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On twisted N= 2 5D super Yang-Mills theory Qiu, Jian ; in Letters in Mathematical Physics (2016), 106(1), 127 Detailed reference viewed: 87 (0 UL)5D super Yang-Mills on Yp,q Sasaki-Einstein manifolds Qiu, Jian ; in Communications in Mathematical Physics (2015), 333(2), Detailed reference viewed: 71 (2 UL)Quantization of Poisson manifolds from the integrability of the modular function ; ; et al in Communications in Mathematical Physics (2014), 331(2), 851885 We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid ... [more ▼] We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular we consider the case when the modular function is "multiplicatively integrable", i.e. when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on CP_n, seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU(n+1). We show that a bihamiltoniam system on CP_n defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras. [less ▲] Detailed reference viewed: 151 (7 UL)On the infinity category of homotopy Leibniz algebras Khudaverdyan, David ; Poncin, Norbert ; Qiu, Jian in Theory and Applications of Categories (2014), 29(12), 332-370 Detailed reference viewed: 194 (41 UL)Wilson Lines from Representations of NQ-Manifolds ; ; Qiu, Jian 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 ▲] Detailed reference viewed: 108 (2 UL)Factorization of 5D super Yang-Mills on Yp,q spaces ; Qiu, Jian 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 ▲] Detailed reference viewed: 65 (1 UL)5D Super Yang-Mills on Y p,q Sasaki-Einstein manifolds Qiu, Jian ; 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 ▲] Detailed reference viewed: 109 (0 UL)The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere ; Qiu, Jian ; in Journal of High Energy Physics (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 ▲] Detailed reference viewed: 104 (2 UL)Lecture Notes on Topological Field Theory Qiu, Jian E-print/Working paper (2012) These notes are based on the lecture the author gave at the workshop 'Geometry of Strings and Fields' held at Nordita, Stockholm. In these notes, I shall cover some topics in both the perturbative and non ... [more ▼] These notes are based on the lecture the author gave at the workshop 'Geometry of Strings and Fields' held at Nordita, Stockholm. In these notes, I shall cover some topics in both the perturbative and non-perturbative aspects of the topological Chern-Simons theory. The non-perturbative part will mostly be about the quantization of Chern-Simons theory and the use of surgery for computation, while the non-perturbative part will include brief discussions about framings, eta invariants, APS-index theorem, torsions and finite type knot invariants. [less ▲] Detailed reference viewed: 56 (2 UL)Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications Qiu, Jian ; 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 ▲] Detailed reference viewed: 55 (0 UL) |
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