59 research outputs found
Twisted Hilbert spaces of 3d supersymmetric gauge theories
We study aspects of 3d N=2 supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the line. We propose a construction of the space of supersymmetric ground states as a graded vector space in terms of a certain cohomology of generalized vortex moduli spaces on the Riemann surface. This exhibits a rich dependence on deformation parameters compatible with the topological twist, including superpotentials, real mass parameters, and background vector bundles associated to flavour symmetries. By matching spaces of supersymmetric ground states, we perform new checks of 3d abelian mirror symmetry
The Superconformal Index of the (2,0) Theory with Defects
We compute the supersymmetric partition function of the six-dimensional (2,0) theory of type AN−1 on S1×S5 in the presence of both codimension two and codimension four defects. We concentrate on a limit of the partition function depending on a single parameter. From the allowed supersymmetric configurations of defects we find a precise match with the characters of irreducible modules of WN algebras and affine Lie algebras of type AN−1.1121sciescopu
Higher representations for extended operators
It is known that local operators in quantum field theory transform in
representations of ordinary global symmetry groups. The purpose of this paper
is to generalise this statement to extended operators such as line and surface
defects. We explain that -dimensional operators transform in
-representations of a finite -group symmetry and thoroughly explore this
statement for . We therefore propose higher representation theory as
the natural framework to describe the action of symmetries on the extended
operator content in quantum field theory.Comment: 60 pages + appendi
Representation theory for categorical symmetries
This paper addresses the question of how categorical symmetries act on
extended operators in quantum field theory. Building on recent results in two
dimensions, we introduce higher tube categories and algebras associated to
higher fusion category symmetries. We show that twisted sector extended
operators transform in higher representations of higher tube algebras and
interpret this result from the perspective of the sandwich construction of
finite symmetries via the Drinfeld center. Focusing on three dimensions, we
discuss a variety of examples to illustrate the general constructions. In the
case of invertible symmetries, we show that higher tube algebras are higher
analogues of twisted Drinfeld doubles of finite groups, generalising known
constructions in two dimensions. Building on this foundation, we discuss
non-invertible Ising-like symmetry categories obtained by gauging finite
subgroups. We also consider non-invertible topological symmetry lines described
by braided fusion categories and discuss connections to the M\"uger center and
braided module categories.Comment: 84 pages + appendix, 59 figure
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