Related papers: Exotic R^4 and quantum field theory
We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli, i.e., embeddings pairwise homeomorphic to the standard embeddings of R^2 and R^2-int D^2 in R^4. We encounter two uncountable…
We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators…
We describe the topological $A$ and $B$ twists of 3d $\mathcal{N}=4$ theories of hypermultiplets gauged by $\mathcal{N}=4$ vector multiplets as certain deformations of the holomorphic-topological ($HT$) twist of those theories, utilizing…
Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon…
We initiate the study of exotic Dehn twists along 3-manifolds $\neq S^3$ inside $4$-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more generally of definite 4-manifolds, and exotic…
The interaction of various algebraic structures describing fusion, braiding and group symmetries in quantum projective field theory is an object of an investigation in the paper. Structures of projective Zamolodchikov al- gebras, their…
We study N=1 field theories with a U(1)_R symmetry on compact four-manifolds M. Supersymmetry requires M to be a complex manifold. The supersymmetric theory on M can be described in terms of conventional fields coupled to background…
We examine the relationship between the notion of Frobenius splitting and ordinarity for varieties. We show the following: a) The de Rham-Witt cohomology groups $H^i(X, W({\mathcal O}_X))$ of a smooth projective Frobenius split variety are…
We apply one of the formalisms of noncommutative geometry to $R^N_q$, the quantum space covariant under the quantum group $SO_q(N)$. Over $R^N_q$ there are two $SO_q(N)$-covariant differential calculi. For each we find a frame, a metric and…
We show that the $R^{(3)}\delta K$ operator in effective field theory is significant for avoiding the instability of nonsingular bounce, where $R^{(3)}$ and $K_{\mu\nu}$ are the three-dimensional Ricci scalar and the extrinsic curvature on…
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries…
Superconformal field theories (SCFT) are known to possess solvable yet nontrivial sectors in their full operator algebras. Two prime examples are the chiral algebra sector on a two dimensional plane in four dimensional $\mathcal{N}=2$…
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…
We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on $K3$, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same…
We examine functorial and homotopy properties of the exotic characteristic homomorphism in the category of Lie algebroids which was lastly obtained by the authors in [4]. This homomorphism depends on a triple (A,B,$\nabla$) where B…
We study properties of vertex (operator) algebras associated with 3d H-twisted $\mathcal{N}=4$ supersymmetric gauge theories with a boundary. The vertex operator algebras (VOAs) are defined by BRST cohomologies of currents with symplectic…
Weighted Rota-Baxter operators on associative algebras are closely related to modified Yang-Baxter equations, splitting of algebras, weighted infinitesimal bialgebras, and play an important role in mathematical physics. For any $\lambda \in…
We propose a method for extracting the Higgs and Coulomb branches of a three-dimensional N = 4 quantum field theory from the algebra of local operators in its holomorphic-topological twist using the formalism of raviolo vertex algebras. Our…
We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…
One of the fundamental objects in the $K$-theoretic enumerative geometry of Nakajima quiver varieties is known as the the capping operator. It is uniquely determined as the fundamental solution to a system of $q$-difference equations. Such…