Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type

We consider a series of massive scaling limits m_1 -> infty, q -> 0, lim m_1 q = Lambda_{3} followed by m_4 -> infty, Lambda_{3} -> 0, lim m_4 Lambda_{3} = (Lambda_2)^2 of the beta-deformed matrix model of Selberg type (N_c=2, N_f=4) which reduce the number of flavours to N_f=3 and subsequently to N_f=2. This keeps the other parameters of the model finite, which include n=N_L and N=n+N_R, namely, the size of the matrix and the "filling fraction". Exploiting the method developed before, we generate instanton expansion with finite g_s, epsilon_{1,2} to check the Nekrasov coefficients (N_f =3,2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator lim frac{1}{C(q)} : e^{(1/2) \alpha_1 \phi(0)}: (int_0^q dz : e^{b_E phi(z)}:)^n : e^{(1/2) alpha_2 phi(q)}: and is subsequently analytically continued.Comment: LaTeX, 21 pages; v2: a reference adde

Wave function renormalization constants and one-particle form factors in Dl(1)D_{l}^{(1)} Toda field theories

We apply the method of angular quantization to calculation of the wave function renormali- zation constants in $D_{l}^{(1)}$ affine Toda quantum field theories. A general formula for the wave function renormalization constants in ADE Toda field theories is proposed. We also calculate all one-particle form factors and some of the two-particle form factors of an exponential field.Comment: harvmac, 28 pages, 2 eps figures, misprints correcte

Scattering of Plane Waves in Self-Dual Yang-Mills Theory

We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient to introduce a scattering operator $\hat{T}$. It acts in the direct product of three linear spaces: 1) universal enveloping of $su(N)$ Lie algebra, 2) $n$-dimensional vector space and 3) space of functions defined on the unit interval.Comment: 16 pages, LaTeX fil

Separability of Gravitational Perturbation in Generalized Kerr-NUT-de Sitter Spacetime

Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr-NUT-de Sitter spacetime. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.Comment: 47 pages, LaTeX; v2: typos corrected; v3: a reference and comments added, details of calculations are moved to appendices, version accepted for publication in IJMP

Normalization of Off-shell Boundary State, g-function and Zeta Function Regularization

We consider the model in two dimensions with boundary quadratic deformation (BQD), which has been discussed in tachyon condensation. The partition function of this model (BQD) on a cylinder is determined, using the method of zeta function regularization. We show that, for closed channel partition function, a subtraction procedure must be introduced in order to reproduce the correct results at conformal points. The boundary entropy (g-function) is determined from the partition function and the off-shell boundary state. We propose and consider a supersymmetric generalization of BQD model, which includes a boundary fermion mass term, and check the validity of the subtraction procedure.Comment: 21 pages, LaTeX, comments and 3 new references adde

Large and small Density Approximations to the thermodynamic Bethe Ansatz

We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field theories related to simply laced Lie algebras to the non-simply laced case. The comparison with semi-classical methods shows perfect agreement for the simply laced case. We derive the Y-systems for affine Toda field theories with real coupling constant and employ them to improve the large density approximations. We test the quality of our analysis explicitly for the Sinh-Gordon model and the $(G_2^{(1)},D_4^{(3)})$-affine Toda field theory.Comment: 19 pages Latex, 2 figure

On the Classification of Brane Tilings

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.Comment: 33 pages, 12 figures, 15 table

The Determinant Representation for a Correlation Function in Scaling Lee-Yang Model

We consider the scaling Lee-Yang model. It corresponds to the unique perturbation of the minimal CFT model M(2,5). This is not a unitary model. We used known expression for form factors in order to obtain a closed expression for a correlation function of a trace of energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representation were proven to be useful not only for quantum correlation functions but also in matrix models.Comment: 14 pages, LaTeX, no figure

Form factor expansion for thermal correlators

We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair-Mussardo proposal.Comment: 41 pages; v2: minor corrections, v3: minor correction

Hermitian Yang-Mills instantons on resolutions of Calabi-Yau cones

We study the construction of Hermitian Yang-Mills instantons over resolutions of Calabi-Yau cones of arbitrary dimension. In particular, in d complex dimensions, we present an infinite family, parametrised by an integer k and a continuous modulus, of SU(d) instantons. A detailed study of their properties, including the computation of the instanton numbers is provided. We also explain how they can be used in the construction of heterotic non-Kahler compactifications.Comment: 20 pages, 1 figure; typos corrected, section 3.1 expande