Two-Dimensional String Theory, Topological Field Theories and the Deformed Matrix Model

In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed matrix model. It is proposed that the deformed matrix model is related to a D-series Landau-Ginzburg superpotential.Comment: 20 pages, Latex CERN-TH.7155. Minor typos correcte

Binding between endohedral Na atoms in Si clathrate I; a first principles study

We investigate the binding nature of the endohedral sodium atoms with the ensity functional theory methods, presuming that the clathrate I consists of a sheaf of one-dimensional connections of Na@Si$_{24}$ cages interleaved in three perpendicular directions. Each sodium atom loses 30% of the 3s$^1$ charge to the frame, forming an ionic bond with the cage atoms; the rest of the electron contributes to the covalent bond between the nearest Na atoms. The presumption is proved to be valid; the configuration of the two Na atoms in the nearest Si$_{24}$ cages is more stable by 0.189 eV than that in the Si$_{20}$ and Si$_{24}$ cages. The energy of the beads of the two distorted Na atoms is more stable by 0.104 eV than that of the two infinitely separated Na atoms. The covalent bond explains both the preferential occupancies in the Si$_{24}$ cages and the low anisotropic displacement parameters of the endohedral atoms in the Si$_{24}$ cages in the [100] directions of the clathrate I.Comment: First page: Affiliation added to PDF and PS versio

N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

We study the elliptic genera of hyperKahler manifolds using the representation theory of N=4 superconformal algebra. We consider the decomposition of the elliptic genera in terms of N=4 irreducible characters, and derive the rate of increase of the multiplicities of half-BPS representations making use of Rademacher expansion. Exponential increase of the multiplicity suggests that we can associate the notion of an entropy to the geometry of hyperKahler manifolds. In the case of symmetric products of K3 surfaces our entropy agrees with the black hole entropy of D5-D1 system.Comment: 25 pages, 1 figur

Numerical results from large N reduced QCD_2

Some results in QCD_2 at large N are presented using the reduced model on the lattice. Overlap fermions are used to compute meson propagators.Comment: 3 pages, contribution to Lattice 2002, Bosto

Issues in M(atrix) Theory Compactification

We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane $v^4$ amplitude, unlike the flat space case. This argument shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.Comment: title modified, references corrected, 11 pages, harvma

Lorentz Invariance and Origin of Symmetries

In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are only generated as accidental consequences of the gauge symmetry.Comment: 10 page LaTeX fil

On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket

In our recent paper we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of PDE's associated to semi-simple Frobenius structures. In the conformal (homogeneous) case, these systems are exactly the hierarchies of Dubrovin-Zhang, and the bracket is the first Poisson structure of their hierarchy. Our approach was based on a very involved computation of a deformation formula for the bracket with respect to the Givental-Y.-P. Lee Lie algebra action. In this paper, we discuss the structure of that deformation formula. In particular, we reprove it using a deformation formula for weak quasi-Miura transformation that relates our hierarchy of PDE's with its dispersionless limit.Comment: 21 page

Givental formula in terms of Virasoro operators

We present a conjecture that the universal enveloping algebra of differential operators \frac{\p}{\p t_k} over $\mathbb{C}$ coincides in the origin with the universal enveloping algebra of the (Borel subalgebra of) Virasoro generators from the Kontsevich model. Thus, we can decompose any (pseudo)differential operator to a combination of the Virasoro operators. Using this decomposition we present the r.h.s. of the Givental formula math.AG/0008067 as a constant part of the differential operator we introduce. In the case of $\mathbb{CP}^1$ studied in hep-th/0103254, the l.h.s. of the Givental formula is a unit, which imposes certain constraints on this differential operator. We explicitly check that these constraints are correct up to $O(q^4)$. We also propose a conjecture of factorization modulo Hirota equation of the differential operator introduced and check this conjecture with the same accuracy.Comment: LaTeX, 11 pages, Some typos correcte

Large spin-orbit splitting and weakly-anisotropic superconductivity revealed with single-crystalline noncentrosymmetric CaIrSi3

We report normal and superconducting properties of the Rashba-type noncentrosymmetric com- pound CaIrSi3, using single crystalline samples with nearly 100% superconducting volume fraction. The electronic density of states revealed by the hard x-ray photoemission spectroscopy can be well explained by the relativistic first-principle band calculation. This indicates that strong spin-orbit interaction indeed affects the electronic states of this compound. The obtained H - T phase diagram exhibits only approximately 10% anisotropy, indicating that the superconducting properties are almost three dimensional. Nevertheless, strongly anisotropic vortex pinning is observed.Comment: 8 pages, 6 figures, 1 table, accepted for publication in Phys. Rev.