Related papers: Finite $\epsilon_2$-corrections to the $\mathcal{N…
We apply the Jeffrey-Kirwan method to compute the multiple integrals for the $BCD$ type Nekrasov partition functions of four dimensional $\mathcal{N}=2$ supersymmetric gauge theories. We construct a graphical distinction rule to determine…
We discuss a number of exact results in N=1 supersymmetric field theories. We review the results obtained by Seiberg in Super-Yang-Mills (SYM) theories with matter in fundamental representation. We then consider Kutasov-type SYM theories,…
Open superstring field theory admits a "hybrid" formulation where N = 1 D = 4 supersymmetry is manifest for Calabi-Yau compactifications to four dimensions. Using this formulation, the half-BPS instanton solution of four-dimensional…
We explicitly determine the instanton corrections to the prepotential for N=2 supersymmetric SU(3) Yang-Mills theory with massless hypermultiplets in the weak coupling regions $u\to\infty$ and $v\to\infty$. We construct the Picard-Fuchs…
A consistent truncation of IIB on S^5 has been obtained in the sector of the metric and the 4-form potential. The ansatz contains 20 scalars and all 15 gauge fields of ${\cal N}=8$ gauged supergravity in five dimensions. With this fully…
Maximally supersymmetric Yang--Mills theory (N=4 SYM) is conformal for any value of the coupling. Lattice regularization breaks conformality through the introduction of a non-zero lattice spacing and a finite lattice volume. This…
The conjecture about the correspondence between instanton partition functions in the N=2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to the case of the N=1 supersymmetric conformal…
Using formulation of ${\cal N}=4$ SYM theory in terms of ${\cal N}=1$ superfields superfields we construct the derivative expansion of the one-loop ${\cal N}=4$ SYM effective action in background fields corresponding to constant Abelian…
The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the…
We study a discretization of ${\cal N}=2$ super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of {\it twisted} fields. In…
The gauge fixing procedure for N=1 supersymmetric Yang-Mills theory (SYM) is proposed in the context of the stochastic quantization method (SQM). The stochastic gauge fixing, which was formulated by Zwanziger for Yang-Mills theory, is…
We study the distribution of partition function zeroes for the $XY$--model in two dimensions. In particular we find the scaling behaviour of the end of the distribution of zeroes in the complex external magnetic field plane in the…
We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d…
Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS$_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy. This…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vev of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings,…
We embed the Seiberg-Witten solution for the low energy dynamics of N=2 super Yang-Mills theory with an even number of massive hypermultiplets into the Whitham hierarchy. Expressions for the first and second derivatives of the prepotential…
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…
The light-like cusp anomalous dimension is a universal function in the analysis of infrared divergences. In maximally ($\mathcal{N}=4$) supersymmetric Yang-Mills theory (SYM) in the planar limit, it is known, in principle, to all loop…
We further explore the correspondence between N=2 supersymmetric SU(2) gauge theory with four flavors on epsilon-deformed backgrounds and conformal field theory, with an emphasis on the epsilon-expansion of the partition function natural…