Related papers: Notes on 5d Partition Functions - I
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…
We study the dependence of supersymmetric partition functions on continuous parameters for the flavor symmetry group, $G_F$, for 2d $\mathcal{N} = (0,2)$ and 4d $\mathcal{N}=1$ supersymmetric quantum field theories. In any…
This is an expositoray article on the topological string partition function promoting an extension of the partition function of open Gromov-Witten theory of CY 3-folds defined by the trace of vertex operators. We also give a brief survey 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…
The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times \Sigma$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the…
Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building…
We study N = 4 quiver theories on the three-sphere. We compute partition functions using the localisation method by Kapustin et al. solving exactly the matrix integrals at finite N, as functions of mass and Fayet-Iliopoulos parameters. We…
Roe's partitioned manifold index theorem applies when a complete Riemannian manifold $M$ is cut into two pieces along a compact hypersurface $N$. It states that a version of the index of a Dirac operator on $M$ localized to $N$ equals the…
We construct families of supersymmetric AdS$_3\times Y_7$ and AdS$_3\times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $\Sigma$, while $Y_8$ is an $S^4$ fibration over…
We study twisted circle compactification of 6d $(2,0)$ SCFTs to 5d $\mathcal{N} = 2$ supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting…
We study reductions of 6d theories on a $d$-dimensional manifold $M_d$, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting $(6-d)$-dimensional theory $T[M_d]$. We refine and generalize the notion of…
We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…
3d N=2 partition functions on the squashed three-sphere and on the twisted product S2xS1 have been shown to factorize into sums of squares of solid tori partition functions, the so-called holomorphic blocks. The same set of holomorphic…
We consider a compactification of 4D $\mathcal{N}=4$ SYM, with $SU(N)$ gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an…
We study 4D N=2 superconformal field theories that arise from the compactification of 6D N=(2,0) theories of type D_N on a Riemann surface, in the presence of punctures twisted by a Z_2 outer automorphism. Unlike the untwisted case, the…
In this paper we state and prove a higher index theorem for an odd-dimensional connected spin riemannian manifold $(M,g)$ which is partitioned by an oriented closed hypersurface $N$. This index theorem generalizes a theorem due to N. Higson…
In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons…
We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of…
We study a supersymmetric partition function of topological vortices in 3d N=4,3 gauge theories on R^2 x S^1, and use it to explore Seiberg-like dualities with Fayet-Iliopoulos deformations. We provide a detailed support of these dualities…
We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…