Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice

We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In order to keep the manifest anti-hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau gauge fixed version of Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity even and odd parts with different coefficients.Comment: 22 pages, 5 figures; v2,v3 added references, v4 added two paragraphs and one figure in the summar

Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2

We propose a new lattice superfield formalism in momentum representation which accommodates species doublers of the lattice fermions and their bosonic counterparts as super multiplets. We explicitly show that one dimensional N=2 model with interactions has exact Lie algebraic supersymmetry on the lattice for all super charges. In coordinate representation the finite difference operator is made to satisfy Leibnitz rule by introducing a non local product, the ``star'' product, and the exact lattice supersymmetry is realized. The standard momentum conservation is replaced on the lattice by the conservation of the sine of the momentum, which plays a crucial role in the formulation. Half lattice spacing structure is essential for the one dimensional model and the lattice supersymmetry transformation can be identified as a half lattice spacing translation combined with alternating sign structure. Invariance under finite translations and locality in the continuum limit are explicitly investigated and shown to be recovered. Supersymmetric Ward identities are shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry algebra of this model suggests a close connection with Hopf algebraic exactness of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure

A suggestion for simplifying the theory of asset prices

Using an ordinal approach to utility, in the spirit of Hicks (1962, 1967a), it is possible to greatly simplify the theory of asset prices. The basic assumption is to summarize any probability distribution into its moments so that preferences over distributions can be mapped into preferences over vectors of moments. This implies that assets, like Lancaster’s (1966) consumption goods, are bundles of characteristics and can be directly priced, at the margin, in terms of the market portfolio. Expected utility is not required and both St.Petersburg and Allais paradoxes may be easily solved

Semiclassical Limits of Extended Racah Coefficients

We explore the geometry and asymptotics of extended Racah coeffecients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly defined. Moreover, it is found that this extension may be geometrically identified with two types of Lorentzian tetrahedra for which all the faces are timelike. The asymptotic formulae derived for the extension are found to have a similar form to the standard Ponzano-Regge asymptotic formulae for the SU(2) 6j symbol and so should be viable for use in a state sum for three dimensional Lorentzian quantum gravity.Comment: Latex2e - 26 pages, 6 figures. Uses AMS-fonts, AMS-LaTeX, epsf.tex and texdraw. Revised version with improved clarity and additional result

Real Intrest Rate and Growth: An Empirical Note

Are restrictive monetary policies harmful to growth? The note aims at providing some empirical evidence to answer the question. A significant negative correlation between growth and real interest emerges over the period 1960-94; in the eighties this relationship strengthens. This result is in agreement with the traditional view of a long run positive link between growth and capital accumulation and a negative long run link between accumulation and the cost of capital. Moreover the outcome is in line with the view that links the slowdown in economic growth of the industrial countries over the last decades appears to the implementation of restrictive monetary policie

Institutional quality, culture, and norms of cooperation: Evidence from behavioral field experiments

We examine the causal effect of legal institutional quality on informal norms of cooperation and study the interaction of institutions and culture in sustaining economic exchange. A total of 346 subjects in Italy and Kosovo played a market game under different and randomly allocated institutional treatments, which generated different incentives to behave honestly, preceded and followed by a noncontractible and nonenforceable trust game. Significant increases in individual trust and trustworthiness followed exposure to better institutions. A 1- percentage-point reduction in the probability of facing a dishonest partner in the market game, which is induced by the quality of legal institutions, increases trust by 7–11 percent and trustworthiness by 13–19 percent. This suggests that moral norms of cooperative behavior can follow improvements in formal institutional quality. Cultural origin, initial trust, and trustworthiness influence opportunistic behavior in markets, but only in the absence of strong formal institutions

Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required.Comment: 45 page

Gauge symmetry enhancement in Hamiltonian formalism

We study the Hamiltonian structure of the gauge symmetry enhancement in the enlarged CP(N) model coupled with U(2) Chern-Simons term, which contains a free parameter governing explicit symmetry breaking and symmetry enhancement. After giving a general discussion of the geometry of constrained phase space suitable for the symmetry enhancement, we explicitly perform the Dirac analysis of our model and compute the Dirac brackets for the symmetry enhanced and broken cases. We also discuss some related issues.Comment: 8 pages, typos correcte

Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group

We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills model. We start from the CKKU model for this system, which is valid only for U(N) gauge group. We give a reduction of U(1) part keeping a part of supersymmetry. In order to suppress artifact vacua, we use an admissibility condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to appear in JHE

Quantum Vortex Strings: A Review

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^{N-1} sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP^{N-1} sigma-model can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg's quantum deformed moduli space.Comment: Adams Prize Essay. 40 pages with 4 colourful picture