Oxidizing SuperYang-Mills from (N=4,d=4) to (N=1,d=10)

We introduce superspace generalizations of the transverse derivatives to rewrite the four-dimensional N=4 Yang-Mills theory into the fully ten-dimensional N=1 Yang-Mills in light-cone form. The explicit SuperPoincare algebra is constructed and invariance of the ten-dimensional action is proved.Comment: 15 page

Maximal supersymmetry and exceptional groups

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself where we describe the N = 8 Supergravity in the light-cone formalism. We show how the Cremmer-Julia E7(7) non-linear symmetry is implemented and how the full supermultiplet is a representation of the E7(7) symmetry. I also show how the E7(7) symmetry is a key to understand the higher order couplings in the theory and is very useful when we discuss possible counterterms for this theory.Comment: Proceedings of Conference in Honour of Murray Gell-Mann's 80th Birthda

Kernel solutions of the Kostant operator on eight-dimensional quotient spaces

After introducing the generators and irreducible representations of the ${\rm su}(5)$ and ${\rm so}(6)$ Lie algebras in terms of the Schwinger's scillators, the general kernel solutions of the Kostant operators on eight-dimensional quotient spaces ${\rm su}(5)/{\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(6)/{\rm so}(4)\times {\rm so}(2)$ are derived in terms of the diagonal subalgebras ${\rm su}(4)\times {\rm u}(1)$ and ${\rm so}(4)\times {\rm so}(2)$, respectively.Comment: 13 pages. Typos correcte

LC_2 formulation of supergravity

We formulate (N=1, d=11) supergravity in components in light-cone gauge (LC_2) to order $\kappa$. In this formulation, we use judicious gauge choices and the associated constraint relations to express the metric, three-form and gravitino entirely in terms of the physical degrees of freedom in the theory.Comment: 11 page

Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.Comment: 25 pages, typos corrected, references adde

Gauge-invariant correlation functions in light-cone superspace

We initiate a study of correlation functions of gauge-invariant operators in N=4 super Yang-Mills theory using the light-cone superspace formalism. Our primary aim is to develop efficient methods to compute perturbative corrections to correlation functions. This analysis also allows us to examine potential subtleties which may arise when calculating off-shell quantities in light-cone gauge. We comment on the intriguing possibility that the manifest N=4 supersymmetry in this approach may allow for a compact description of entire multiplets and their correlation functions.Comment: 35 pages, several figure

The N=8 Supergravity Hamiltonian as a Quadratic Form

We conjecture that the light-cone Hamiltonian of N=8 Supergravity can be expressed as a quadratic form. We explain why this rewriting is unique to maximally supersymmetric theories. The N=8 quartic interaction vertex is constructed and used to verify that this conjecture holds to second order in the coupling constant

Estimating Demand Uncertainty Using Judgmental Forecasts

Measuring demand uncertainty is a key activity in supply chain planning. Of various methods of estimating the standard deviation of demand, one that has been employed successfully in the recent literature uses dispersion among expertsâ forecasts. However, there has been limited empirical validation of this methodology. In this paper we provide a general methodology for estimating the standard deviation of a random variable using dispersion among expertsâ forecasts. We test this methodology using three datasets, demand data at item level, sales data at firm level for retailers, and sales data at firm level for manufacturers. We show that the standard deviation of a random variable (demand and sales for our datasets) is positively correlated with dispersion among expertsâ forecasts. Further we use longitudinal datasets with sales forecasts made 3-9 months before earnings report date for retailers and manufacturers to show that the effects of dispersion and scale on standard deviation of forecast error are consistent over time.Operations Management Working Papers Serie

On the Concurrent Composition of Quantum Zero-Knowledge

We study the notion of zero-knowledge secure against quantum polynomial-time verifiers (referred to as quantum zero-knowledge) in the concurrent composition setting. Despite being extensively studied in the classical setting, concurrent composition in the quantum setting has hardly been studied. We initiate a formal study of concurrent quantum zero-knowledge. Our results are as follows: -Bounded Concurrent QZK for NP and QMA: Assuming post-quantum one-way functions, there exists a quantum zero-knowledge proof system for NP in the bounded concurrent setting. In this setting, we fix a priori the number of verifiers that can simultaneously interact with the prover. Under the same assumption, we also show that there exists a quantum zero-knowledge proof system for QMA in the bounded concurrency setting. -Quantum Proofs of Knowledge: Assuming quantum hardness of learning with errors (QLWE), there exists a bounded concurrent zero-knowledge proof system for NP satisfying quantum proof of knowledge property. Our extraction mechanism simultaneously allows for extraction probability to be negligibly close to acceptance probability (extractability) and also ensures that the prover's state after extraction is statistically close to the prover's state after interacting with the verifier (simulatability). The seminal work of [Unruh EUROCRYPT'12], and all its followups, satisfied a weaker version of extractability property and moreover, did not achieve simulatability. Our result yields a proof of quantum knowledge system for QMA with better parameters than prior works

Electron transport properties of sub-3-nm diameter copper nanowires

Density functional theory and density functional tight-binding are applied to model electron transport in copper nanowires of approximately 1 nm and 3 nm diameters with varying crystal orientation and surface termination. The copper nanowires studied are found to be metallic irrespective of diameter, crystal orientation and/or surface termination. Electron transmission is highly dependent on crystal orientation and surface termination. Nanowires oriented along the [110] crystallographic axis consistently exhibit the highest electron transmission while surface oxidized nanowires show significantly reduced electron transmission compared to unterminated nanowires. Transmission per unit area is calculated in each case, for a given crystal orientation we find that this value decreases with diameter for unterminated nanowires but is largely unaffected by diameter in surface oxidized nanowires for the size regime considered. Transmission pathway plots show that transmission is larger at the surface of unterminated nanowires than inside the nanowire and that transmission at the nanowire surface is significantly reduced by surface oxidation. Finally, we present a simple model which explains the transport per unit area dependence on diameter based on transmission pathways results