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Nieri, F., Pan, Y. & Zabzine, M. (2019). q-Virasoro Modular Triple. Communications in Mathematical Physics, 366(1), 397-422
Open this publication in new window or tab >>q-Virasoro Modular Triple
2019 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 366, no 1, p. 397-422Article in journal (Refereed) Published
Abstract [en]

Inspired by 5d supersymmetric Yang-Mills theories placed on the compact space S5, we propose an intriguing algebraic construction for the q-Virasoro algebra. We show that, when multiple q-Virasoro chiral sectors have to be fused together, a natural SL(3,Z) structure arises. This construction, which we call the modular triple, is consistent with the observed triple factorization properties of supersymmetric partition functions derived from localization arguments. We also give a 2d CFT-like construction of the modular triple, and conjecture for the first time a (non-local) Lagrangian formulation for a q-Virasoro model, resembling ordinary Liouville theory.

National Category
Subatomic Physics Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-379942 (URN)10.1007/s00220-019-03371-1 (DOI)000460545700010 ()
Funder
Swedish Research Council, 2014-5517Knut and Alice Wallenberg Foundation
Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-03-26Bibliographically approved
Nieri, F., Pan, Y. & Zabzine, M. (2018). 3d expansions of 5d instanton partition functions. Journal of High Energy Physics (JHEP) (4), Article ID 092.
Open this publication in new window or tab >>3d expansions of 5d instanton partition functions
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 092Article in journal (Refereed) Published
Abstract [en]

We propose a set of novel expansions of Nekrasov's instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on C-q,t(2) 1 x S-1, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces C-q x S-1, Ct-1 x S-1 and their intersection along S-1. These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with W-q,W-t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.

Keywords
Matrix Models, Solitons Monopoles and Instantons, Supersymmetric Gauge Theory
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-354119 (URN)10.1007/JHEP04(2018)092 (DOI)000430567800012 ()
Funder
Swedish Research Council, W2014-5517Knut and Alice Wallenberg Foundation
Available from: 2018-06-19 Created: 2018-06-19 Last updated: 2018-06-26Bibliographically approved
Nieri, F., Pan, Y. & Zabzine, M. (2018). 3D mirror symmetry from S-duality. Physical Review D. Particles and fields, D98(12)
Open this publication in new window or tab >>3D mirror symmetry from S-duality
2018 (English)In: Physical Review D. Particles and fields, ISSN 0556-2821, E-ISSN 1089-4918, Vol. D98, no 12Article in journal (Refereed) Published
Abstract [en]

We consider type IIB SL(2, Z) symmetry to relate the partition functions of different 5d supersymmetric Abelian linear quiver Yang-Mills theories in the Omega-background and squashed S-5 background. By Higgsing S-dual theories, we extract new and old 3d mirror pairs. Generically, the Higgsing procedure yields 3d defects on intersecting spaces, and we derive new hyperbolic integral identities expressing the equivalence of the squashed S-3 partition functions with additional degrees of freedom on the S-1 intersection.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371299 (URN)10.1103/PhysRevD.98.126002 (DOI)000452327900005 ()
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationThe Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-01-22Bibliographically approved
Nieri, F., Pan, Y. & Zabzine, M. (2018). Bootstrapping the S-5 partition function. In: EPJ Web of Conferences: XXth International Seminar on High Energy Physics (QUARKS-2018). Paper presented at 20th International Seminar on High Energy Physics (QUARKS-2018), Valday, Russia, May 27-June 2, 2018. EDP Sciences, 191, Article ID 06005.
Open this publication in new window or tab >>Bootstrapping the S-5 partition function
2018 (English)In: EPJ Web of Conferences: XXth International Seminar on High Energy Physics (QUARKS-2018), EDP Sciences, 2018, Vol. 191, article id 06005Conference paper, Published paper (Refereed)
Abstract [en]

We consider U(N) SQCD on S-5 and propose a Higgs branch-like expression for its partition function. We support the result by arguing that the knowledge of certain BPS codimension 2 and 4 defects arising from Higgsing is enough to reconstruct the bulk partition function, and that the defect partition functions satisfy a set of non-perturbative Schwinger-Dyson equations. We show that the result is consistent with, and naturally come from, the BPS/CRT perspective. In this language, the defect partition functions are identified with free boson correlators of the q-Virasoro modular triple, and the constraint equations with Ward identities satisfied by the corresponding Dotsenko-Fateev q-conformal blocks, providing a natural basis to expand the S-5 partition function.

Place, publisher, year, edition, pages
EDP Sciences, 2018
Series
EPJ Web of Conferences, E-ISSN 2100-014X
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371307 (URN)10.1051/epjconf/201819106005 (DOI)000482971700071 ()
Conference
20th International Seminar on High Energy Physics (QUARKS-2018), Valday, Russia, May 27-June 2, 2018
Funder
Swedish Research Council, 2014-5517Knut and Alice Wallenberg FoundationThe Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-10-25Bibliographically approved
Lodin, R., Nieri, F. & Zabzine, M. (2018). Elliptic modular double and 4d partition functions. Journal of Physics A: Mathematical and Theoretical, 51(4), Article ID 045402.
Open this publication in new window or tab >>Elliptic modular double and 4d partition functions
2018 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 4, article id 045402Article in journal (Refereed) Published
Abstract [en]

We consider 4d supersymmetric (special) unitary Gamma quiver gauge theories on compact manifolds which are T-2 fibrations over S-2. We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic W-q,(t);(q ')(Gamma) algebras. We also consider a generating function of BPS surface defects supported on T-2 and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2018
Keywords
supersymmetric gauge theories, deformed W algebras, matrix models
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-338956 (URN)10.1088/1751-8121/aa9a2d (DOI)000418550700002 ()
Funder
Swedish Research Council, 2014-5517The Swedish Foundation for International Cooperation in Research and Higher Education (STINT)Knut and Alice Wallenberg Foundation
Available from: 2018-01-18 Created: 2018-01-18 Last updated: 2018-01-18Bibliographically approved
Bischoff, F., Gualtieri, M. & Zabzine, M. (2018). Morita equivalence and the generalized Kähler potential.
Open this publication in new window or tab >>Morita equivalence and the generalized Kähler potential
2018 (English)In: Article in journal (Refereed) Epub ahead of print
Abstract [en]

We solve the problem of determining the fundamental degrees of freedom underlying a generalized Kähler structure of symplectic type. For a usual Kähler structure, it is well-known that the geometry is determined by a complex structure, a Kähler class, and the choice of a positive (1,1)-form in this class, which depends locally on only a single real-valued function: the Kähler potential. Such a description for generalized Kähler geometry has been sought since it was discovered in 1984. We show that a generalized Kähler structure of symplectic type is determined by a pair of holomorphic Poisson manifolds, a holomorphic symplectic Morita equivalence between them, and the choice of a positive Lagrangian brane bisection, which depends locally on only a single real-valued function, which we call the generalized Kähler potential. Our solution draws upon, and specializes to, the many results in the physics literature which solve the problem under the assumption (which we do not make) that the Poisson structures involved have constant rank. To solve the problem we make use of, and generalize, two main tools: the first is the notion of symplectic Morita equivalence, developed by Weinstein and Xu to study Poisson manifolds; the second is Donaldson's interpretation of a Kähler metric as a real Lagrangian submanifold in a deformation of the holomorphic cotangent bundle

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371329 (URN)
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-04-26Bibliographically approved
Bonechi, F., Cattaneo, A. S., Iraso, R. & Zabzine, M. (2018). Observables in the equivariant $A$-model.
Open this publication in new window or tab >>Observables in the equivariant $A$-model
2018 (English)In: Article in journal (Refereed) Epub ahead of print
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371308 (URN)
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-04-26Bibliographically approved
Lodin, R., Popolitov, A., Shakirov, S. & Zabzine, M. (2018). Solving q-Virasoro constraints.
Open this publication in new window or tab >>Solving q-Virasoro constraints
2018 (English)Manuscript (preprint) (Other academic)
Abstract [en]

We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for beta-ensembles. From free-field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{-1} Z = 0. We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on D^2 \cross S^1 and S^3.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371291 (URN)
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-05-13Bibliographically approved
Polydorou, K., Rocén, A. & Zabzine, M. (2017). 7D supersymmetric Yang-Mills on curved manifolds. Journal of High Energy Physics (JHEP) (12), Article ID 152.
Open this publication in new window or tab >>7D supersymmetric Yang-Mills on curved manifolds
2017 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 12, article id 152Article in journal (Refereed) Published
Abstract [en]

We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for the full non-perturbative answer.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Differential and Algebraic Geometry, Supersymmetric Gauge Theory
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-340461 (URN)10.1007/JHEP12(2017)152 (DOI)000419111400010 ()
Available from: 2018-02-15 Created: 2018-02-15 Last updated: 2019-07-31Bibliographically approved
Pestun, V. & Zabzine, M. (2017). Introduction to localization in quantum field theory. Journal of Physics A: Mathematical and Theoretical, 50(44), Article ID 443001.
Open this publication in new window or tab >>Introduction to localization in quantum field theory
2017 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 44, article id 443001Article, review/survey (Refereed) Published
Abstract [en]

This is the introductory chapter to this issue. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of the localization calculations for supersymmetric theories. We explain the focus of the present issue.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-346751 (URN)10.1088/1751-8121/aa5704 (DOI)000412932800001 ()
Funder
EU, Horizon 2020, 677368Swedish Research Council, 2014-5517
Available from: 2018-03-27 Created: 2018-03-27 Last updated: 2018-03-27Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-5845-2283

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