Related papers: Twisted Index on Hyperbolic Four-Manifolds
The winding number has been widely used as an invariant for diagnosing topological phases in one-dimensional chiral-symmetric systems. We put forward a real-space representation for the winding number. Remarkably, our method reproduces an…
We develop techniques for describing the derived moduli spaces of solutions to the equations of motion in twists of supersymmetric gauge theories as derived algebraic stacks. We introduce a holomorphic twist of N=4 supersymmetric gauge…
Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two…
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models…
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the $N$ site $\mathfrak{sl}_{2}$ $XXX$ spin chain (for infinite dimensional…
We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type $A_{N-1}$, which are worldvolume theories on $N$ M5-branes at…
We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The…
We present a review of Witten index calculations in different supersymmetric gauge theories in four dimensions: supersymmetric electrodynamics, pure N=1 supersymmetric Yang-Mills theories and also SYM theories including matter multiplets --…
We study four-dimensional N=1, 2 superconformal theory in class S obtained by compactifying the 6d N=(2, 0) theory on a Riemann surface C with outer-automorphism twist lines. From the pair-of-pants decompositions C we find various dual…
We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a topological supercharge we construct an…
We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $G_2 \times SU(2)$ holonomy. Our derivation starts with an explicit description of the Batalin-Vilkovisky…
Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a…
We propose a six-dimensional framework to calculate the supersymmetric index of M-theory 5-branes wrapped on a six-manifold with product topology $M_4\times T^2$, where $M_4$ is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is…
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models…
We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the…
We study duality-twisted dimensional reductions on a group manifold G, where the twist is in a group \tilde{G} and examine the conditions for consistency. We find that if the duality twist is introduced through a group element \tilde{g} in…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
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.…
We study holographic renormalization and the variational problem in four-dimensional Einstein gravity coupled to a self-interacting scalar field in asymptotically AdS spacetimes with mixed, designer-gravity boundary conditions. For static…
We study four dimensional $N=2$ supersymmetric gauge theories on $R^3 \times S^1$ with a circle of radius $R$. They interpolate between four dimensional gauge theories ($R=\infty$) and $N=4$ supersymmetric gauge theories in three dimensions…