Corpus ID: 235899153

# Batalin--Vilkovisky quantization and supersymmetric twists

@inproceedings{Safronov2021BatalinVilkoviskyQA,
title={Batalin--Vilkovisky quantization and supersymmetric twists},
author={P. Safronov and B. Williams},
year={2021}
}
• Published 2021
• Physics, Mathematics
We show that a family of topological twists of a supersymmetric mechanics with a Kähler target exhibits a Batalin–Vilkovisky quantization. Using this observation we make a general proposal for the Hilbert space of states after a topological twist in terms of the cohomology of a certain perverse sheaf. We give several examples of the resulting Hilbert spaces including the categorified Donaldson–Thomas invariants, Haydys–Witten theory and the 3-dimensional A-model.

#### References

SHOWING 1-10 OF 62 REFERENCES
A Taxonomy of Twists of Supersymmetric Yang--Mills Theory
• Physics, Mathematics
• 2020
We give a complete classification of twists of supersymmetric Yang--Mills theories in dimensions $2\leq n \leq 10$. We formulate supersymmetric Yang--Mills theory classically using the BV formalism,Expand
Higher-dimensional analogues of Donaldson-Witten theory
• Physics, Mathematics
• 1997
Abstract We present a Donaldson-Witten-type field theory in eight dimensions on manifolds with Spin (7) holonomy. We prove that the stress tensor is BRST exact for metric variations preserving theExpand
Twisting gauged non-linear sigma-models
We consider gauged sigma-models from a Riemann surface into a Kahler and hamiltonian G-manifold X. The supersymmetric = 2 theory can always be twisted to produce a gauged A-model. This modelExpand
Five-dimensional topologically twisted maximally supersymmetric Yang-Mills theory
A bstractHerein, we consider a topologically twisted version of maximally supersymmetric Yang-Mills theory in five dimensions which was introduced by Witten in 2011. We consider this theory on a fiveExpand
Fivebranes and Knots
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is aExpand
Hyperkähler metrics and supersymmetry
• Mathematics
• 1987
We describe two constructions of hyperkähler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinearExpand
Chiral de Rham complex and the half-twisted sigma-model
On any Calabi-Yau manifold X one can define a certain sheaf of chiral N=2 superconformal field theories, known as the chiral de Rham complex of X. It depends only on the complex structure of X, andExpand
A-branes and Noncommutative Geometry
We argue that for a certain class of symplectic manifolds the category of A-branes (which includes the Fukaya category as a full subcategory) is equivalent to a noncommutative deformation of theExpand
Electric-Magnetic Duality And The Geometric Langlands Program
• Mathematics, Physics
• 2006
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients areExpand
Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry
• Mathematics, Physics
• 2017
Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplecticExpand