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Zabzine, Maximorcid.org/0000-0002-5845-2283

Open this publication in new window or tab >>q-Virasoro Modular Triple### Nieri, Fabrizio

### Pan, Yiwen

### Zabzine, Maxim

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##### Abstract [en]

##### National Category

Subatomic Physics Mathematical Analysis
##### Identifiers

urn:nbn:se:uu:diva-379942 (URN)10.1007/s00220-019-03371-1 (DOI)000460545700010 ()
#####

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##### 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

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.

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.

Open this publication in new window or tab >>3d expansions of 5d instanton partition functions### Nieri, Fabrizio

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Pan, Yiwen

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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##### 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

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.

Open this publication in new window or tab >>3D mirror symmetry from *S*-duality### Nieri, Fabrizio

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Pan, Yiwen

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Subatomic Physics
##### Identifiers

urn:nbn:se:uu:diva-371299 (URN)10.1103/PhysRevD.98.126002 (DOI)000452327900005 ()
#####

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##### 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

Sun Yat Sen Univ, Sch Phys, Guangdong, Peoples R China.

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.

Open this publication in new window or tab >>Bootstrapping the S-5 partition function### Nieri, Fabrizio

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Pan, Yiwen

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: EPJ Web of Conferences: XX^{th} International Seminar on High Energy Physics (QUARKS-2018), EDP Sciences, 2018, Vol. 191, article id 06005Conference paper, Published paper (Refereed)
##### Abstract [en]

##### 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
#####

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##### 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

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.

Open this publication in new window or tab >>Elliptic modular double and 4d partition functions### Lodin, Rebecca

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Nieri, Fabrizio

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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##### 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

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.

Open this publication in new window or tab >>Morita equivalence and the generalized Kähler potential### Bischoff, Francis

### Gualtieri, Marco

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### National Category

Subatomic Physics
##### Identifiers

urn:nbn:se:uu:diva-371329 (URN)
#####

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Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-04-26Bibliographically approved

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

Open this publication in new window or tab >>Observables in the equivariant $A$-model### Bonechi, F.

### Cattaneo, A. S.

### Iraso, R.

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Article in journal (Refereed) Epub ahead of print
##### National Category

Subatomic Physics
##### Identifiers

urn:nbn:se:uu:diva-371308 (URN)
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Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-04-26Bibliographically approved

Open this publication in new window or tab >>Solving *q*-Virasoro constraints### Lodin, Rebecca

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Popolitov, Aleksandr

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Shakirov, Shamil

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2018 (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Subatomic Physics
##### Identifiers

urn:nbn:se:uu:diva-371291 (URN)
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Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-05-13Bibliographically approved

Society of Fellows, Harvard University, Cambridge, USA; Mathematical Sciences Research Institute, Berkeley, USA.

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.

Open this publication in new window or tab >>7D supersymmetric Yang-Mills on curved manifolds### Polydorou, Konstantina

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.### Rocén, Andreas

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
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Available from: 2018-02-15 Created: 2018-02-15 Last updated: 2019-07-31Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

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.

Open this publication in new window or tab >>Introduction to localization in quantum field theory### Pestun, Vasily

### Zabzine, Maxim

Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 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]

##### National Category

Physical Sciences
##### Identifiers

urn:nbn:se:uu:diva-346751 (URN)10.1088/1751-8121/aa5704 (DOI)000412932800001 ()
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##### Funder

EU, Horizon 2020, 677368Swedish Research Council, 2014-5517
Available from: 2018-03-27 Created: 2018-03-27 Last updated: 2018-03-27Bibliographically approved

Inst Hautes Etud Sci, Les Ulis, France.

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.