Holomorphic blocks in three dimensions

By Christopher Beem, Tudor Dimofte, Sara Pasquetti. 2012

322 citations recorded by the source corpus.

A bstractWe decompose sphere partition functions and indices of three-dimensional N$$ \mathcal{N} $$ = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The blocks count BPS states and are in one-to-one correspondence with the theory’s massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a reduction to supersymmetric quantum mechanics. The blocks turn out to possess a wealth of surprising properties, such as a Stokes phenomenon that integrates nicely with actions of three-dimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the six-dimensional (2, 0) theory on a three-manifold M, the blocks belong to a basis of wave-functions in analytically continued Chern-Simons theory on M. For theories engineered on branes in Calabi-Yau geometries, the blocks offer a non-perturbative perspective on open topological string partition functions.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/483962eca8b88dda1646c005ca9098e2206ca389

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

Supersymmetric field theories on three-manifolds (2012, background): “Some more general geometries were recently considered in [23-29].”
Localization techniques in quantum field theories (2016, methodology): “On the other hand, for the identity fusing, which should give the S2 × S1 partition function, we have q̃ = q−1, and the block variables x and x̃ can be shown to be related to the variables z and m in the index by x = zq−m/2 and x̃ = z−1q−m/2 [71].”
BPS spectra and 3-manifold invariants (2017, background): “Motivated by the topological/anti-topological fusion [23] and its recent 3d incarnation [24,25,30,31], we would like to make the following conjecture: (11)Such factor can appear even without singularity, when there is only g = 1 adjoint chiral with R-charge 0.”
Defects and quantum Seiberg-Witten geometry (2014, methodology): “Then the S transformation on the 3d partition function can be written as [13]”
1-efficient triangulations and the index of a cusped hyperbolic 3-manifold (2013, background): “Before we get to the details, we should stress that the origin of the 3D index is the exciting work of Dimofte, Gaiotto and Gukov [10; 11] (see also Beem, Dimofte and Pasquetti [5]) who studied gauge theories with N D2 supersymmetry that are associated to an ideal triangulation T of an oriented 3–ma”
Elliptic stable envelopes (2016, background): “9See [2] for a fairly accessible review, [3] for more details.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “The linear ambiguity in ua reflects the fact that Ua is a constrained twisted chiral fields, with the twisted F -term given by the twodimensional gauge flux [32, 43].”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “As first observed in [14] and later elaborated upon in [15, 16], both the S3 partition function of [29], the S2×S1 supersymmetric index of [47, 48] and the lens space index of [49] “factorize” into building elements which can be interpreted as the partition function on R(2)Ω×S(1) in an Ω-background.”