We investigate the relation between the four dimensional N=2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic expansion of the spectrum for the Schrödinger operator, we are able to fix the precise relation between the energy spectrum and the instanton partition function of the gauge theory. We also study asymptotic expansions for the spectrum which correspond to the strong coupling regions of the Seiberg-Witten theory.
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the elliptic $R$-matrices, which satisfy the classical and the associative Yang-Baxter equations.
We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries $\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $ T^2$. We introduce supersymmetric indices of three dimensional $\mathcal{N}=2$ theories on $I \times T^2$ that couple to elliptic genera of 2d $\mathcal{N}=(0,2)$ theories at the two boundaries. We evaluate the $I \times T^2$ indices in terms of supersymmetric localization and study dualities on the $I \times M_2$. We consider the dimensional reduction of $I \times T^2$ to $I …
We study a relation between asymptotic spectra of the quantum mechanics problem with a four components elliptic function potential, the Darboux-Treibich-Verdier (DTV) potential, and the Omega background deformed N=2 supersymmetric SU(2) QCD models with four massive flavors in the Nekrasov-Shatashvili limit. The weak coupling spectral solution of the DTV potential is related to the instanton partition function of supersymmetric QCD with surface operator. There are two strong coupling spectral solutions of the DTV potential, they are related to strong coupling expansions of gauge theory prepoten…
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic $R$-matrices. They are shown to satisfy the classical Yang-Baxter equation and the associative Yang-Baxter equation. The quantum Yang-Baxter is discussed as well. It acquires additional term in the case of supersymmetric $R$-matrices.
We study two phases of supersymmetric QCD associated to the singularities of the renormalization constant of the fermion mass operator. We find a behavior of the potential between two charges for the phases of interest that it is consistent with Seiberg results on these aspects based on a different method.
We introduce in supersymmetric QCD with $N_f<N$ additional meson singlet degrees of freedom made of $2N_f-2$ supermultiplets. We construct an alternative superpotential with $N_f^2$ constraints and show its consistency. Based on this superpotential we prove that for $\frac{N}{2}<N_f<N$ the supersymmetry is unbroken whereas for $N_f\leq\frac{N}{2}$ is dynamically broken.
This paper studies $3d$ $\mathcal{N}=4$ supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection for supersymmetric ground states in the presence of mass parameters and flat connections for flavour symmetries, which results in a natural construction of the equivariant elliptic cohomology variety of the Higgs branch. We then investigate supersymmetric boundary conditions and show from an analysis of boundary 't Hooft anomalies that t…
We study dynamical supersymmetry breaking in supersymmetric QCD theories for $N_f<N_c$. We consider a model with a singlet chiral superfield coupled to the infrared meson chiral superfield through a classical superpotential. We examine the vacuum structure of this model and show that in a particular limit of the parameter space with the large $N_c$ limit, it has a vacuum that dynamically breaks supersymmetry. The supersymmetric vacuum, in this limit, is being pushed to infinity.
We study the different quantum phases that occur in massive ${\cal N}=2$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling $Λ/M$ is gradually increased from 0 to infinity. The phases can be identified by computing the exact partition function by saddle-points, combining supersymmetric localization and the Seiberg-Witten formalism. In all cases, we find two phases, a weak coupling and a strong coupling phase, separated by a critical point described by a superconformal field theory or involving superconformal sectors. In crossing the critical point, the dominant saddle-poi…
Duality Symmetries for N=2 Supersymmetric QCD with Vanishing beta-Functions
我们构造了N=2超对称QCD的对偶群，规范群为SU（2n+1），N_f= 4 n +2超多重态为基本表象。这些组由满足关系$(STS^{-1}T)^{2n+1}=1$的两个元素$S$和$T$生成。因此，这些组不是$SL(2,Z)$的亚组。我们还构造了自守函数，将$T$和$STS$生成的群的基本区域映射到黎曼球面。这些自守函数忠实地代表了塞伯格-威滕曲线的对偶对称性。
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…
