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  • 1.
    Longhi, Pietro
    et al.
    Swiss Fed Inst Technol, Inst Theoret Phys, CH-8093 Zurich, Switzerland.
    Nieri, Fabrizio
    DESY Theory, Notkestr 85, D-20607 Hamburg, Germany.
    Pittelli, Antonio
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Localization of 4d N=1 theories on D-2 x T-22019In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 12, article id 147Article in journal (Refereed)
    Abstract [en]

    We consider 4d N = 1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d N = 1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.

  • 2.
    Pittelli, Antonio
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Yangian symmetry of string theory on AdS(3) x S-3 x S-3 x S-1 with mixed 3-form flux2018In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 935, p. 271-289Article in journal (Refereed)
    Abstract [en]

    We find the Yangian symmetry underlying the integrability of type IIB superstrings on AdS(3) x S-3 x S-3 x S-1 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string tension limit the Yangian becomes a deformation of a unitary loop algebra and we derive its universal classical r-matrix.

  • 3.
    Pittelli, Antonio
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Preti, Michelangelo
    KTH Royal Inst Technol, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden;Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Integrable fishnet from gamma-deformed N=2 quivers2019In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 798, article id 134971Article in journal (Refereed)
    Abstract [en]

    We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of N = 2 superconformal field theories with deformation parameter gamma and prove that bi-fermion models emerge in the limit of large imaginary gamma and vanishing 't Hooft coupling g, with ge(-i/2 gamma) fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any gamma and in presence of double-trace deformations.

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