We apply the exact WKB analysis to the quantum Seiberg-Witten curve for 4-dimensional $\mathcal{N} = 2\ SU(2)\ N_f=2$ SQCD with the flavor symmetry. The discontinuity and the asymptotic behavior of the quantum periods define a Riemann-Hilbert problem. We derive the thermodynamic Bethe ansatz (TBA) equations as a solution to this problem. We also compute the effective central charge of the underlying CFT, which is shown to be proportional to the one-loop beta function of the SQCD.
We study supersymmetric domain walls of four dimensional $SU(N)$ SQCD with $N$ and $N+1$ flavors. In $4d$ we analyze the BPS differential equations numerically. In $3d$ we propose the $\mathcal{N}=1$ Chern-Simons-Matter gauge theories living on the walls. Compared with the previously studied regime of $F<N$ flavors, we encounter a couple of novelties: with $N$ flavors, there are solutions/vacua breaking the $U(1)$ baryonic symmetry; with $N+1$ flavors, our $3d$ proposal includes a linear monopole operator in the superpotential.
We construct holographic duals to N=1 SQCD with a quartic superpotential and unquenched massive flavors. Our backgrounds are generated by D5-branes wrapping two-dimensional submanifolds of an internal space. The flavor degrees of freedom are introduced by means of D5-branes extended along two-dimensional calibrated surfaces, and act as sources of the different supergravity fields. The backgrounds we get include the backreaction of the flavor branes and generalize the geometries obtained so far to the case in which the fundamental matter is massive. The supergravity solutions we find are regula…
We consider supersymmetric domain walls of four-dimensional $\mathcal{N}\!=\!1$ $Sp(N)$ SQCD with $F\!=\!N+1$ and $F\!=\!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions. When $F\!=\!N+2$, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue. Second, we discuss the $3d$ $\mathcal{N}\!=\!1$ Chern-Simons-matter theories that should describe the effective dynamics on th…
We obtain gravity duals to supersymmetric gauge theories in two and three spacetime dimensions with unquenched flavor. The supergravity solutions are generated by a set of color branes wrapping a compact cycle in a Calabi-Yau threefold, together with another set of flavor branes extended along the directions orthogonal to the cycle wrapped by the color branes. We construct supergravity backgrounds which include the backreaction induced by a smeared set of flavor branes, which act as delocalized dynamical sources of the different supergravity fields.
We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but noneth…
In arXiv:0811.1909 Spiridonov and Vartanov, using the superconformal index technique, found that 4-dimensional N=1 SQCD theory with SU(2) gauge group and four flavors has 72 dual representations. Recently in arXiv:1209.1404 the authors showed that these dual theories, when coupled to 5d hypermultiplets with specific boundary conditions have an extended E_7 global symmetry. In this work we find that for a reduced theory with 3 flavors the explicit SU(6) global symmetry is enhanced to an E_6 symmetry in the presence of 5d hypermultiplets. We also show connections between indices of different the…
In this note we describe how N=1 SQCD-like theories with a large number of flavors can be given a dual description in terms of a string background containing a large number of additional D5-branes. The dual geometries account for the backreaction of the additional branes: they depend on the ratio between the number of flavors and colors of the gauge theory. This note is based on hep-th/0602027. We present here also a new set of solutions, which are not included in the original paper.
In this paper we study dualities for $\mathcal{N}=2$ gauge theories in three dimensions with matter in the fundamental and adjoint representation. The duality we propose, analogous to mirror symmetry, is obtained starting from $\mathcal{N}=4$ mirror theories and turning on a certain superpotential deformation involving monopole operators. We study the role of emergent symmetries in the dual theory, focusing on the case of models with gauge symmetry $U(2)$ or $SU(2)$. We find that $SU(2)$ adjoint SQCD with one flavor and zero superpotential is dual to SQED with two flavors and three singlets. A…
We study the dimensions of non-chiral operators in the Veneziano limit of N=1 supersymmetric QCD in the conformal window. We show that when acting on gauge-invariant operators built out of scalars, the 1-loop dilatation operator is equivalent to the spin chain Hamiltonian of the 1D Ising model in a transverse magnetic field, which is a nontrivial integrable system that is exactly solvable at finite length. Solutions with periodic boundary conditions give the anomalous dimensions of flavor-singlet operators and solutions with fixed boundary conditions give the anomalous dimensions of operators …
Recently a very interesting three-dimensional $\mathcal{N}=2$ supersymmetric theory with $SU(3)$ global symmetry was discussed by several authors. We denote this model by $T_x$. This was conjectured to have two dual descriptions, one with explicit supersymmetry and emergent flavor symmetry and the other with explicit flavor symmetry and emergent supersymmetry. We discuss a third description of the model which has both flavor symmetry and supersymmetry manifest. We then investigate models which can be constructed by using $T_x$ as a building block gauging the global symmetry and paying special …
We show that supersymmetry and R-symmetry can be dynamically broken in a long-lived metastable vacuum of SQCD with massive and massless flavors. The vacuum results from a competition of a (leading) two-loop effect and small "Planck" suppressed higher-dimension operators. This mechanism provides a particularly simple realization of dynamical SUSY and R-symmetry breaking, and as such it is a good starting point for building phenomenologically viable models of gauge mediation. We take a preliminary step in this direction by constructing a complete model of minimal gauge mediation. Here we find th…
We revisit the study of singular points in the Coulomb branch of $\mathcal{N}=2$ SQCD in four dimensions with gauge group $SU(N)$ and odd number of flavors. For certain choices of the mass parameters these vacua are not lifted by a mass term for the chiral multiplet in the adjoint representation. By using recent results about the M5 brane description of $\mathcal{N}=1$ theories we study the resulting vacua and argue that the low-energy effective theory has a simple Lagrangian description involving a free chiral multiplet in the adjoint representation of the flavor symmetry group, a system some…
We consider supersymmetric QCD in the free magnetic phase with massless and massive flavors. The theory has a supersymmetry breaking pseudo-moduli space of vacua and a runaway behavior far away from the origin. A two-loop computation reveals that the origin is destabilized and there is no meta-stable SUSY breaking solution. We also study the embedding of this model in type IIA string theory and find evidence for similar behavior. The perturbative brane dynamics involves simple interactions between branes, correctly predicting the two-loop result in the gauge theory. Our results also apply to t…
We study the quantum Seiberg-Witten periods of ${\cal N}=2$ superconformal field theories which are obtained by taking the scaling limit of ${\cal N}=2$ $SU(N_c)$ SQCD around the superconformal fixed point. The quantum Seiberg-Witten curves of these superconformal field theories are shown to be classified into the Schrödinger type and the SQCD type, which depend on flavor symmetry at the fixed point. We study the quantum periods and compute the differential operators which relate the quantum periods to the classical ones up to the fourth-order in the deformation parameter.
This paper continues our studies in arXiV:1608.06452 [hep-th] of ${\cal N}=1$ gauge theories in the strongly coupled regimes. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual), with $N_F$ flavors of light quarks and $N_F^2$ additional colorless flavored scalars $Φ^j_i$, but now with $N_F$ in the range $N_F>3N_c$. The mass spectra of these direct and dual theories in various vacua are calculated within the dynamical scenario introduced by the author in [8]. It assumes that quarks in such ${\cal N}=1$ SQCD-like theories without elementary …
Using the ADHM instanton calculus, we evaluate the one-instanton contribution to the low-energy effective prepotential of N=2 supersymmetric SU(N) Yang-Mills theory with N_F flavors of hypermultiplets in the fundamental representation and a hypermultiplet in the symmetric rank two tensor representation. For N_F<N-2, when the theory is asymptotically free, our result is compared with the exact solution that was obtained using M-theory and we find complete agreement.
In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N=(2,2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattic…
N=1 SQCD with N_c colors and two types of light quarks: N_l flavors with smaller masses m_l and N_h=N_F-N_l flavors with larger masses m_h, N_c<N_F<3N_c, 0<m_l \leq m_h \ll Λ, is considered within the dynamical scenario in which quarks can form the coherent colorless diquark-condensate. There are several phase states at different values of parameters r=m_l/m_h, N_l, and N_F. Properties of these phases and the mass spectra therein are described.
We study BPS domain walls in four-dimensional $\mathcal{N}=1$ massive SQCD with gauge group $SU(N)$ and $F<N$ flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, …
This paper continues our previous study of similar theories in \cite{ch5}. We also consider here the ${\cal N}=1$ SQCD-like theories with $SU(N_c)$ colors (and their Seiberg's dual with $SU(N_F-N_c)$ dual colors) and $N_F$ flavors of light quarks, and with $N_F^2$ additional colorless flavored fields $Φ^j_i$, but now with $N_F$ in the range $2N_c<N_F<3N_c$. The multiplicities of various vacua and quark and gluino condensates in these vacua are found. The mass spectra of the direct and Seiberg's dual theories in various vacua are calculated within the dynamical scenario which assumes that quark…
We deconstruct the fifth dimension of 5D SCQD with general numbers of colors and flavors and general 5D Chern-Simons level; the latter is adjusted by adding extra quarks to the 4D quiver. We use deconstruction as a non-stringy UV completion of the quantum 5D theory; to prove its usefulness, we compute quantum corrections to the SQCD_5 prepotential. We also explore the moduli/parameter space of the deconstructed SQCD_5 and show that for |K_CS| < N_F/2 it continues to negative values of 1/(g_5)^2. In many cases there are flop transitions connecting SQCD_5 to exotic 5D theories such as E0, and we…
Considered is the ${\cal N}=1$ SQCD-like theory with $SU(N_c)$ colors and $0< N_F<2N_c$ flavors of equal mass $0< m_Q\llΛ_Q$ quarks. Besides, it includes $N^2_F$ additional colorless but flavored fields $Φ_{i}^{j}$, with the large mass parameter $μ_Φ\ggΛ_Q$. The mass spectra of this $Φ$-theory are first directly calculated at $0<N_F<N_c$ where the quarks are weakly coupled, in all different vacua with the unbroken or spontaneously broken flavor symmetry $U(N_F)\rightarrow U(n_1)\times U(n_2)$. Further, the mass spectra of this direct $Φ$-theory and its Seiberg's dual variant, the $dΦ$-theory, …
We study new supergravity solutions related to large-$N_c$ ${\cal N}=1$ supersymmetric gauge field theories with a large number $N_f$ of massive flavors. We use a recently proposed framework based on configurations with $N_c$ color D5 branes and a distribution of $N_f$ flavor D5 branes, governed by a function $N_f S(r)$. Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of $x\equiv N_f/N_c$. In the IR region, the solution smoothly approaches the deformed Maldacena-Núñez solution. In the UV region it appro…
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 pr…
We consider the ${\cal N}=1$ $SU(N_c)$ SQCD-like (direct) theory (and its Seiberg's dual with $SU(N_F-N_c)$ dual colors), and with $N_F$ flavors of light quarks ${\overline Q}_j, Q^i$ with the mass term in the superpotential $m_Q{\rm Tr}({\overline Q} Q),\,\, m_Q\llΛ_Q$. Besides, there are $N_F^2$ additional colorless but flavored fields $Φ^j_i$ with the large mass parameter $μ_Φ\ggΛ_Q$. But now considered is the region $N_c+1<N_F<3N_c/2$ where the UV free direct $SU(N_c)$ theory is strongly coupled at scales $μ<Λ_Q$. The mass spectra of this direct theory in various vacua and at different val…
Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{\rm Tr}\,({\bar Q} Q)$ in the superpotential. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $μ_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $μ_{\rm x}\llΛ_2$ ($Λ_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken flavor symmetry, $U(N_F)\rightarrow U({\rm n}_1)\times U({\rm n}_2)$. We consider in this p…
We suggest how to consistently calculate the anomalous dimension $γ_*$ of the $\barψψ$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $γ_*$ can be calculated exactly and fully scheme independently through $O(Δ_f^n )$ where $Δ_f = \bar{N_f} - N_f$ and $N_f$ is the number of flavors and $\bar{N}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry order by order in $Δ_f$. We th…
Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ equal mass quark flavors. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $μ_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $μ_{\rm x}\llΛ_2$ ($Λ_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken global flavor symmetry, $U(N_F)\rightarrow U({\rm n}_1)\times U({\rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken …
Considered is the direct ${\cal N}=1$ SQCD-like $Φ$-theory with $SU(N_c)$ colors and $3N_c/2< N_F<2N_c$ flavors of light quarks ${\overline Q},\,Q$. Besides, it includes $N^2_F$ additional colorless but flavored fields $Φ_{i}^{j}$ with the large mass parameter $μ_Φ\ggΛ_Q$, interacting with quarks through the Yukawa coupling. In parallel, is considered its Seiberg's dual variant, i.e. the $dΦ$-theory with $(N_F-N_c)$ dual colors, $N_F$ flavors of dual quarks ${\overline q},\,{q}$ and $N_F^2$ elementary mion fields $M^i_j\rightarrow ({\overline Q}_j Q^i)$. In considered here vacua, the quarks of…
We study two related problems in the context of a supergravity dual to N=1 SYM. One of the problems is finding kappa symmetric D5-brane probes in this particular background. The other is the use of these probes to add flavors to the gauge theory. We find a rich and mathematically appealing structure of the supersymmetric embeddings of a D5-brane probe in this background. Besides, we compute the mass spectrum of the low energy excitations of N=1 SQCD (mesons) and match our results with some field theory aspects known from the study of supersymmetric gauge theories with a small number of flavors…
N=1 SQCD with SU(N_c) colors and N_F flavors of light quarks is considered within the dynamical scenario which assumes that quarks can be in two different phases only. These are: a) either the HQ (heavy quark) phase where they are confined, b) or they are higgsed, at the appropriate values of parameters of the Lagrangian. The mass spectra of this (direct) theory and its Seiberg's dual are obtained and compared, for quarks of equal or unequal masses. It is shown that in all cases when there is the additional small parameter at hand (it is 0<(3N_c-N_F)/N_F << 1 for the direct theory, or its anal…
Recently we discovered and discussed non-Abelian duality in the quark vacua of N=2 super-Yang-Mills theory with the U(N) gauge group and N_f flavors (N_f>N). Both theories from the dual pair support non-Abelian strings which confine monopoles. Now we introduce an N=2-breaking deformation, a mass term μ{\mathcal A}^2 for the adjoint fields. Starting from a small deformation we eventually make it large which enforces complete decoupling of the adjoint fields. We show that the above non-Abelian duality fully survives in the limit of N=1 SQCD, albeit some technicalities change. For instance, non-A…
The dynamical scenario is considered for N=1 SQCD, with N_c colors and N_c<N_F<3N_c flavors with small but nonzero current quark masses m_Q\neq 0, in which quarks form the diquark-condensate phase. This means that colorless chiral quark pairs condense coherently in the vacuum, <{\bar Q}Q>\neq 0, while quarks alone don't condense, <Q>=<\bar Q>=0, so that the color is confined. Such condensation of quarks results in formation of dynamical constituent masses μ_C \gg m_Q of quarks and appearance of light "pions" (similarly to QCD). The mass spectrum of SQCD in this phase is described and compariso…
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 …
Responding to the recent claim that the origin of moduli space may be unstable in "magnetic" supersymmetric quantum chromodynamics (SQCD) with N_f <= 3N_c/2 (N_c>2) for N_f flavors and N_c colors of quarks, we explore the possibility of finding nonperturbative physics for "electric" SQCD. We present a recently discussed effective superpotential for "electric" SQCD with N_c+2 <= N_f <= 3N_c/2 (N_c>2) that generates chiral symmetry breaking with a residual nonabelian symmetry of SU(N_c)_{L+R}xSU(N_f-N_c)_Lx SU(N_f-N_c)_R. Holomorphic decoupling property is shown to be respected. For massive N_f-…
We study in detail the Schrödinger equation corresponding to the four dimensional $SU(2)$ $\mathcal{N}=2$ SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schrödinge…
The dimension of the Hilbert space of QFT scales exponentially with the volume of the space in which the theory lives, yet in supersymmetric theories, one can define a graded dimension (such as the supersymmetric index) that counts just the number of bosonic minus fermionic ground states. Can we make this observation useful in non-supersymmetric QFTs in four dimensions? In this work, we construct symmetry graded state sums for a variety of non-supersymmetric theories. Among the theories we consider is one that is remarkably close to QCD: Yang--Mills theory with $N_f = N_c$ fundamental Dirac fe…
We discuss supersymmetric surface defects in compactifications of six dimensional minimal conformal matter of type SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are N=1 quiver gauge theories with SU(3) and SU(4) gauge groups respectively. The defects are engineered by giving space-time dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter the defects carry SU(2) flavor symmetry which is not a symmetry of the four dimensional model. The simplest case of a model in this class is SU(3) SQ…
By the use of an effective superpotential in supersymmetric quantum chromodynamics (SQCD) with N_f flavors and N_c colors of quarks for N_f>=N_c+2, the influence of soft supersymmetry (SUSY) breakings is examined to clarify dynamics of chiral symmetry breakings near the SUSY limit. In case that SQCD triggers spontaneous chiral symmetry breakings, it is possible to show that our superpotential dynamically favors the successive formation of condensates, leaving either SU(N_f-N_c) or SU(N_f-N_c+1) unbroken as a chiral nonabelian symmetry.
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.
We study U(N) SQCD with N_f <= N flavors of quarks and antiquarks by engineering it with a configuration of fractional D3-branes on a C^3 / Z_2 x Z_2 orbifold. In particular we show how the moduli space of the gauge theory naturally emerges from the classical geometry produced by the D3-branes, and how the non-perturbatively generated superpotential is recovered from geometrical data.
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…
Critical Non-Abelian Vortex String and 2D N=2 Black Hole
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·基础物理研究所）；Dept. Math., HSE University（高等经济大学数学系）；Theory Department of LPI（列宁格勒物理研究所理论部）；National Research Center “Kurchatov Institute”, Petersburg Nuclear Physics Institute（库尔恰托夫国家研究中心圣彼得堡核物理研究所）；HSE University（高等经济大学）
We consider the lagrangian description of Argyres-Douglas theories of type $A_{2N-1}$, which is a $SU(N)$ gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD "abelianizes": in the infrared it is equivalent to a $\mathcal{N}=4$ linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to "sequentially confine" quivers tails with balanced nodes, we show that the mirror RG flow lands on …
One interesting feature of 3d $\mathcal{N}=2$ theories is that gauge-invariant operators can decouple by strong-coupling effects, leading to emergent flavor symmetries in the IR. The details of such decoupling, however, depends very delicately on the gauge group and matter content of the theory. We here systematically study the IR behavior of 3d $\mathcal{N}=2$ SQCD with $N_f$ flavors, for gauge groups $\mathrm{SU}(N_c), \mathrm{USp}(2N_c)$ and $\mathrm{SO}(N_c)$. We apply a combination of analytical and numerical methods, both to small values of $N_c, N_f$ and also to the Veneziano limit, whe…
We study certain N=1 preserving deformations of four-dimensional N=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N=1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2 supersymmetric fixed points in the infrared under the deformation. …
Hadrons in $\mathcal{N}=2$ supersymmetric QCD from non-Abelian string on 2D black hole
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·费因理论物理研究所）；Skoltech（斯科尔科沃科学技术大学）；Dept. Math., HSE University（高等经济大学数学系）；NRC ‘‘Kurchatov Institute’’ - PNPI（库尔恰托夫国家研究中心——彼得堡核物理研究所）；HSE University（高等经济大学）
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…
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.
We determine the vacuum structure and phases of N=1 theories obtained via a mass μfor the adjoint chiral superfield in N=2, SO(n_c) SQCD. For large number of flavors these theories have two groups of vacua. The first exhibits dynamical breaking of flavor symmetry \USp(2n_f) \to U(n_f) and arises as a relevant deformation of a non-trivial superconformal theory. These are in the confined phase. The second group, in an IR-free phase with unbroken flavor symmetry, is produced from a Coulomb branch singularity with Seiberg's dual gauge symmetry. In the large-μregime both groups of vacua are well-de…
When N = 2 gauge theories are compactified on $S^4$, the large $N_c$ limit then selects a unique vacuum of the theory determined by saddle-point equations, which remains determined even in the flat-theory limit. We show that exactly the same equations can be reproduced purely from Seiberg-Witten theory, describing a vacuum where magnetically charged particles become massless, and corresponding to a specific degenerating limit of the Seiberg-Witten spectral curve where $2N_c-2$ branch points join pairwise giving $a_{Dn}=0$, $n=1,...,N_c-1$. We consider the specific case of N = 2 $SU(N_c)$ SQCD …
