Related papers: On modular semifinite index theory
Through the example of the quantum symplectic 4-sphere, we discuss how the notion of twisted spectral triple fits into the framework of quantum homogeneous spaces.
We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on…
We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the…
Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider…
The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum…
In this paper we analytically explore the modularity of the flavored Schur index of 4d $\mathcal{N} = 2$ SCFTs. We focus on the $A_1$ theories of class-$\mathcal{S}$ and $\mathcal{N} = 4$ theories with $SU(N)$ gauge group. We work out the…
We establish the integral kernel associated with the Koecher-Maass series of degree three twisted by an Eisenstein series. We prove that such a kernel admits an analytic continuation and determine its functional equations. We find a second…
Zagier proved that the generating series for the traces of singular moduli is a \textit{weakly holomorphic} modular form of weight 3/2 on $\Gamma_0(4)$. Bruinier and Funke extended the results of Zagier to modular curves of arbitrary genus.…
We compute the Schur indices in the presence of some line operators based on our con- jectural formula introduced in [1]. In particular, we focus on the rank 1 superconformal field theories with the enhanced global symmetry and the free…
We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory…
This paper is the second part of a series of papers on noncommutative geometry and conformal geometry. In this paper, we compute explicitly the Connes-Chern character of an equivariant Dirac spectral triple. The formula that we obtain for…
We study 2-cocycle twists, or equivalently Zhang twists, of semigroup algebras over a field k. If the underlying semigroup is affine, that is abelian, cancellative and finitely generated, then Spec k[S] is an affine toric variety over k,…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
In noncommutative geometry one is interested in invariants such as the Fredholm index or spectral flow and their calculation using cyclic cocycles. A variety of formulae have been established under side conditions called summability…
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum…
In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral…
We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…
We study countable sums of two dimensional modules for the continuous complex functions on a compact metric space and show that it is possible to construct a spectral triple which gives the original metric back. This spectral triple will be…
We prove an explicit formula for the total Chern character of the Verlinde bundle over the moduli space of pointed stable curves in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the…
We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…