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In this paper we develop a technique of computation of correlation functions in theories with action being cubic or higher degree form in terms of discriminants of corresponding tensors. These are analogues of formula $\int \exp…
In this study, we examine the modular transformations of the (root-)$\text{T}\overline{\text{T}}$ deformed torus partition function of a two-dimensional CFT (with a gravitational anomaly) from the holographic perspective by computing the…
The partition function of 2d conformal field theory is a modular invariant function. It is known that the partition function of a holomorphic CFT whose central charge is a multiple of 24 is a polynomial in the Klein function. In this paper,…
We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a functor on non-negatively graded commutative cochain algebras, which we think of as functions on Lie algebroids or stacky affine schemes. There is a notion of…
To a simple graph we associate a so-called graph series, which can be viewed as the Hilbert--Poincar\'e series of a certain infinite jet scheme. We study new $q$-representations and examine modular properties of several examples including…
In this paper we find automorphic functions of coset manifolds with special K\"ahler geometry. We use \zeta-functions to regularize an infinite product over integers which belong to a duality-invariant lattice, this product is known to…
Kleshchev, Mathas and Ram (2012) gave a presentation for graded Specht modules over Khovanov-Lauda-Rouquier algebras of finite and affine type A. We show that this construction can be applied more generally to skew shapes to give a…
Modular graph functions associate to a graph an $SL(2,Z)$-invariant function on the upper half plane. We obtain the Fourier series of modular graph functions of arbitrary weight $w$ and two-loop order. The motivation for this work is to…
We consider the 3-category $2\mathfrak{C}at$ whose objects are 2-categories, 1-morphisms are lax functors, 2-morphisms are lax transformations and 3-morphisms are modifications. The aim is to show that it carries interesting…
Vertex operator algebras (VOAs) arise in protected subsectors of supersymmetric quantum field theories, notably in 4d ${\mathcal N}=2$ superconformal field theories (SCFT) via the Schur sector and in twisted 3d ${\mathcal N}=4$ theories via…
We continue the analysis of modular invariant functions, subject to inhomogeneous Laplace eigenvalue equations, that were determined in terms of Poincar\'e series in a companion paper. The source term of the Laplace equation is a product of…
We develop a graphical calculus for monoidal categories equipped with twisted pivotal structures, which are a generalization of pivotal structures originating from the study of orientation structures in the context of the Cobordism…
We customize the existing models for the bounded derived category of gentle algebras to obtain simple graph theoretic tools to analyze indecomposable objects, Auslander-Reiten triangles, and their interaction with the associated homological…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In…
We study Nekrasov's instanton partition function of four-dimensional N=2 gauge theories in the presence of surface operators. This can be computed order by order in the instanton expansion by using results available in the mathematical…
In this note we study $SL(2,\mathbb{Z})$-invariant functions such as modular graph functions or coefficient functions of higher derivative corrections in type IIB string theory. The functions solve inhomogeneous Laplace equations and we…
We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de…
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…
Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have…