Topological String Partition Functions as Polynomials

We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus.Comment: 22 pages, 6 figures. v2:typos correcte

FeAs-based superconductivity: a case study of the effects of transition metal doping on BaFe2As2

The recently discovered FeAs-based superconductors are a new, promising set of materials for both technological as well as basic research. They offer transition temperatures as high as 55 K as well as essentially isotropic and extremely large upper, superconducting critical fields in excess of 40 T at 20 K. In addition they may well provide insight into exotic superconductivity that extends beyond just FeAs-based superconductivity, perhaps even shedding light on the still perplexing CuO-based high-Tc materials. Whereas superconductivity can be induced in the RFeAsO (R = rare earth) and AEFe2As2 (AE = Ba, Sr, Ca)) families by a number of means, transition metal doping of BaFe2As2, e.g. Ba(Fe1-xTMx)2As2, offers the easiest experimental access to a wide set of materials. In this review we present an overview and summary of the effect of TM doping (TM = Co, Ni, Cu, Pd, and Rh) on BaFe2As2. The resulting phase diagrams reveal the nature of the interaction between the structural, magnetic and superconducting phase transitions in these compounds and delineate a region of phase space that allows for the stabilization of superconductivity.Comment: edited and shortened version is accepted to AR:Condensed Matter Physic

A Simple Algebraic Derivation of the Covariant Anomaly and Schwinger Term

An expression for the curvature of the "covariant" determinant line bundle is given in even dimensional space-time. The usefulness is guaranteed by its prediction of the covariant anomaly and Schwinger term. It allows a parallel derivation of the consistent anomaly and Schwinger term, and their covariant counterparts, which clarifies the similarities and differences between them. In particular, it becomes clear that in contrary to the case for anomalies, the difference between the consistent and covariant Schwinger term can not be extended to a local form on the space of gauge potentials.Comment: 16 page

On the least redundancy problem of the queries of order two in combinatorial filing scheme

The paper concerns a least redundancy problem of queries of order two in a combinatorial file organization scheme. Every record will be assumed to have m attributes, each of them having n levels, and the queries of order two will be identified with edges of a complete m-partite graph Km(n,…, n). S. Yamamoto, S. Tazawa, K. Ushio, and H. Ikeda have proved that if c ⩽ (m − 1), then the graph, termed “claw with degree c,” has the least redundancy among all the graphs consisting of c edges over Km(n,…, n), and they presented a file organization scheme realizing the least redundancy. S. Tazawa and S. Yamamoto have proved that the claw with degree c has the least redundancy even in the case of c ⩽ n(m − 1). The purpose of this paper is to introduce some transformations of graphs over Km(n,…, n) and to prove that a graph termed “complete normal form” has the least redundancy in any case of c > 0. In mathematical language, the problem here is stated as follows: Let V be an n-dimensional lattice point space {1,…, m} × … × {1,…, m}. For fixed i, j (i ≠ j), p, p′, we define a subset V(i,j,p,p′) = {v} ∈ V; vi = p}, vj = p′} ⊂ V. For a given possible integer c, how should we select c mutually different V(i,j, p, p′) such that the number of lattice points contained in the union of them is minimum. The solution is Theorem 5, and Theorem 7 gives a formula for finding the minimum number

A Geometrical Description of the Consistent and Covariant Chiral Anomaly

A geometrical interpretation of the consistent and covariant chiral anomaly is done in the space-time respective Hamiltonian framework.Comment: 12 page

Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open string invariants in the spirit of Katz-Liu, defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of [C^3/Z_3], where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main object of our study is the richer case of [C^3/Z_4], where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected, version to appear on Selecta Mathematica; v3: last minute mistake found and fixed for the symmetric brane setup of [C^3/Z_4]; in pres

Magnetic order in CaFe1-xCoxAsF (x = 0, 0.06, 0.12) superconductor compounds

A Neutron Powder Diffraction (NPD) experiment has been performed to investigate the structural phase transition and magnetic order in CaFe1-xCoxAsF superconductor compounds (x = 0, 0.06, 0.12). The parent compound CaFeAsF undergoes a tetragonal to orthorhombic phase transition at 134(3) K, while the magnetic order in form of a spin-density wave (SDW) sets in at 114(3) K. The antiferromagnetic structure of the parent compound has been determined with a unique propagation vector k = (1,0,1) and the Fe saturation moment of 0.49(5)uB aligned along the long a-axis. With increasing Co doping, the long range antiferromagnetic order has been observed to coexist with superconductivity in the orthorhombic phase of the underdoped CaFe0.94Co0.06AsF with a reduced Fe moment (0.15(5)uB). Magnetic order is completely suppressed in optimally doped CaFe0.88Co0.12AsF. We argue that the coexistence of SDW and superconductivity might be related to mesoscopic phase separation.Comment: 4pages, 4figure

Epilogue: Superconducting Materials Past, Present and Future

Experimental contributors to the field of Superconducting Materials share their informal views on the subject.Comment: Epilogue to Physica C Special Issue on Superconducting Materials, Volume 514 (2015