Recent zbMATH articles in MSC 81Thttps://www.zbmath.org/atom/cc/81T2021-02-27T13:50:00+00:00WerkzeugEquivariant higher Hochschild homology and topological field theories.https://www.zbmath.org/1453.570252021-02-27T13:50:00+00:00"Müller, Lukas"https://www.zbmath.org/authors/?q=ai:muller.lukas"Woike, Lukas"https://www.zbmath.org/authors/?q=ai:woike.lukasSummary: We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group \(G\). As coefficients, we allow \(E_{\infty}\)-algebras with \(G\)-action. For this homology theory, we establish an equivariant version of excision and prove that it extends to an equivariant topological field theory with values in the \((\infty , 1)\)-category of cospans of \(E_{\infty}\)-algebras.Correction to: The standard model in noncommutative geometry: fundamental fermions as internal forms.https://www.zbmath.org/1453.580032021-02-27T13:50:00+00:00"Dąbrowski, Ludwik"https://www.zbmath.org/authors/?q=ai:dabrowski.ludwik"D'Andrea, Francesco"https://www.zbmath.org/authors/?q=ai:dandrea.francesco"Sitarz, Andrzej"https://www.zbmath.org/authors/?q=ai:sitarz.andrzejSummary: Corrects a grant number in the authors's paper [ibid. 108, No. 5, 1323--1340 (2018; Zbl 1395.58007)].The algebra of Wick polynomials of a scalar field on a Riemannian manifold.https://www.zbmath.org/1453.810502021-02-27T13:50:00+00:00"Dappiaggi, Claudio"https://www.zbmath.org/authors/?q=ai:dappiaggi.claudio"Drago, Nicolò"https://www.zbmath.org/authors/?q=ai:drago.nicolo"Rinaldi, Paolo"https://www.zbmath.org/authors/?q=ai:rinaldi.paoloHeat kernel: proper-time method, Fock-Schwinger gauge, path integral, and Wilson line.https://www.zbmath.org/1453.810482021-02-27T13:50:00+00:00"Ivanov, A. V."https://www.zbmath.org/authors/?q=ai:ivanov.aleksandr-valentinovich"Kharuk, N. V."https://www.zbmath.org/authors/?q=ai:kharuk.n-vSummary: This paper is devoted to the proper-time method and describes a model case that reflects the subtleties of constructing the heat kernel, is easily extended to more general cases (curved space, manifold with a boundary), and contains two interrelated parts: an asymptotic expansion and a path integral representation. We discuss the significance of gauge conditions and the role of ordered exponentials in detail, derive a new nonrecursive formula for the Seeley-DeWitt coefficients on the diagonal, and show the equivalence of two main approaches using the exponential formula.Coincidences between Calabi-Yau manifolds of Berglund-Hübsch type and Batyrev polytopes.https://www.zbmath.org/1453.810512021-02-27T13:50:00+00:00"Belavin, A. A."https://www.zbmath.org/authors/?q=ai:belavin.aleksandr-abramovich"Belakovskiy, M. Yu."https://www.zbmath.org/authors/?q=ai:belakovskiy.m-yuSummary: We consider the phenomenon of the complete coincidence of key properties of Calabi-Yau manifolds realized as hypersurfaces in two different weighted projective spaces. More precisely, the first manifold in such a pair is realized as a hypersurface in a weighted projective space, and the second is realized as a hypersurface in an orbifold of another weighted projective space. The two manifolds in each pair have the same Hodge numbers and the same geometry on the complex structure moduli space and are also associated with the same \(N=2\) gauged linear sigma model. We explain these coincidences using the correspondence between Calabi-Yau manifolds and the Batyrev reflexive polyhedra.Strange duality revisited.https://www.zbmath.org/1453.810552021-02-27T13:50:00+00:00"Pauly, Christian"https://www.zbmath.org/authors/?q=ai:pauly.christianSummary: We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-\(0\) result, obtained by \textit{T. Nakanishi} and \textit{A. Tsuchiya} [Commun. Math. Phys. 144, No. 2, 351--372 (1992; Zbl 0751.17024)], to higher genus curves via the sewing procedure. The new ingredient of the proof is an explicit use of the branching rules of the conformal embedding of affine Lie algebras \(\widehat{\mathfrak{sl}(r)} \times \widehat{\mathfrak{sl}(l)} \subset \widehat{\mathfrak{sl}(rl)}\). We recover the strange duality of spaces of generalized theta functions obtained by Belkale, Marian-Oprea, as well as by Oudompheng in the parabolic case.Nonlinear radion interactions.https://www.zbmath.org/1453.810612021-02-27T13:50:00+00:00"Volobuev, I. P."https://www.zbmath.org/authors/?q=ai:volobuev.igor-p"Keizerov, S. I."https://www.zbmath.org/authors/?q=ai:keizerov.s-i"Rakhmetov, E. R."https://www.zbmath.org/authors/?q=ai:rakhmetov.e-rSummary: We consider the Randall-Sundrum model with two branes in which the fields of the Standard Model are localized on the brane with negative tension and the gravitational field and an additional stabilizing scalar Goldberg-Wise field propagate in the space between the branes. We construct a Lagrangian for scalar fluctuations of the gravitational and scalar fields against the background solution. We obtain an effective four-dimensional Lagrangian describing nonlinear self-coupling terms of the scalar radion field in a polynomial approximation up to the fourth order and also nonlinear terms of the coupling of the radion and Standard Model fields. We estimate possible values of the self-coupling constant.Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background.https://www.zbmath.org/1453.810472021-02-27T13:50:00+00:00"Bogdanov, L. V."https://www.zbmath.org/authors/?q=ai:bogdanov.leonid-vitalevichSummary: We obtain a dispersionless integrable system describing a local form of a general three-dimensional Einstein-Weyl geometry with a Euclidean (positive) signature, construct its matrix extension, and show that it leads to the Bogomolny equations for a non-Abelian monopole on an Einstein-Weyl background. We also consider the corresponding dispersionless integrable hierarchy, its matrix extension, and the dressing scheme.Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra.https://www.zbmath.org/1453.810402021-02-27T13:50:00+00:00"Stukopin, V. A."https://www.zbmath.org/authors/?q=ai:stukopin.vladimir-alekseevichSummary: Using the approach developed by Gautam and Toledano Laredo, we introduce analogues of the category \(\mathfrak{O}\) for representations of the Yangian \(Y_{\hbar}(A(m,n))\) of a special linear Lie superalgebra and the quantum loop superalgebra \(U_q(LA(m,n))\). We investigate the relation between them and conjecture that these categories are equivalent.Quantum anomalies via differential properties of Lebesgue-Feynman generalized measures.https://www.zbmath.org/1453.810312021-02-27T13:50:00+00:00"Gough, John E."https://www.zbmath.org/authors/?q=ai:gough.john-e"Ratiu, Tudor S."https://www.zbmath.org/authors/?q=ai:ratiu.tudor-stefan"Smolyanov, Oleg G."https://www.zbmath.org/authors/?q=ai:smolyanov.oleg-georgievichSummary: We address the problem concerning the origin of quantum anomalies, which has been the source of disagreement in the literature. Our approach is novel as it is based on the differentiability properties of families of generalized measures. To this end, we introduce a space of test functions over a locally convex topological vector space, and define the concept of logarithmic derivatives of the corresponding generalized measures. In particular, we show that quantum anomalies are readily understood in terms of the differential properties of the Lebesgue-Feynman generalized measures (equivalently, of the Feynman path integrals). We formulate a precise definition for quantum anomalies in these terms.Hurwitz numbers from Feynman diagrams.https://www.zbmath.org/1453.810522021-02-27T13:50:00+00:00"Natanzon, S. M."https://www.zbmath.org/authors/?q=ai:natanzon.sergei-m"Orlov, A. Yu."https://www.zbmath.org/authors/?q=ai:orlov.aleksandr-yuSummary: To obtain a generating function of the most general form for Hurwitz numbers with an arbitrary base surface and arbitrary ramification profiles, we consider a matrix model constructed according to a graph on an oriented connected surface \(\Sigma\) with no boundary. The vertices of this graph, called stars, are small discs, and the graph itself is a clean dessin d'enfants. We insert source matrices in boundary segments of each disc. Their product determines the monodromy matrix for a given star, whose spectrum is called the star spectrum. The surface \(\Sigma\) consists of glued maps, and each map corresponds to the product of random matrices and source matrices. Wick pairing corresponds to gluing the set of maps into the surface, and an additional insertion of a special tau function in the integration measure corresponds to gluing in Möbius strips. We calculate the matrix integral as a Feynman power series in which the star spectral data play the role of coupling constants, and the coefficients of this power series are just Hurwitz numbers. They determine the number of coverings of \(\Sigma \) (or its extensions to a Klein surface obtained by inserting Möbius strips) for any given set of ramification profiles at the vertices of the graph. We focus on a combinatorial description of the matrix integral. The Hurwitz number is equal to the number of Feynman diagrams of a certain type divided by the order of the automorphism group of the graph.Discrete symmetries of complete intersection Calabi-Yau manifolds.https://www.zbmath.org/1453.141092021-02-27T13:50:00+00:00"Lukas, Andre"https://www.zbmath.org/authors/?q=ai:lukas.andre"Mishra, Challenger"https://www.zbmath.org/authors/?q=ai:mishra.challengerSummary: In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi-Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi-Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.Planar Ising model at criticality: state-of-the-art and perspectives.https://www.zbmath.org/1453.820062021-02-27T13:50:00+00:00"Chelkak, Dmitry"https://www.zbmath.org/authors/?q=ai:chelkak.dmitryEdge contraction on dual ribbon graphs and 2D TQFT.https://www.zbmath.org/1453.141342021-02-27T13:50:00+00:00"Dumitrescu, Olivia"https://www.zbmath.org/authors/?q=ai:dumitrescu.olivia"Mulase, Motohico"https://www.zbmath.org/authors/?q=ai:mulase.motohicoSummary: We present a new set of axioms for 2D TQFT formulated on the category of cell graphs with edge-contraction operations as morphisms. We construct a functor from this category to the endofunctor category consisting of Frobenius algebras. Edge-contraction operations correspond to natural transformations of endofunctors, which are compatible with the Frobenius algebra structure. Given a Frobenius algebra \(A\), every cell graph determines an element of the symmetric tensor algebra defined over the dual space \(A^\ast\). We show that the edge-contraction axioms make this assignment depending only on the topological type of the cell graph, but not on the graph itself. Thus the functor generates the TQFT corresponding to \(A\).Fracton phases via exotic higher-form symmetry-breaking.https://www.zbmath.org/1453.810462021-02-27T13:50:00+00:00"Qi, Marvin"https://www.zbmath.org/authors/?q=ai:qi.marvin"Radzihovsky, Leo"https://www.zbmath.org/authors/?q=ai:radzihovsky.leo"Hermele, Michael"https://www.zbmath.org/authors/?q=ai:hermele.michaelSummary: We study \(p\)-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor \(\operatorname{U}(1)\) scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe \(p\)-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. We also give a general discussion on interpreting \(p\)-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.Vertical D4-D2-D0 bound states on \(K3\) fibrations and modularity.https://www.zbmath.org/1453.141012021-02-27T13:50:00+00:00"Bouchard, Vincent"https://www.zbmath.org/authors/?q=ai:bouchard.vincent"Creutzig, Thomas"https://www.zbmath.org/authors/?q=ai:creutzig.thomas"Diaconescu, Duiliu-Emanuel"https://www.zbmath.org/authors/?q=ai:diaconescu.duiliu-emanuel"Doran, Charles"https://www.zbmath.org/authors/?q=ai:doran.charles-f"Quigley, Callum"https://www.zbmath.org/authors/?q=ai:quigley.callum"Sheshmani, Artan"https://www.zbmath.org/authors/?q=ai:sheshmani.artanSummary: An explicit formula is derived for the generating function of vertical D4-D2-D0 bound states on smooth \(K3\) fibered Calabi-Yau threefolds, generalizing previous results of \textit{A. Gholampour} and \textit{A. Sheshmani} [Adv. Math. 326, 79--107 (2018; Zbl 1386.14193); Adv. Theor. Math. Phys. 19, No. 3, 673--699 (2015; Zbl 1333.81242)]. It is also shown that this formula satisfies strong modularity properties, as predicted by string theory. This leads to a new construction of vector valued modular forms which exhibit some of the features of a generalized Hecke transform.Spinor-helicity formalism for massless fields in \(\mathrm{AdS}_4\). II: Potentials.https://www.zbmath.org/1453.810542021-02-27T13:50:00+00:00"Nagaraj, Balakrishnan"https://www.zbmath.org/authors/?q=ai:nagaraj.balakrishnan"Ponomarev, Dmitry"https://www.zbmath.org/authors/?q=ai:ponomarev.dmitry-m|ponomarev.dmitry-vSummary: In a recent letter we suggested a natural generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane-wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.Convergent perturbation theory for studying phase transitions.https://www.zbmath.org/1453.810492021-02-27T13:50:00+00:00"Nalimov, M. Yu."https://www.zbmath.org/authors/?q=ai:nalimov.m-yu"Ovsyannikov, A. V."https://www.zbmath.org/authors/?q=ai:ovsyannikov.a-vSummary: We propose a method for constructing a perturbation theory with a finite radius of convergence for a rather wide class of quantum field models traditionally used to describe critical and near-critical behavior in problems in statistical physics. For the proposed convergent series, we use an instanton analysis to find the radius of convergence and also indicate a strategy for calculating their coefficients based on the diagrams in the standard (divergent) perturbation theory. We test the approach in the example of the standard stochastic dynamics A-model and a matrix model of the phase transition in a system of nonrelativistic fermions, where its application allows explaining the previously observed quasiuniversal behavior of the trajectories of a first-order phase transition.On \(\mathbb{Z}_2\)-indices for ground states of fermionic chains.https://www.zbmath.org/1453.810572021-02-27T13:50:00+00:00"Bourne, Chris"https://www.zbmath.org/authors/?q=ai:bourne.chris"Schulz-Baldes, Hermann"https://www.zbmath.org/authors/?q=ai:schulz-baldes.hermannIntroduction to the BV-BFV formalism.https://www.zbmath.org/1453.810562021-02-27T13:50:00+00:00"Cattaneo, Alberto S."https://www.zbmath.org/authors/?q=ai:cattaneo.alberto-sergio"Moshayedi, Nima"https://www.zbmath.org/authors/?q=ai:moshayedi.nimaHigher-rank tensor field theory of non-abelian fracton and embeddon.https://www.zbmath.org/1453.810532021-02-27T13:50:00+00:00"Wang, Juven"https://www.zbmath.org/authors/?q=ai:wang.juven"Xu, Kai"https://www.zbmath.org/authors/?q=ai:xu.kaiSummary: We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The ``gauge structure'' can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang-Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle-hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.On the geometry of magnetic skyrmions on thin films.https://www.zbmath.org/1453.820922021-02-27T13:50:00+00:00"Walton, Edward"https://www.zbmath.org/authors/?q=ai:walton.edwardSummary: We study the recently introduced `critically coupled' model of magnetic Skyrmions, generalising it to thin films with curved geometry. The model feels keenly the extrinsic geometry of the film in three-dimensional space. We find exact Skyrmion solutions on spherical, conical and cylindrical thin films. Axially symmetric solutions on cylindrical films are described by kinks tunnelling between `vacua'. For the model defined on general compact thin films, we prove the existence of energy minimising multi-Skyrmion solutions and construct the (resolved) moduli space of these solutions.Quantum line defects and refined BPS spectra.https://www.zbmath.org/1453.141322021-02-27T13:50:00+00:00"Cirafici, Michele"https://www.zbmath.org/authors/?q=ai:cirafici.micheleSummary: In this note, we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class \(\mathcal{S}\). Such defects can be specified via geometric engineering in the UV by assigning a path on a certain curve. In the IR, they are described by framed BPS quivers. We study the associated BPS spectral problem, including the spin content. The relevant BPS invariants arise from the \(K\)-theoretic enumerative geometry of the moduli spaces of quiver representations, adapting a construction by Nekrasov and Okounkov. In particular, refined framed BPS states are described via Euler characteristics of certain complexes of sheaves.