Related papers: Modularity of supersymmetric partition functions
We provide a general formula for the partition function of three-dimensional $\mathcal{N}=2$ gauge theories placed on $S^2 \times S^1$ with a topological twist along $S^2$, which can be interpreted as an index for chiral states of the…
We discuss the Cardy limit of 3d supersymmetric partition functions which allow the factorization into the hemisphere indices: the generalized superconformal index, the refined topologically twisted index and the squashed sphere partition…
The partition function of a massless scalar field on a Euclidean spacetime manifold $\mathbb{R}^{d-1}\times\mathbb{T}^2$ and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is…
We revisit the factorisation of supersymmetric partition functions of 3d $\mathcal{N}=4$ gauge theories. The building blocks are hemisphere partition functions of a class of UV $\mathcal{N}=(2,2)$ boundary conditions that mimic the presence…
We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where…
Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of…
It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…
The supersymmetric R\'enyi entropy across a spherical entangling surface in a $d$-dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on $\mathbb{H}^{d-1} \times \mathbb{S}^1$, which can be computed…
We describe applications of the gluing formalism discussed in the companion paper. When a $d$-dimensional local theory $\text{QFT}_d$ is supersymmetric, and if we can find a supersymmetric polarization for $\text{QFT}_d$ quantized on a…
In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The…
We study issues related to F-theory on Calabi-Yau fourfolds and its duality to heterotic theory for Calabi-Yau threefolds. We discuss principally fourfolds that are described by reflexive polyhedra and show how to read off some of the data…
For $l,n \in \mathbb{N}$ we define tonal partition algebra $P^l_n$ over $\mathbb{Z}[\delta]$. We construct modules $\{ \Delta_{\underline{\mu}} \}_{\underline{\mu}}$ for $P^l_n$ over $\mathbb{Z}[\delta]$, and hence over any integral domain…
We give a new proof of the rearrangement lemma that works for all dimensions and all heat coefficients in the study of modular geometry on noncommutative tori. The building blocks of the spectral functions are landed in a hypergeometric…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
Worldsheet (0,2) gauged linear sigma models are often used to study supersymmetric heterotic string compactifications with non-trivial vector bundles. We make use of supersymmetric localization techniques to determine their one-loop…
We consider compactifications of heterotic string theory to four dimensions on CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries. The exact partition functions of the quarter-BPS dyons in these models are given in terms of…
The most recent studies on the supersymmetric localization reveal many non-trivial features of supersymmetric field theories in diverse dimensions, and 3d gauge theory provides a typical example. It was conjectured that the index and the…
We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments,…
Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A-modules, analogous to rank-1 Donaldson-Thomas invariants of Calabi-Yau threefolds. For the special…
We consider static black holes, which are bosonic solutions of supersymmetric theories. We will show that supersymmetry provides a natural framework for a discussion of various properties of such static black holes. The most fundamental…