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  • 1. Bonechi, Francesco
    et al.
    Qiu, Jian
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Tarlini, Marco
    Complete integrability from Poisson-Nijenhuis structures on compact hermitian symmetric spaces2015Article in journal (Refereed)
    Abstract [en]

    We study a class of Poisson-Nijenhuis systems defined on compact hermitian symmetric spaces, where the Nijenhuis tensor is defined as the composition of Kirillov-Konstant-Souriau symplectic form with the so called Bruhat-Poisson structure. We determine its spectrum. In the case of Grassmannians the eigenvalues are the Gelfand-Tsetlin variables. We introduce the abelian algebra of collective hamiltonians defined by a chain of nested subalgebras and prove complete integrability. By construction, these models are integrable with respect to both Poisson structures. The eigenvalues of the Nijenhuis tensor are a choice of action variables. Our proof relies on an explicit formula for the contravariant connection defined on vector bundles that are Poisson with respect to the Bruhat-Poisson structure.

  • 2.
    Festuccia, Guido
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Qiu, Jian
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Winding, Jacob
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    N=2 supersymmetric gauge theory on connected sums of S2xS22017In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 03, article id 026Article in journal (Refereed)
    Abstract [en]

    We construct 4D N = 2 theories on an infinite family of 4D toric manifolds with the topology of connected sums of S-2 x S-2. These theories are constructed through the dimensional reduction along a non -trivial U(1) -fiber of 5D theories on toric Sasaki Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on S-4.

  • 3.
    Pestun, Vasily
    et al.
    Inst Hautes Etudes Sci, Bures Sur Yvette, France..
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Benini, Francesco
    Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy.;Imperial Coll London, Blackett Lab, London SW7 2AZ, England..
    Dimofte, Tudor
    Perimeter Inst Theoret Phys, 31 Caroline St N, Waterloo, ON N2J 2Y5, Canada.;Univ Calif Davis, Dept Math, Davis, CA 95616 USA..
    Dumitrescu, Thomas T.
    Harvard Univ, Dept Phys, Cambridge, MA 02138 USA..
    Hosomichi, Kazuo
    Natl Taiwan Univ, Dept Phys, Taipei 10617, Taiwan..
    Kim, Seok
    Seoul Natl Univ, Dept Phys & Astron, Seoul 151747, South Korea.;Seoul Natl Univ, Ctr Theoret Phys, Seoul 151747, South Korea..
    Lee, Kimyeong
    Korea Inst Adv Study, Sch Phys, Seoul 130722, South Korea..
    Le Floch, Bruno
    Princeton Univ, Princeton Ctr Theoret Sci, Princeton, NJ 08544 USA..
    Marino, Marcos
    Univ Geneva, Dept Phys Theor & Sect Math, CH-1211 Geneva, Switzerland..
    Minahan, Joseph A.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Morrison, David R.
    Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA.;Univ Calif Santa Barbara, Dept Phys, Santa Barbara, CA 93106 USA..
    Pasquetti, Sara
    Univ Milano Bicocca, Dipartimento Fis, Piazza Sci 3, I-20126 Milan, Italy..
    Qiu, Jian
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Rastelli, Leonardo
    SUNY Stony Brook, CN Yang Inst Theoret Phys, Stony Brook, NY 11794 USA..
    Razamat, Shlomo S.
    Technion, Dept Phys, Haifa, Israel..
    Pufu, Silvu S.
    Princeton Univ, Joseph Henry Labs, Princeton, NJ 08544 USA..
    Tachikawa, Yuji
    Univ Tokyo, Kavli Inst Phys & Math Universe, Kashiwa, Chiba 2778583, Japan..
    Willett, Brian
    UC Santa Barbara, KITP, Santa Barbara, CA USA..
    Zarembo, Konstantin
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. NORDITA, KTH Royal Inst Technol, Stockholm, Sweden..
    Localization techniques in quantum field theories2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 44, article id 440301Article in journal (Other academic)
    Abstract [en]

    This is the foreword to the special issue on localization techniques in quantum field theory. The summary of individual chapters is given and their interrelation is discussed.

  • 4.
    Qiu, Jian
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Dimensional Regularization and Dimensional Reduction in the Light Cone2008In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 77, no 125032Article in journal (Refereed)
    Abstract [en]

    We calculate all the 2 to 2 scattering process in Yang-Mills theory in the Light Cone gauge, with the dimensional regulator as the UV regulator. The IR is regulated with a cutoff in q+" role="presentation" style="display: inline; line-height: normal; font-size: 13.6px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">q+q+. It supplements our earlier work, where a Lorentz non-covariant regulator was used and the final results bear some problems in gauge fixing. Supersymmetry relations among various amplitudes are checked using the light cone superfields.

  • 5.
    Qiu, Jian
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Tizzano, Luigi
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Winding, Jacob
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Zabzine, Maxime
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Modular properties of full 5D SYM partition function2016In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 16, no 03, article id 193Article in journal (Refereed)
    Abstract [en]

    We study properties of the full partition function for the U(1) 5D N=2∗ gauge theory with adjoint hypermultiplet of mass M. This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function GC2 associated with a certain moment map cone C. The answer exhibits a curious SL(4,ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5D supersymmetric partition function with the insertion of defects of various co-dimensions.

  • 6.
    Qiu, Jian
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Knot invariants and new weight systems from general 3D TFTs2012In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 62, no 2, p. 242-271Article in journal (Refereed)
    Abstract [en]

    We introduce and study the Wilson loops in general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in the Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the Ward identities of these theories imply that the expectation value of the Wilson loop is a pairing of two dual constructions of (co)cycles of certain extended graph complex (extended from Kontsevich's graph complex to accommodate the Wilson loop). We also prove that there is an isomorphism between the same complex and certain extended Chevalley-Eilenberg complex of Hamiltonian vector fields. This isomorphism allows us to generalize the Lie algebra weight system for knots to weight systems associated with any homological vector field and its representations. As an example we construct knot invariants using holomorphic vector bundle over hyperKahler manifolds.

  • 7.
    Qiu, Jian
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes2010In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 300, no 3, p. 789-833Article in journal (Refereed)
    Abstract [en]

    We investigate the generic 3D topological field theory within the AKSZ-BV framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue that the perturbative partition function gives rise to secondary characteristic classes. We investigate a toy model which is an odd analogue of Chern-Simons theory, and we give some explicit computation of two point functions and show that its perturbation theory is identical to the Chern-Simons theory. We give a concrete example of the homomorphism taking Lie algebra cocycles to Q-characteristic classes, and we reinterpret the Rozansky-Witten model in this light.

  • 8.
    Qiu, Jian
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    On twisted N=2 5D super Yang-Mills theory2016In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 106, no 1, p. 1-27Article in journal (Refereed)
    Abstract [en]

    On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys-Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa-Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys-Witten equations on product manifolds M5=M4×R arise in the context of twisting the 5D maximally supersymmetric Yang-Mills theory. In this paper, we present the construction of twisted N=2 Yang-Mills theory on Sasaki-Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys-Witten equation.

  • 9.
    Qiu, Jian
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Max Planck Inst Math, Bonn, Germany.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Review of localization for 5d supersymmetric gauge theories2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 44, article id 443014Article, review/survey (Refereed)
    Abstract [en]

    We give a pedagogical review of the localisation of supersymmetric gauge theories on 5d toric Sasaki-Einstein manifolds. We construct certain cohomological complex from the supersymmetry complex and consider its natural toric deformations with all equivariant parameters turned on. We also give detailed discussion on how the Sasaki-Einstein geometry manifests itself in every aspect of the calculation, from Killing spinor, vanishing theorems to the index theorems.

1 - 9 of 9
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