Related papers: Super W-Symmetries, Covariantly Constant Forms And…
We study the cohomology of Lie superalgebras for the full complex of forms: superforms, pseudoforms and integral forms. We use the technique of spectral sequences to abstractly compute the Chevalley-Eilenberg cohomology. We first focus on…
The Coulomb branch of $N=2$ supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…
We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…
Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the…
Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of St\"ackel transformations (also…
A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields.…
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter number,…
Current-current deformations for WZW models of semisimple compact groups are discussed in a sigma model approach. We start with the abelian rank one group U(1). Afterwards, we keep the rank one but allow for non abelian structures by…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
I show that physical quantities in several two-dimensional condensed-matter models are related to the Seiberg-Witten calculation of exact quantities in supersymmetric gauge theory. In particular, the magnetization in the Kondo problem and…
A consistent N=1 supersymmetric $\sigma$-model can be constructed, given a K\"ahler manifold by adding chiral matter multiplets. Their scalar components are covariant tensors on the underlying K\"ahler manifold. The K\"ahler U(1)-charges…
We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…
The strong homotopy Lie algebra, controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is constructed. Isomorphism of the cohomology of this strong homotopy Lie algebra with the classical…
We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{\xi_1,...,\xi_s\}$. We use this sequence to…
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra.…
In this paper we quantize superconformal $\sigma$-models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a DFF term, are considered. Without a DFF term (Calogero potential only) the…
Duality groups as (spontaneously broken) gauge symmetries for toroidal backgrounds, and their role in ($\infty$-dimensional) underlying string gauge algebras are reviewed. For curved backgrounds, it is shown that there is a duality in the…
We complete the process of classifying all supersymmetric theories with quantum modified moduli. We present all the supersymmetric gauge theories based on a simple orthogonal or exceptional group that exhibit a quantum modified moduli…