Related papers: Holomorphic blocks and the 5d AGT correspondence
A class of 3d $\mathcal{N}=2$ supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d…
The noncommutative space $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$, supports a $3$-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders.…
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
We compute the factorization homology of a polynomial algebra over a compact and closed manifold with trivialized tangent bundle up to weak equivalence in a new way. This calculation is based on the model of a graph complex and an explicit…
We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…
Much insight into the dynamics of quantum field theories can be gained by studying the relationship between field theories in different dimensions. An interesting observation is that when two theories are related by dimensional reduction on…
We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic…
We present a unified framework for the holographic computation of Virasoro conformal blocks at large central charge. In particular, we provide bulk constructions that correctly reproduce all semiclassical Virasoro blocks that are known…
Two-dimensional diffeomorphism symmetry can be described by an operator algebra extension of the well-known Virasoro algebra description of conformal symmetry. Utilizing this extension, this note explains why the conformal symmetry that…
We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in…
In this paper we show that the worldline reparametrization for particles with higher derivative interactions appears as a higher dimensional symmetry, which is generated by the truncated Virasoro algebra. We also argue that for generic…
Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
We analyze aspects of the holographic principle relevant to the quantum gravity partition functions in Euclidean sector of AdS$_3$. The sum of the known contributions to the partitions functions can be presented exactly, including…
Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift…
In this paper we briefly review the main idea of the localization technique and its extension suitable in supersymmetric gauge field theory. We analyze the partition function of the vector multiplets with supercharges and its blocks on the…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
We construct generating technique for 5D minimal and $U(1)^3$ supergravities based on hidden symmetries arising in dimensional reduction to three dimensions. In the three-vector case the symmetry is SO(4,4), and the minimal case corresponds…
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…