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  • 1.
    Björnberg, Jakob E.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Infrared Bound and Mean-Field Behaviour in the Quantum Ising Model2013In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 323, no 1, p. 329-366Article in journal (Refereed)
    Abstract [en]

    We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical exponent gamma for the susceptibility attains its mean-field value gamma = 1 in dimension at least 4 (positive temperature), respectively 3 (ground state), with logarithmic corrections in the boundary cases.

  • 2. Bonechi, Francesco
    et al.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Poisson Sigma Model on the Sphere2009In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 285, no 3, p. 1033-1063Article in journal (Refereed)
    Abstract [en]

    We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.

  • 3.
    de la Ossa, Xenia
    et al.
    Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England.
    Larfors, Magdalena
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Svanes, Eirik E.
    Sorbonne Univ, UPMC Paris 06, LPTHE, UMR 7589, F-75005 Paris, France;Sorbonne Univ, Inst Lagrange Paris, 98 Bis Bd Arago, F-75014 Paris, France.
    The Infinitesimal Moduli Space of Heterotic G2 Systems2018In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 360, no 2, p. 727-775Article in journal (Refereed)
    Abstract [en]

    Heterotic string compactifications on integrable G(2) structure manifolds Y with instanton bundles (V, A), (TY, (theta) over tilde )yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative D and show that it is equivalent to a heterotic G(2) system encoding the geometry of the heterotic string compactifications. This operator D acts on a bundle Q = T*Y circle plus End (V) circle plus End (TY) and satisfies a nilpotency condition (sic)(2) = 0, for an appropriate projection of D. Furthermore, we determine the infinitesimal moduli space of these systems and show that it corresponds to the finite-dimensional cohomology group (sic)(1)((sic)) (Q). We comment on the similarities and differences of our result with Atiyah's well-known analysis of deformations of holmorphic vector bundles over complex manifolds. Our analysis leads to results that are of relevance to all orders in the alpha' expansion.

  • 4.
    Ekstrand, Joel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Heluani, Reimundo
    Department of Mathematics, University of California, Berkeley.
    Källén, Johan
    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.
    Chiral de Rham complex on Riemannian manifolds and special holonomy2013In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 318, no 3, p. 575-613Article in journal (Refereed)
    Abstract [en]

    Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We discuss classical and partial quantum results. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau 3-fold. This is the first example of such a vertex subalgebra which is non-linearly generated by a finite number of superfields.

  • 5.
    Enciso, Alberto
    et al.
    CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
    Luque, Alejandro
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Peralta-Salas, Daniel
    CSIC, Inst Ciencias Matemat, Madrid 28049, Spain.
    Stationary Phase Methods and the Splitting of Separatrices2019In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 368, no 3, p. 1297-1322Article in journal (Refereed)
    Abstract [en]

    Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov function turns out to be computable using very little information on the separatrix and in the case of non-analytic systems. This is related to a priori stable systems coupled with low regularity perturbations. A natural physical application is to perturbations controlled by wave-type equations, so in particular we also illustrate this result with the motion of charged particles in a rapidly oscillating electromagnetic field. Quasi-periodic perturbations are discussed too.

  • 6.
    Gaidashev, Denis
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    On the Scaling Ratios for Siegel Disks2015In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 333, no 2, p. 931-957Article in journal (Refereed)
    Abstract [en]

    The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point and the rotation number whose continued fraction expansion is preperiodic has been observed to be self-similar with a certain scaling ratio. The restriction of the dynamics of the quadratic polynomial to the boundary of the Siegel disk is known to be quasisymmetrically conjugate to the rigid rotation with the same rotation number. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. In this paper we provide an estimate on the quasisymmetric constant of the conjugacy, and use it to prove bounds on the scaling ratio lambda of the form alpha(gamma) <= |lambda| <= C delta(s), where s is the period of the continued fraction, and alpha is an element of (0, 1) depends on the rotation number in an explicit way, while C > 1, delta is an element of (0, 1) and gamma is an element of (0, 1) depend only on the maximum of the integers in the continued fraction expansion of the rotation number.

  • 7.
    He, Yang-Hui
    et al.
    Univ Oxford, Merton Coll, Oxford OX1 4JD, England;Nankai Univ, Sch Phys, Tianjin 300071, Peoples R China;City Univ London, Dept Math, London EC1V 0HB, England.
    Seong, Rak-Kyeong
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Yau, Shing-Tung
    Harvard Univ, Dept Math, Jefferson Phys Lab, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA.
    Calabi-Yau Volumes and Reflexive Polytopes2018In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 361, no 1, p. 155-204Article in journal (Refereed)
    Abstract [en]

    We study various geometrical quantities for Calabi-Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki-Einstein base of the corresponding Calabi-Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki-Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence.

  • 8. Heluani, Reimundo
    et al.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Superconformal Structures on Generalized Calabi-Yau Metric Manifolds2011In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 306, no 2, p. 333-364Article in journal (Refereed)
    Abstract [en]

    We construct an embedding of two commuting copies of the N = 2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kahler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kahler manifold. The classical limit of this result allows one to recover the celebrated generalized Kahler identities as the degree zero part of an infinite dimensional Lie superalgebra attached to any generalized Kahler manifold. As a byproduct of our study we investigate the properties of generalized Calabi-Yau metric manifolds in the Lie algebroid setting.

  • 9.
    Killip, Rowan
    et al.
    Univ Calif Los Angeles, Dept Math, Box 951555, Los Angeles, CA 90095 USA..
    Kozhan, Rostyslav
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Matrix Models and Eigenvalue Statistics for Truncations of Classical Ensembles of Random Unitary Matrices2017In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, no 3, p. 991-1027Article in journal (Refereed)
    Abstract [en]

    We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these ensembles. This allows us to compute the joint law of the eigenvalues, which have a natural interpretation as resonances for open quantum systems or as electrostatic charges located in a dielectric medium. Our methods allow us to consider all values of , not merely .

  • 10.
    Lilja, Dan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    On the Invariant Cantor Sets of Period Doubling Type of Infinitely Renormalizable Area-Preserving Maps2018In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 358, no 3, p. 1027-1039Article in journal (Refereed)
    Abstract [en]

    Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser the study of renormalization operators in dynamics has been very successful at explaining universality phenomena observed in certain families of dynamical systems. The first proof of existence of a hyperbolic fixed point for renormalization of area-preserving maps was given by Eckmann et al. (Mem Am Math Soc 47(289):vi+122, 1984). However, there are still many things that are unknown in this setting, in particular regarding the invariant Cantor sets of infinitely renormalizable maps. In this paper we show that the invariant Cantor set of period doubling type of any infinitely renormalizable area-preserving map in the universality class of the Eckmann-Koch-Wittwer renormalization fixed point is always contained in a Lipschitz curve but never contained in a smooth curve. This extends previous results by de Carvalho, Lyubich and Martens about strongly dissipative maps of the plane close to unimodal maps to the area-preserving setting. The method used for constructing the Lipschitz curve is very similar to the method used in the dissipative case but proving the nonexistence of smooth curves requires new techniques.

  • 11.
    Lindström, Ulf
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
    Rocek, Martin
    Properties of Hyperkahler Manifolds and Their Twistor Spaces2010In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 293, no 1, p. 257-278Article in journal (Refereed)
    Abstract [en]

    We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.

  • 12.
    Lindström, Ulf
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Rocek, Martin
    von Unge, Rikard
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
    Generalized Kähler manifolds and off-shell supersymmetry2007In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 269, no 3, p. 833-849Article in journal (Refereed)
    Abstract [en]

    We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kähler potential for any generalized Kähler manifold; this potential is the superspace Lagrangian.

  • 13. Marklof, Jens
    et al.
    Strömbergsson, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Free Path Lengths in Quasicrystals2014In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 330, no 2, p. 723-755Article in journal (Refereed)
    Abstract [en]

    Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g., at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present paper we investigate quasicrystalline scatterer configurations, which are non-periodic, yet strongly correlated. A famous example is the vertex set of a Penrose tiling. Our main result proves the existence of a limit distribution for the free path length, which answers a question of Wennberg. The limit distribution is characterised by a certain random variable on the space of higher dimensional lattices, and is distinctly different from the exponential distribution observed for random scatterer configurations. The key ingredients in the proofs are equidistribution theorems on homogeneous spaces, which follow from Ratner's measure classification.

  • 14.
    Mazorchuk, Volodymyr
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Frisk, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Regular strongly typical blocks of O-q2009In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 291, no 2, p. 533-542Article in journal (Refereed)
  • 15.
    Nedelin, Anton
    et al.
    Univ Milano Bicocca, Dipartimento Fis, Piazza Sci 3, I-20126 Milan, Italy.;INFN, Sez Milano Bicocca, I-20126 Milan, Italy..
    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.
    q-Virasoro Modular Double and 3d Partition Functions2017In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 353, no 3, p. 1059-1102Article in journal (Refereed)
    Abstract [en]

    We study partition functions of 3d gauge theories on compact manifolds which are S (1) fibrations over S-2. We show that the partition functions are free field correlators of vertex operators and screening charges of the q-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two-related commuting sets of q-Virasoro constraints. We generalize our construction to 3d unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.

  • 16.
    Nieri, Fabrizio
    et al.
    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.
    q-Virasoro Modular Triple2019In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 366, no 1, p. 397-422Article in journal (Refereed)
    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.

  • 17. Qiu, Jian
    et al.
    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, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Gluing Nekrasov partition functions2015In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 337, no 2, p. 785-816Article in journal (Refereed)
    Abstract [en]

    In this paper we summarise the localisation calculation of 5D superYang-Mills on simply connected toric Sasaki-Einstein (SE) manifolds. We showhow various aspects of the computation, including the equivariant index, theasymptotic behaviour and the factorisation property are governed by thecombinatorial data of the toric geometry. We prove that the full perturbativepartition function on a simply connected SE manifold corresponding to an n-gontoric diagram factorises to n copies of perturbative Nekrasov partitionfunction. This leads us to conjecture the full partition function as gluing ncopies of full Nekrasov partition function. This work is a generalisation ofsome earlier computation carried out on $Y^{p,q}$ manifolds, whose moment mapcone has a quadrangle and our result is valid for manifolds whose moment mapcones have pentagon base, hexagon base, etc. The algorithm we used for dealingwith general cones may also be of independent interest.

  • 18. Qiu, Jian
    et al.
    Zabzine, Maxim
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    5D Super Yang-Mills on Y-p,Y-q Sasaki-Einstein Manifolds2015In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 333, no 2, p. 861-904Article in journal (Refereed)
    Abstract [en]

    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,Y-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 a 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.

  • 19.
    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.

  • 20.
    Viklund, Fredrik Johansson
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Sola, Alan
    Turner, Amanda
    Small-Particle Limits in a Regularized Laplacian Random Growth Model2015In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 334, no 1, p. 331-366Article in journal (Refereed)
    Abstract [en]

    We study a regularized version of Hastings-Levitov planar random growth that models clusters formed by the aggregation of diffusing particles. In this model, the growing clusters are defined in terms of iterated slit maps whose capacities are given by where c > 0 is the capacity of the first particle, {I broken vertical bar (n) } (n) are the composed conformal maps defining the clusters of the evolution, {theta (n) } (n) are independent uniform angles determining the positions at which particles are attached, and sigma > 0 is a regularization parameter which we take to depend on c. We prove that under an appropriate rescaling of time, in the limit as c -> 0, the clusters converge to growing disks with deterministic capacities, provided that sigma does not converge to 0 too fast. We then establish scaling limits for the harmonic measure flow over longer time periods showing that, by letting alpha -> 0 at different rates, this flow converges to either the Brownian web on the circle, a stopped version of the Brownian web on the circle, or the identity map. As the harmonic measure flow is closely related to the internal branching structure within the cluster, the above three cases intuitively correspond to the number of infinite branches in the model being either 1, a random number whose distribution we obtain, or unbounded, in the limit as c -> 0. We also present several findings based on simulations of the model with parameter choices not covered by our rigorous analysis.

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