Related papers: Comments on the Nekrasov-type formula for E-string…
We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson…
We construct the Seiberg-Witten curve for the E-string theory in six-dimensions. The curve is expressed in terms of affine E_8 characters up to level 6 and is determined by using the mirror-type transformation so that it reproduces the…
We discuss various properties of the Seiberg-Witten curve for the E-string theory which we have obtained recently in hep-th/0203025. Seiberg-Witten curve for the E-string describes the low-energy dynamics of a six-dimensional (1,0) SUSY…
We study the E-string theory on $\mathbb{R}^4\times T^2$ with Wilson lines. We consider two examples where interesting automorphisms arise. In the first example, the spectrum is invariant under the $F_4$ Weyl group acting on the Wilson line…
In this work we study the quantisation of the Seiberg-Witten curve for the E-string theory compactified on a two-torus. We find that the resulting operator expression belongs to the class of elliptic quantum curves. It can be rephrased as…
We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves…
N=2 supersymmetric Yang-Mills theories for all classical gauge groups, that is, for SU(N), SO(N), and Sp(N) is considered. The formal expression for almost all models accepted by the asymptotic freedom are obtained. The equations which…
We develop a matrix model for the SO(32) Heterotic string with certain Wilson lines on the lightlike circle. This is done by using appropriate T-dualities. The method works for an infinite number of Wilson lines, but not for all. The matrix…
We reformulate twistor-string theory as a heterotic string based on a twisted (0,2) model. The path integral localizes on holomorphic maps, while the (0,2) moduli naturally correspond to the states of N=4 super Yang-Mills and conformal…
In this note it is demonstrated how the Seiberg-Witten solutions and related integrable systems may arise from certain brane configurations in M-theory. Some subtleties of the formulation of the Seiberg-Witten theory via integrable systems…
We study the Seiberg-Witten curves for N=2 SUSY gauge theories arising from type IIA string configurations with two orientifold sixplanes. Such theories lift to elliptic models in M-theory. We express the M-theory background for these…
We exploit a conjectured continuity between super Yang-Mills on $\mathbb R^3\times \mathbb S^1$ and pure Yang-Mills to study $k$-strings in the latter theory. As expected, we find that Wilson-loop correlation functions depend on the N-ality…
We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8…
We consider 5d Sp(1) gauge theory with $E_{N_f+1}$ global symmetries based on toric(-like) diagram constructed from (p,q)-web with 7-branes. We propose a systematic procedure to compute the Seiberg-Witten curve for generic toric-like…
In earlier work we proposed a string theory dual to two dimensional Yang-Mills theory at zero coupling (which can also be thought of as a $BF$ theory), given by a Polyakov-like generalization of Ho\v rava's topological rigid string theory,…
We discuss Jacobi forms that are invariant under the action of the Weyl group of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of generators of the algebra of E_n weak Jacobi forms. We first construct n+1 independent E_n…
Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We…
Wilson lines in N=4SYM can be computed in terms of branes carrying electric flux, i.e. F-strings dissolved in their worldvolumes. It is then natural to think that those configurations are the effective description of strings expanding due…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These…