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  • Poisson vertex algebras in supersymmetric field theories
    Lett. Math. Phys. (IF 1.203) Pub Date : 2020-05-25
    Jihwan Oh, Junya Yagi

    A large class of supersymmetric quantum field theories, including all theories with \({\mathcal {N}}= 2\) supersymmetry in three dimensions and theories with \({\mathcal {N}}= 2\) supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional \({\mathcal {N}}= 2\)

    更新日期:2020-05-25
  • Chern–Simons–Schrödinger theory on a one-dimensional lattice
    Lett. Math. Phys. (IF 1.203) Pub Date : 2020-05-23
    Hyungjin Huh, Swaleh Hussain, Dmitry E. Pelinovsky

    We propose a gauge-invariant system of the Chern–Simons–Schrödinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square summable sequences for the scalar field. We also study the existence region of the stationary bound states, which depends on the lattice spacing and the nonlinearity power

    更新日期:2020-05-23
  • Variational representations related to Tsallis relative entropy
    Lett. Math. Phys. (IF 1.203) Pub Date : 2020-05-07
    Guanghua Shi, Frank Hansen

    We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden–Thompson’s trace inequality to deformed exponentials with deformation parameter \( q\in [0,1], \) thus complementing the second author’s previous study of the cases with deformation parameter

    更新日期:2020-05-07
  • Log expansions from combinatorial Dyson–Schwinger equations
    Lett. Math. Phys. (IF 1.203) Pub Date : 2020-04-07
    Olaf Krüger

    We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling constant \(\alpha \) and a logarithmic energy scale L—a reordering of terms as \(G(\alpha ,L) = 1 \pm \sum _{j \ge 0} \alpha ^j H_j(\alpha L)\) is the corresponding log expansion. In a first part of this

    更新日期:2020-04-07
  • Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data
    Lett. Math. Phys. (IF 1.203) Pub Date : 2020-04-02
    Alexander Tsymbaliuk

    We introduce super Yangians of \(\mathfrak {gl}(V),\mathfrak {sl}(V)\) (in the new Drinfeld realization) associated with all Dynkin diagrams. We show that all of them are isomorphic to the super Yangians introduced by Nazarov (Lett Math Phys 21(2), 123–131, 1991), by identifying them with the corresponding RTT super Yangians. However, their “positive halves” are not pairwise isomorphic, and we obtain

    更新日期:2020-04-02
  • The non-abelian self-dual string
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-18
    Christian Sämann, Lennart Schmidt

    We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e., a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the

    更新日期:2019-12-18
  • Cyclic orbifolds of lattice vertex operator algebras having group-like fusions
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-18
    Ching Hung Lam

    Let L be an even (positive definite) lattice and \(g\in O(L)\). In this article, we prove that the orbifold vertex operator algebra \(V_{L}^{{\hat{g}}}\) has group-like fusion if and only if g acts trivially on the discriminant group \({\mathcal {D}}(L)=L^*/L\) (or equivalently \((1-g)L^*

    更新日期:2019-12-18
  • Reduction of a bi-Hamiltonian hierarchy on $$T^*\mathrm{U}(n)$$T∗U(n) to spin Ruijsenaars–Sutherland models
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-16
    L. Fehér

    We first exhibit two compatible Poisson structures on the cotangent bundle of the unitary group \(\mathrm{U}(n)\) in such a way that the invariant functions of the \({\mathfrak {u}}(n)^*\)-valued momenta generate a bi-Hamiltonian hierarchy. One of the Poisson structures is the canonical one and the other one arises from embedding the Heisenberg double of the Poisson–Lie group \(\mathrm{U}(n)\) into

    更新日期:2019-12-16
  • Bannai–Ito algebras and the universal R -matrix of $$\pmb {\mathfrak {osp}}(1|2)$$osp(1|2)
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-14
    Nicolas Crampé, Luc Vinet, Meri Zaimi

    The Bannai–Ito algebra BI(n) is viewed as the centralizer of the action of \(\mathfrak {osp}(1|2)\) in the n-fold tensor product of the universal algebra of this Lie superalgebra. The generators of this centralizer are constructed with the help of the universal R-matrix of \(\mathfrak {osp}(1|2)\). The specific structure of the \(\mathfrak {osp}(1|2)\) embeddings to which the centralizing elements

    更新日期:2019-12-14
  • Relative entropy for coherent states in chiral CFT
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-10
    Stefan Hollands

    We consider the relative entropy between the vacuum state and a state obtained by applying an exponentiated stress tensor to the vacuum of a chiral conformal field theory on the lightray. The smearing function of the stress tensor can be viewed as a vector field on the real line generating a diffeomorphism. We show that the relative entropy is equal to c times the so-called Schwarzian action of the

    更新日期:2019-12-10
  • The quantum DELL system
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-04
    Peter Koroteev, Shamil Shakirov

    We propose quantum Hamiltonians of the double-elliptic many-body integrable system (DELL) and study its spectrum. These Hamiltonians are certain elliptic functions of coordinates and momenta. Our results provide quantization of the classical DELL system which was previously found in the string theory literature. The eigenfunctions for the N-body model are instanton partition functions of 6d SU(N) gauge

    更新日期:2019-12-04
  • A solvable tensor field theory
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-03
    Romain Pascalie

    We solve the closed Schwinger–Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert’s W function, using a perturbative expansion and Lagrange–Bürmann resummation. Higher-point functions are then obtained recursively.

    更新日期:2019-12-03
  • Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-03
    P. Exner, S. Kondej

    We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite case, the discrete spectrum is nonempty if the star arms are long enough. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maximized when the arms are arranged in one of the

    更新日期:2019-12-03
  • Discrete spectrum of Schrödinger operators with potentials concentrated near conical surfaces
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-12-02
    Sebastian Egger, Joachim Kerner, Konstantin Pankrashkin

    In this paper, we study spectral properties of a three-dimensional Schrödinger operator \(-\Delta +V\) with a potential V given, modulo rapidly decaying terms, by a function of the distance to an infinite conical surface with a smooth cross section. As a main result, we show that there are infinitely many discrete eigenvalues accumulating at the bottom of the essential spectrum which itself is identified

    更新日期:2019-12-02
  • Inequalities for the Schmidt number of bipartite states
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-25
    Daniel Cariello

    In this short note, we show two completely opposite methods of constructing bipartite entangled states. Given a bipartite state \(\gamma \in M_k\otimes M_k\), define \(\gamma _S=(Id+F)\gamma (Id+F)\), \(\gamma _A=(Id-F)\gamma (Id-F)\), where \(F\in M_k\otimes M_k\) is the flip operator. In the first method, entanglement is a consequence of the inequality \( {\text {rank}}(\gamma _S)<\sqrt{{\text {rank}}(\gamma

    更新日期:2019-11-25
  • Kähler quantization of vortex moduli
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-25
    Dennis Eriksson, Nuno M. Romão

    We discuss the Kähler quantization of moduli spaces of vortices in line bundles over compact surfaces \(\Sigma \). This furnishes a semiclassical framework for the study of quantum vortex dynamics in the Schrödinger–Chern–Simons model. We employ Deligne’s approach to Quillen’s metric in determinants of cohomology to construct all the quantum Hilbert spaces in this context. An alternative description

    更新日期:2019-11-25
  • Rigidity of Kac–Schwarz operators
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-20
    Martin T. Luu

    In his work on the mathematical formulation of 2d quantum gravity Schwarz established a rigidity result for Kac–Schwarz operators for the n-KdV hierarchies. Later on, Adler and van Moerbeke as well as Fastré obtained different proofs of this result. We give yet another proof of the rigidity, one that in fact holds for all Drinfeld–Sokolov hierarchies.

    更新日期:2019-11-20
  • Conformal classical Yang–Baxter equation, S -equation and $${\mathcal {O}}$$O -operators
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-18
    Yanyong Hong, Chengming Bai

    Conformal classical Yang–Baxter equation and S-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In this paper, they are interpreted in terms of a kind of operators, namely \(\mathcal O\)-operators in the conformal sense. Explicitly, the skew-symmetric part of a conformal linear map T where \(T_0=T_\lambda \mid _{\lambda =0}\) is an \({\mathcal

    更新日期:2019-11-18
  • Born’s rule for arbitrary Cauchy surfaces
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-15
    Matthias Lienert, Roderich Tumulka

    Suppose that particle detectors are placed along a Cauchy surface \(\Sigma \) in Minkowski space-time, and consider a quantum theory with fixed or variable number of particles (i.e., using Fock space or a subspace thereof). It is straightforward to guess what Born’s rule should look like for this setting: The probability distribution of the detected configuration on \(\Sigma \) has density \(|\psi

    更新日期:2019-11-15
  • Levi-Civita connections for a class of spectral triples
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-15
    Jyotishman Bhowmick, Debashish Goswami, Sugato Mukhopadhyay

    We give a new definition of Levi-Civita connection for a noncommutative pseudo-Riemannian metric on a noncommutative manifold given by a spectral triple. We prove the existence–uniqueness result for a class of modules of one-forms over a large class of noncommutative manifolds, including the matrix geometry of the fuzzy 3-sphere, the quantum Heisenberg manifolds and Connes–Landi deformations of spectral

    更新日期:2019-11-15
  • Variational symmetries and Lagrangian multiforms
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-14
    Duncan Sleigh, Frank Nijhoff, Vincent Caudrelier

    By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether’s theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic method for constructing Lagrangian multiforms for which the closure property and the multiform Euler–Lagrange (EL) both hold. We present three examples, including the

    更新日期:2019-11-14
  • Observables in the equivariant A -model
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-11-13
    F. Bonechi, A. S. Cattaneo, R. Iraso, M. Zabzine

    We discuss observables of an equivariant extension of the A-model in the framework of the AKSZ construction. We introduce the A-model observables, a class of observables that are homotopically equivalent to the canonical AKSZ observables but are better behaved in the gauge fixing. We discuss them for two different choices of gauge fixing: The first one is conjectured to compute the correlators of the

    更新日期:2019-11-13
  • Fermionic behavior of ideal anyons.
    Lett. Math. Phys. Pub Date : 2018-10-30
    Douglas Lundholm,Robert Seiringer

    We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter α . The lower bounds extend to Lieb-Thirring inequalities for all anyons except bosons.

    更新日期:2019-11-01
  • Reduction of quantum systems and the local Gauss law.
    Lett. Math. Phys. Pub Date : 2018-10-30
    Ruben Stienstra,Walter D van Suijlekom

    We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by

    更新日期:2019-11-01
  • Normal forms of dispersive scalar Poisson brackets with two independent variables.
    Lett. Math. Phys. Pub Date : 2018-09-18
    Guido Carlet,Matteo Casati,Sergey Shadrin

    We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants

    更新日期:2019-11-01
  • Aharonov and Bohm versus Welsh eigenvalues.
    Lett. Math. Phys. Pub Date : 2018-08-14
    P Exner,S Kondej

    We consider a class of two-dimensional Schrödinger operator with a singular interaction of the δ type and a fixed strength β supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an Aharonov-Bohm flux α∈[0,12] in the center. It is shown that if β≠0 , there is a critical value αcrit∈(0,12) such

    更新日期:2019-11-01
  • A noncommutative catenoid.
    Lett. Math. Phys. Pub Date : 2018-05-22
    Joakim Arnlind,Christoffer Holm

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a

    更新日期:2019-11-01
  • Regularized Laplacian determinants of self-similar fractals.
    Lett. Math. Phys. Pub Date : 2018-05-15
    Joe P Chen,Alexander Teplyaev,Konstantinos Tsougkas

    We study the spectral zeta functions of the Laplacian on fractal sets which are locally self-similar fractafolds, in the sense of Strichartz. These functions are known to meromorphically extend to the entire complex plane, and the locations of their poles, sometimes referred to as complex dimensions, are of special interest. We give examples of locally self-similar sets such that their complex dimensions

    更新日期:2019-11-01
  • Star product on complex sphere [Formula: see text].
    Lett. Math. Phys. Pub Date : 2018-05-15
    A Mudrov

    We construct a [Formula: see text]-equivariant local star product on the complex sphere [Formula: see text] as a non-Levi conjugacy class [Formula: see text].

    更新日期:2019-11-01
  • On the effective field theory of heterotic vacua.
    Lett. Math. Phys. Pub Date : 2018-04-03
    Jock McOrist

    The effective field theory of heterotic vacua that realise [Formula: see text] preserving [Formula: see text] supersymmetry is studied. The vacua in question admit large radius limits taking the form [Formula: see text], with [Formula: see text] a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle [Formula: see text]. In a previous paper we calculated the kinetic

    更新日期:2019-11-01
  • Magnetic zero-modes, vortices and Cartan geometry.
    Lett. Math. Phys. Pub Date : 2018-04-03
    Calum Ross,Bernd J Schroers

    We exhibit a close relation between vortex configurations on the 2-sphere and magnetic zero-modes of the Dirac operator on [Formula: see text] which obey an additional nonlinear equation. We show that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth

    更新日期:2019-11-01
  • Generalizations of the short pulse equation.
    Lett. Math. Phys. Pub Date : 2018-04-03
    Andrew N W Hone,Vladimir Novikov,Jing Ping Wang

    We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.

    更新日期:2019-11-01
  • Orbispaces as differentiable stratified spaces.
    Lett. Math. Phys. Pub Date : 2018-03-03
    Marius Crainic,João Nuno Mestre

    We present some features of the smooth structure and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures-it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object analogous to a separated stack in algebraic geometry) presented by the proper Lie groupoid

    更新日期:2019-11-01
  • Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.
    Lett. Math. Phys. Pub Date : 2018-03-03
    Pedro Frejlich,Ioan Mărcuț

    Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals,

    更新日期:2019-11-01
  • Filtrations on Springer fiber cohomology and Kostka polynomials.
    Lett. Math. Phys. Pub Date : 2018-03-03
    Gwyn Bellamy,Travis Schedler

    We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are

    更新日期:2019-11-01
  • Poisson traces, D-modules, and symplectic resolutions.
    Lett. Math. Phys. Pub Date : 2018-03-03
    Pavel Etingof,Travis Schedler

    We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical

    更新日期:2019-11-01
  • Constructions and classifications of projective Poisson varieties.
    Lett. Math. Phys. Pub Date : 2018-03-03
    Brent Pym

    This paper is intended both as an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past 20 years. It is based on the lecture series delivered by the author at the Poisson 2016 Summer School in Geneva. The paper begins with a detailed treatment of Poisson surfaces, including

    更新日期:2019-11-01
  • Un-reduction in field theory.
    Lett. Math. Phys. Pub Date : 2018-01-23
    Alexis Arnaudon,Marco Castrillón López,Darryl D Holm

    The un-reduction procedure introduced previously in the context of classical mechanics is extended to covariant field theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter). Other possibilities are also explored: nonlinear [Formula: see text]-models

    更新日期:2019-11-01
  • An elliptic Virasoro symmetry in 6d.
    Lett. Math. Phys. Pub Date : 2017-11-07
    Fabrizio Nieri

    We define an elliptic deformation of the Virasoro algebra. We conjecture that the [Formula: see text] Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special points in the moduli space the 6d Nekrasov partition function reduces to the partition function of a 4d vortex theory supported on [Formula: see text], which is in turn captured

    更新日期:2019-11-01
  • Spectral stability of periodic waves in the generalized reduced Ostrovsky equation.
    Lett. Math. Phys. Pub Date : 2017-10-27
    Anna Geyer,Dmitry E Pelinovsky

    We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations

    更新日期:2019-11-01
  • Invariants of families of flat connections using fiber integration of differential characters
    Lett. Math. Phys. (IF 1.203) Pub Date : 2019-10-29
    Ishan Mata

    Let \(E\rightarrow B\) be a smooth vector bundle of rank n, and let \(P \in I^p(GL(n,{\mathbb {R}}))\) be a \(GL(n,{\mathbb {R}})\)-invariant polynomial of degree p compatible with a universal integral characteristic class \( u \in H^{2p}(BGL(n,{\mathbb {R}}),{\mathbb {Z}})\). Cheeger–Simons theory associates a rigid invariant in \(H^{2p-1}(B,{\mathbb {R}}/{\mathbb {Z}})\) to any flat connection on

    更新日期:2019-10-29
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