We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the char...

It has been shown recently that extended supersymmetry in twisted firstorder sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining the model. We study in the Hamiltonian formalism the case of vanishing metric...

The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detai1ed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A g...

Starting from the most general harmonic superspace action of self-interacting Q+ hypermultiplets in the background of N = 2 conformal supergravity, we derive the general action for the bosonic sigma model with a generic 4n dimensional quaternionic-Kähler (QK) manifold as the target space. The action is determined by the analytic harmonic QK potential and supplies an efficient systematic procedu...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

Amenability is a cohomological property of Banach algebras which was introduced by Johnson in [14]. Let A be a Banach algebra, and suppose that X is a Banach A−bimodule such that the following statements hold ∥a · x∥ ≤ ∥a∥∥x∥ and ∥x · a∥ ≤ ∥a∥∥x∥ for each a ∈ A and x ∈ X. We can define the right and left actions of A on dual space X∗ of X via ⟨x, λ · a⟩ = ⟨a · x, λ⟩ ⟨x, a · λ⟩ = ⟨x · a, λ⟩, for...