BV Quantization of Topological Open Membranes

We study bulk-boundary correlators in topological open membranes. The basic example is the open membrane with a WZ coupling to a 3-form. We view the bulk interaction as a deformation of the boundary string theory. This boundary string has the structure of a homotopy Lie algebra, which can be viewed as a closed string field theory. We calculate the leading order perturbative expansion of this structure. For the 3-form field we find that the C-field induces a trilinear bracket, deforming the Lie algebra structure. This paper is the first step towards a formal universal quantization of general quasi-Lie bialgebroids.Dept. of Particle Physics, Weizmann Institute, Rehovot, IsraelMathematics Graduate Center, CUNY, New York, USA     

String representation of field correlators in the Dual Abelian Higgs Model

By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and the Stochastic Model of the QCD vacuum. Received: 28 September 1998 / Revised version: 18 November 1998 / Published online: 11 March 1999     

Topological boundary conditions in abelian Chern–Simons theory

We study topological boundary conditions in abelian Chern–Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern–Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern–Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.     

TFT construction of RCFT correlators IV:: Structure constants and correlation functions

We compute the fundamental correlation functions in two-dimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary field on the disk, three boundary fields on the disk, and one bulk field on the cross cap. We also consider conformal defects and calculate the correlators of three defect fields on the sphere and of one defect field on the cross cap.Each of these correlators is presented as the product of a structure constant and the appropriate conformal two- or three-point block. The structure constants are expressed as invariants of ribbon graphs in three-manifolds.     

Orbifolds and Topological Defects

We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu–Schwarz and Ramond sectors of the orbifold theory, as well as bulk-boundary correlators from a novel, universal perspective. This entails a structure somewhat weaker than ordinary TFT, which however still describes a sector of the underlying conformal theory. The case of B-twisted Landau–Ginzburg models is discussed in detail, where we compute charge vectors and superpotential terms for B-type branes. Our construction also works in the absence of supersymmetry and for generalised “orbifolds” that need not arise from symmetry groups. In general, this involves a natural appearance of Hochschild (co)homology in a 2-categorical setting, in which among other things we provide simple presentations of Serre functors and a further generalisation of the Cardy condition.     

Boundary correlators in supergroup WZNW models

We investigate correlation functions for maximally symmetric boundary conditions in the WZNW model on GL(1|1)$\mathrm{GL}(1|1)$. Special attention is payed to volume filling branes. Generalizing earlier ideas for the bulk sector, we set up a Kac–Wakimoto-like formalism for the boundary model. This first order formalism is then used to calculate bulk-boundary 2-point functions and the boundary 3-point functions of the model. The note ends with a few comments on correlation functions of atypical fields, point-like branes and generalizations to other supergroups.     

Elastic Ising-like model for the nucleation and domain formation in spin crossover molecular solids

We investigate the nucleation, domain formation and propagation mechanisms observed in Spin Crossover materials, in the framework of an Ising-like model taking into account the elastic nature of the interactions. In Spin Crossover materials, the intermolecular coupling originates from a volume difference between the High Spin and the Low Spin molecular states and is simulated by anharmonic interaction potentials whose strengths are molecular-state-dependent. Using Monte Carlo methods, the phase diagram has been established. We show that the model contains both Ising short-range couplings and long-range elastic interactions. In particular, the results of long-range elastic models are reproduced. The introduction of lattice dynamics leads to the existence of spatial distributions of interaction energy and crystal field, corresponding to a local definition of physical properties. The nucleation process becomes highly dependent on the structural inhomogeneities induced by the spin transition. In this approach, connections strength between neighboring molecules are no more equivalent and have different ability to propagate domains. The presence of short-range Ising couplings gives rise to the occurrence of strong bonds forming a volume in which domains of the daughter phase can grow; in this case a macroscopic phase separation appears during the first order transition, even in a system with periodic boundary conditions. By contrast, in the case of a model with only long-range elastic interactions; strong bonds are uniformly spread in the lattice and a homogeneous phase transformation is observed, in good agreement with previous theoretical investigations.     

Potts q-color field theory and scaling random cluster model

We study structural properties of the q-color Potts field theory which, for real values of q, describes the scaling limit of the random cluster model. We show that the number of independent n-point Potts spin correlators coincides with that of independent n-point cluster connectivities and is given by generalized Bell numbers. Only a subset of these spin correlators enters the determination of the Potts magnetic properties for q integer. The structure of the operator product expansion of the spin fields for generic q is also identified. For the two-dimensional case, we analyze the duality relation between spin and kink field correlators, both for the bulk and boundary cases, obtaining in particular a sum rule for the kink-kink elastic scattering amplitudes.     

Form factors of boundary exponential operators in the sinh-Gordon model

Using the recently introduced boundary form factor bootstrap equations, the form factors of boundary exponential operators in the sinh-Gordon model are constructed. We also give a general method to evaluate the ultraviolet properties of boundary correlators by extending the bulk cumulant expansion to the boundary case. As an application, the ultraviolet scaling dimension and the normalization of the operators corresponding to the form factor solutions are checked against previously known results for boundary exponential operators. The construction presented in this paper can be applied to determine form factors of relevant primary boundary operators in general integrable boundary quantum field theories.     

GIMPs from extra dimensions

We study a scalar field theory in a flat five-dimensional setup, where a scalar field lives in a bulk with a Dirichlet boundary condition, and give an implementation of this setup to the Froggatt–Nielsen (FN) mechanism. It is shown that all couplings of physical field of the scalar with the all brane localized standard model particles are vanishing while realizing the usual FN mechanism. This setup gives the scalar a role as an only Gravitationally Interacting Massive Particle (GIMP), which is a candidate for dark matter.     

Activation energies for quantum diffusion of hydrogen in metals and on metal surfaces using delocalized nuclei within the density-functional theory

Hydrogen diffusion on the Cu(001) surface and in bulk Nb and Ta is studied in the quantum regime using first-principles electronic-structure calculations. We present, for the first time, a direct density-functional calculation of the activation energy required to establish the quantum-mechanically delocalized hydrogen coincidence configuration and of the corresponding tunneling matrix element. For the two bulk systems a direct comparison can be made with nuclear magnetic resonance data, and we find excellent agreement for both the coincidence energy and the tunneling matrix element.     

Notes on integrable boundary interactions of open SU(4) alternating spin chains

Ref. [J. High Energy Phys. 1708, 001(2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena(ABJM)theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001(2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.     

BRS symmetry for Yang-Mills theory with exact renormalization group

In the exact renormalization-group (RG) flow in the infrared cutoff Λ one needs boundary conditions. In a previous paper on SU(2) Yang-Mills theory we proposed to use the nine physical relevant couplings of the effective action as boundary conditions at the physical point Λ= 0 (these couplings are defined at some non-vanishing subtraction point μ≠ 0). In this paper we show perturbatively that it is possible to appropriately fix these couplings in such a way that the full set of Slavnov-Taylor (ST) identities are satisfied. Three couplings are given by the vector and ghost wave-function normalization and the three-vector coupling at the subtraction point; three of the remaining six are vanishing (e.g. the vector mass) and the others are expressed by irrelevant vertices evaluated at the subtraction point. We follow the method used by Becchi to prove ST identities in the RG framework. There the boundary conditions are given at a non-physical point Λ = Λ′ ≠ 0, so that one avoids the need of a non-vanishing subtraction point.     

Subtracted dispersion relations for in-medium meson correlators in QCD sum rules

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out the importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels for the case of the Fermi gas of nucleons.     

Theory for the first-order spin-wave instability threshold in ferromagnetic insulating thin films

A theory for the first-order Suhl and the parallel pumping instability in thin films is presented. Significant differences for the critical microwave field and wave vector to former calculations occur, which discuss the problem in terms of bulk spin-waves neglecting boundary conditions. A coupling matrixC _kk′ is introduced, which describes the couplings between the modes and the driving microwave field. For bulk standing spin-wavesC _kk′ is always diagonal. For the true discrete standing modes of a thin filmC _kk′ changes only in case of 1. Suhl instability and if the wavevector has a non vanishing component perpendicular to the film plane. Here the diagonal bulk couplings have to be replaced in part by off diagonal terms, describing couplings between modes, which perpendicular wave vector componentk _⊥ differs byπ/d (d=film thickness). The decisive quantity, which decides if the finite thickness of the film is of importance or if the film can be treated as a bulk system, is the frequency difference δω _k of the coupled modes. For δω _k much smaller than the spin-wave damping η _k the bulk approximation is correct. For \(\delta \omega _k > > \eta _k \) two experimental situations for 1. Suhl instability are discussed: For a perpendicular to the film plane magnetized film the critical microwave field is by π/2 bigger than in the bulk case. In an in-plane magnetized film the critical spin-waves propagate always in the film plane, as only hereC _kk′ remains identical to the bulk case.     

Homology in Abelian Lattice Models

We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes which are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. Irregularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a general vanishing theorem for Wilson line correlators.     

Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram,which is also confirmed by the energy spectra from our numerical results.It is shown that,in sharp contrast to Hermitian systems,the conventional(Bloch)bulk-boundary correspondence breaks down in non-Hermitian topological semimetals,which is caused by the non-Hermitian skin effect.We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals:the topological edge modes are determined by the non-Bloch Chern number of the bulk bands.Moreover,these topological edge modes can manifest as the unidirectional edge motion,and their signatures are consistent with the non-Bloch bulk-boundary correspondence.Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.     

Note on the stability in affine Toda field theories

We show that certain vanishing couplings in the Â Ê affine Toda field theories remain vanishing even after higher order corrections are included. This is a requisite property for the lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the Dynkin automorphism of the Lie algebra leads to the non-renormalization of the vanishing couplings.