for non-Supersymmetric Fermions Coupled to a non-Abelian String and Electric Charge Quantization

Non-Abelian strings are considered in {\em non}-supersymmetric theories with fermions in various appropriate representations of the gauge group U($N$). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases, we observe a non-trivial $N$ dependence.

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arXiv2017

Fradkin-Shenker Continuity and "Instead-of-Confinement" Phase

In 1979 Fradkin and Shenker observed \cite{Frad} that if one considers a Yang-Mills theory fully Higgsed by virtue of scalar fields in the fundamental representation of the ${\rm SU}(N)$ gauge group there is no phase transition in passing from the Higgs regime (weak coupling) to the "QCD confinement" regime at strong coupling. The above two regimes are continuously connected. We combine this observations with lessons from supersymmetric gauge theories which show that the Higgs phase is continuously connected to what is called "instead-of-confinement" phase rather than the phase with quark confinement. In the "instead-of-confinement" phase monopoles are confined and play a role of "constituent" quarks inside hadrons. In contrast, the Seiberg-Witten phase of quark confinement is not analytically connected to the Higgs phase. We propose dedicated lattice studies of Yang-Mills theories with scalar quarks.

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arXiv2017

Non-Abelian strings in N=1 supersymmetric QCD

Non-Abelian flux tubes (strings) are well studied in N=2 supersymmetric QCD in (3+1) dimensions. In addition to translational zero modes they have also orientational moduli associated with rotations of their fluxes inside a non-Abelian group. The dynamics of the orientational moduli is described by the two dimensional CP(N-1) model living on the world sheet of the non-Abelian string. In this paper we consider a deformation of N=2 supersymmetric QCD with the U(N) gauge group and N_f=N quark flavors with a mass term $μ$ of the adjoint matter. In the limit of large $μ$ the theory flows to an N=1 supersymmetric QCD. We study the solution for the non-Abelian string in this limit and derive an effective theory on the string world sheet. The bosonic sector of this theory is still given by the CP(N-1) model but its scale is exponentially small as compared to the scale of the four dimensional bulk theory in contrast to the N=2 case where these scales are equal. We study also the fermionic sector of the world sheet theory. Upon the deformation the non-Abelian string is no longer BPS and we show that the fermionic superorientational zero modes are all lifted. This leaves us with the pure bosonic CP(N-1) model on the string world sheet in the limit of N=1 QCD. We also discuss what happens to confined monopoles at large $μ$.

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arXiv2017

Critical Non-Abelian Vortex in Four Dimensions and Little String Theory

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 states which emerge in four dimensions (4D) and identify them with hadrons of four-dimensional ${\cal N}=2$ QCD. One massless state was found previously: it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper we find a number of massive states. To this end we exploit the approach used in LST, "Little String Theory," namely equivalence between the critical string on the conifold and non-critical $c=1$ string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.

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