281 research outputs found
5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
In this paper we apply the idea of Higgs branch localization to 5d
supersymmetric theories of vector multiplet and hypermultiplets, obtained as
the rigid limit of supergravity with all auxiliary fields. On
supersymmetric K-contact/Sasakian background, the Higgs branch BPS equations
can be interpreted as 5d generalizations of the Seiberg-Witten equations. We
discuss the properties and local behavior of the solutions near closed Reeb
orbits. For gauge theories, we show the suppression of the deformed
Coulomb branch, and the partition function is dominated by 5d Seiberg-Witten
solutions at large -limit. For squashed and manifolds, we
show the matching between poles in the perturbative Coulomb branch matrix
model, and the bound on local winding numbers of the BPS solutions.Comment: v1: 48 Pages; v2: references added; v3: various details and remarks
are added, fix the signs and factors in the suppression bound, where a bound
on hypermultiplet mass arises, v4: acknowledgement modifie
Schur correlation functions on
The Schur limit of the superconformal index of four-dimensional superconformal field theories has been shown to equal the supercharacter
of the vacuum module of their associated chiral algebra. Applying localization
techniques to the theory suitably put on , we obtain a direct
derivation of this fact. We also show that the localization computation can be
extended to calculate correlation functions of a subset of local operators,
namely of the so-called Schur operators. Such correlators correspond to
insertions of chiral algebra fields in the trace-formula computing the
supercharacter. As a by-product of our analysis, we show that the standard lore
in the localization literature stating that only off-shell supersymmetrically
closed observables are amenable to localization, is incomplete, and we
demonstrate how insertions of fermionic operators can be incorporated in the
computation.Comment: 49 page
Intersecting Surface Defects and Instanton Partition Functions
We analyze intersecting surface defects inserted in interacting
four-dimensional N = 2 supersymmetric quantum field theories. We employ the
realization of a class of such systems as the infrared fixed points of
renormalization group flows from larger theories, triggered by perturbed
Seiberg-Witten monopole-like configurations, to compute their partition
functions. These results are cast into the form of a partition function of
4d/2d/0d coupled systems. Our computations provide concrete expressions for the
instanton partition function in the presence of intersecting defects and we
study the corresponding ADHM model.Comment: 66 pages; v2: minor typos correcte
Ellipsoid partition function from Seiberg-Witten monopoles
We study Higgs branch localization of N=2 supersymmetric theories placed on
compact Euclidean manifolds. We analyze the resulting localization equations in
detail on the four-sphere and find that in this case the path integral is
dominated by vortex-like configurations as well as singular Seiberg-Witten
monopoles located at the north and south pole. The partition function is
written accordingly.Comment: 37 pages; v2: minor typos corrected, published versio
On rigid supersymmetry and notions of holomorphy in five dimensions
We study the equations governing rigid N=1 supersymmetry in five dimensions.
If the supersymmetry spinor satisfies a reality condition, these are foliations
admitting families of almost complex structures on the leaves. In other words,
all these manifolds have families of almost Cauchy-Riemann (CR) structures.
After deriving integrability conditions under which circumstances the almost CR
structure defines a CR manifold or a transversally holomorphic foliation (THF),
we discuss implications on localization. We also discuss potential global
obstructions to the existence of solutions.Comment: 14 pages; typos corrected; references adde
Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry
In this note we generalize the methods of [1][2][3] to 5-dimensional
Riemannian manifolds M. We study the relations between the geometry of M and
the number of solutions to a generalized Killing spinor equation obtained from
a 5-dimensional supergravity. The existence of 1 pair of solutions is related
to almost contact metric structures. We also discuss special cases related to
, which leads to M being foliated by submanifolds with
special properties, such as Quaternion-Kahler. When there are 2 pairs of
solutions, the closure of the isometry sub-algebra generated by the solutions
requires M to be S3 or T3-fibration over a Riemann surface. 4 pairs of
solutions pin down the geometry of M to very few possibilities. Finally, we
propose a new supersymmetric theory for N = 1 vector multiplet on K-contact
manifold admitting solutions to the Killing spinor equation.Comment: 53 pages, v2: refs added, typos correction, v3: refs added, typos
corrections and linguistic modifications in sec. 2 for readability, v4:
Acknowledgement modifie
Deformation quantizations from vertex operator algebras
In this note we address the question whether one can recover from the vertex
operator algebra associated with a four-dimensional N=2 superconformal field
theory the deformation quantization of the Higgs branch of vacua that appears
as a protected subsector in the three-dimensional circle-reduced theory. We
answer this question positively if the UV R-symmetries do not mix with
accidental (topological) symmetries along the renormalization group flow from
the four-dimensional theory on a circle to the three-dimensional theory. If
they do mix, we still find a deformation quantization but at different values
of its period.Comment: 40 pages; v2: argument in section 4.1 refined, references added; v3:
minor improvements, published versio
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