References of "Zabzine, Maxim"
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See detailOn twisted N= 2 5D super Yang-Mills theory
Qiu, Jian UL; Zabzine, Maxim

in Letters in Mathematical Physics (2016), 106(1), 127

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See detail5D super Yang-Mills on Yp,q Sasaki-Einstein manifolds
Qiu, Jian UL; Zabzine, Maxim

in Communications in Mathematical Physics (2015), 333(2),

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See detailWilson Lines from Representations of NQ-Manifolds
Bonechi, Francesco; Zabzine, Maxim; Qiu, Jian UL

in International Mathematics Research Notices (2013), 2013(24),

An NQ-manifold is a nonnegatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study ... [more ▼]

An NQ-manifold is a nonnegatively graded supermanifold with a degree 1 homological vector field. The focus of this paper is to define the Wilson loops/lines in the context of NQ-manifolds and to study their properties. The Wilson loops/lines, which give the holonomy or parallel transport, are familiar objects in usual differential geometry, we analyze the subtleties in the generalization to the NQ-setting and we also sketch some possible applications of our construction. [less ▲]

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See detailFactorization of 5D super Yang-Mills on Yp,q spaces
Zabzine, Maxim; Qiu, Jian UL

E-print/Working paper (2013)

We continue our study on the partition function for 5D supersymmetric Yang-Mills theory on toric Sasaki-Einstein Yp,q manifolds. Previously, using the localisation technique we have computed the ... [more ▼]

We continue our study on the partition function for 5D supersymmetric Yang-Mills theory on toric Sasaki-Einstein Yp,q manifolds. Previously, using the localisation technique we have computed the perturbative part of the partition function. In this work we show how the perturbative part factorises into four pieces, each corresponding to the perturbative answer of the same theory on R4×S1. This allows us to identify the equivariant parameters and to conjecture the full partition functions (including the instanton contributions) for Yp,q spaces. The conjectured partition function receives contributions only from singular contact instantons supported along the closed Reeb orbits. At the moment we are not able to prove this fact from the first principles. [less ▲]

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See detail5D Super Yang-Mills on Y p,q Sasaki-Einstein manifolds
Qiu, Jian UL; Zabzine, Maxim

E-print/Working paper (2013)

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki ... [more ▼]

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as Y p,q manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large N behaviour for the case of single hypermultiplet in adjoint representation and we derive the N 3-behaviour in this case. [less ▲]

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See detailThe perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
Kallen, Johan; Qiu, Jian UL; Zabzine, Maxim

in Journal of High Energy Physics [=JHEP] (2012), 157

Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation ... [more ▼]

Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g^2, where g is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed. [less ▲]

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See detailIntroduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications
Qiu, Jian UL; Zabzine, Maxim

in Archivum Mathematicum (2011), 47

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded ... [more ▼]

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV-formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of formal Hamiltonian vectors fields. We briefly discuss how these ideas can be extended to the infinite dimensional setting. These notes should be accessible to both physicists and mathematicians. [less ▲]

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