Related papers: Quantum periods and prepotential in ${\cal N}=2$ S…
We study the Argyres-Douglas theories realized at the superconformal point in the Coulomb moduli space of $\mathcal{N}=2$ supersymmetric $SU(2)$ QCD with $N_f=1,2,3$ hypermultiplets in the Nekrasov-Shatashvili limit of the Omega-background.…
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…
We derive a simple formula for the periods associated with the low energy effective action of $N=2$ supersymmetric $SU(2)$ Yang-Mills theory with massive $N_f\le 3$ hypermultiplets. This is given by evaluating explicitly the integral…
We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory…
In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived from M-theory that encode the low energy solution of N=2 supersymmetric theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2) gauge theory…
We study the non-perturbative, instanton-corrected effective action of the N=2 SU(2) x SU(2) supersymmetric Yang-Mills theory with a massless hypermultiplet in the bifundamental representation. Starting from the appropriate hyperelliptic…
We solve N=2 supersymmetric Yang-Mills theories for arbitrary classical gauge group, i.e. SU(N), SO(N), Sp(N). In particular, we derive the prepotential of the low-energy effective theory, and the corresponding Seiberg-Witten curves. We…
Omega-deformation of the Seiberg-Witten curve is known to be written in terms of the qq-character, namely the trace of a specific operator acting in a Hilbert space spanned by certain Young diagrams. We define a differential form acting on…
We calculate the prepotential of the low-energy effective action for $N=2$ $SU(2)$ supersymmetric Yang-Mills theory with $N_f$ massless hypermultiplets ($N_f=1,\, 2,\, 3$). The precise evaluation of the instanton corrections is performed by…
The Picard-Fuchs equations for $N=2$ supersymmetric $SU(N_{c})$ Yang-Mills theories with massless hypermultiplets are obtained for $N_{c}=2$ and $3$. For $SU(2)$ we derive the non-linear differential equations for the prepotentials and…
We consider the exact superpotential of N=1 super Yang-Mills theory with gauge group SO(N) and arbitrary tree-level polynomial superpotential of one adjoint Higgs field. A field-theoretic derivation of the glueball superpotential is given,…
The Nekrasov-Shatashvili limit of beta-ensembles with polynomial potential and N=2 supersymmetric gauge theories in the Omega-background is intimately related to complex one-dimensional quantum mechanics. Multi-instanton corrections in…
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…
We give a unified analysis of four-dimensional elliptic models with N=2 supersymmetry and a simple gauge group, and their relation to M-theory. Explicit calculations of the Seiberg-Witten curves and the resulting one-instanton prepotential…
The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle…
We study various non-perturbative approaches to the quantization of the Seiberg-Witten curve of ${\cal N}=2$, $SU(2)$ super Yang-Mills theory, which is closely related to the modified Mathieu operator. The first approach is based on the…
One-instanton predictions for the prepotential are obtained from the Seiberg-Witten curve for the Coulomb branch of N=2 supersymmetric gauge theory for the product group \prod_{n=1}^{m} SU(N_n) with a massless matter hypermultiplet in the…
We present a general analysis of all the possible soft breakings of N=2 supersymmetric QCD, preserving the analytic properties of the Seiberg-Witten solutions for the SU(2) group with Nf=1, 2, 3 hypermultiplets. We obtain all the couplings…
In the case of SU(2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon model. If the same construction is literally applied to…
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 $\Lambda/M$ is gradually increased from 0 to infinity. The phases can be identified by…