The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

D-Instanton Corrections as (p,q)-String Effects and Non-Renormalization Theorems

We discuss higher derivative interactions in the type IIB superstring in ten dimensions. From the fundamental string point of view, the non-perturbative corrections are due to D-instantons. We argue that they can alternatively be understood as arising from $(p,q)$-strings. We derive a non-renormalization theorem for eight-derivative bosonic interactions, which states that terms involving either NS-NS or R-R fields occur at tree-level and one-loop only. By using the $SL(2, Z)$ symmetry of M-theory on $T^2$, we show that in order for the possible $R^{3m+1} (m=1,2,...)$ interactions in M-theory to have a consistent perturbative expansion in nine dimensions, $m$ must be odd. Thus, only $R^{6N+4} (N=0,1,...)$ terms can be present in M-theory and their string theory counterparts arise at $N$ and $2N+1$ loops. Finally, we treat an example of fermionic term.Comment: 24 pages, latex, additional arguments for the perturbative form of the eight-derivative interaction

Nondecoupling of Maximal Supergravity from the Superstring

We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10-d) torus. For dimensions d=2 and d=3, it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d>=4, there are infinite towers of additional massless and finite-mass states. These correspond to Kaluza-Klein charges, wound strings, Kaluza-Klein monopoles, or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions >=4. In particular, we conjecture that pure [script N]=8 supergravity in four dimensions is in the Swampland

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.Comment: 31 pages, harvmac (b); minor correction

Light-cone Quantum Mechanics of the Eleven-dimensional Superparticle

The linearized interactions of eleven-dimensional supergravity are obtained in a manifestly supersymmetric light-cone gauge formalism. These vertices are used to calculate certain one-loop processes involving external gravitini, antisymmetric three-form potentials and gravitons, thereby determining some protected terms in the effective action of M-theory compactified on a two-torus.Comment: 31 pages, harvmac (b); A minor TeX error correcte

D-instanton partition functions

Duality arguments are used to determine D-instanton contributions to certain effective interaction terms of type II supergravity theories in various dimensions. This leads to exact expressions for the partition functions of the finite N D-instanton matrix model in d=4 and 6 dimensions that generalize our previous expression for the case d=10. These results are consistent with the fact that the Witten index of the T-dual D-particle process should only be non-vanishing for d=10.Comment: 20 pages, harvmac, typos corrected, reference adde

Thermal DD-Brane Boundary States from Green-Schwarz Superstrings

In this paper we thermalize the type II superstrings in the GS formulation by applying the TFD formalism. The thermal boundary conditions on the thermal Hilbert space are obtained from the BPS $D$-brane boundary conditions at zero temperature. We show that thermal boundary states can be obtained by thermalization from the BPS $D$-branes at zero temperature. These new states can be interpreted as thermal $D$-branes. Next, we discuss the supersymmetry breaking of the thermal string in the TFD approach. We identify the broken supersymmetry with the $\epsilon$-transformation while the $\eta$-transformation is preserved. Also, we compute the thermal partition function and the entropy of the thermal string.Comment: 23 pages, LATeX fil

Relativistic Harmonic Oscillator Revisited

The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory) while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approach that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.Comment: 41 pages, 2 figures, LaTe

The Food Retailing Structure of the Northwest Territories

Food retailers in the Northwest Territories face dramatically different conditions from those of southern food retailers. There are three main differences: (1) small market size, (2) limited geographical access to suppliers and (3) different types of competitors. These differences have resulted in higher food prices and smaller, more general, stores with a wider variety of merchandise than southern supermarkets. Resupply is much less frequent than in southern supermarkets because resupply must be made via either air or barge shipment rather than truck delivery. The N.W.T. food retailing structure comprises three types of food retailers: the independently operated stores, the cooperatives and chain stores. This first examination of the similarities and differences between the store types is drawn from a mail survey of all the food retailers in the N.W.T. The food retailers have adapted to the small, isolated northern markets by expanding their merchandise line well beyond food products. The Hudson's Bay Company stores carry the widest variety of merchandise, while the others carry a more limited product line. Inventory management varies among the store types. The cooperatives generally fail to use the cheaper alternative transportation modes (road or water) where possible. This is not due to location but may reflect poor managerial skills or simply a lack of profit motivation.Key words: food retailing, Northwest Temtories, mode, retail structure, management, Hudson’s Bay Company, cooperatives, independentsLes détaillants en alimentation des Territoires du Nord-Ouest font face à des conditions radicalement différentes de celles des détaillants en alimentation du Sud. Il y a trois différences principales: (1) le marché est plus petit, (2) l’accès géographique aux fournisseurs est limité et (3) les concurrents sont d’un genre différent. Ces différences font que le prix de la nourriture est plus élevé, que les magasins sont plus petits et qu’ils ressemblent plus à un magasin général, offrant une plus grande variété de marchandises que les supermarchés du Sud. La fréquence du réapprovisionnement est moindre que pour ces derniers, car l’approvisionnement doit se faire par avion ou par péniche plutôt que par camion. La structure de l’alimentation de détail dans les T.N.-O. comprend trois types de détaillants les magasins indépendants, les coopératives et les magasins appartenant à des chaînes. Ce premier examen des ressemblances et des différences entre les types de magasins a été obtenu à partir d’une enquête postée à tous les détaillants en alimentation des T. N.-O. Les détaillants en alimentation se sont adaptés aux petits marchés isolés du Nord en élargissant la gamme de leurs produits bien au-delà des produits alimentaires. Les magasins de la Compagnie de la Baie d’Hudson ont la plus grande variété de marchandises, tandis que les autres ont une gamme de produits plus limitée. La gestion des inventaires varie entre les différents types de magasins. En général, les coopératives ne profitent pas des autres moyens de transport (routiers et par voie d’eau) là où elles le pourraient. Cela n’est pas dû à leur situation géographique, mais c’est plutôt le reflet d’un manque d’expérience en gestion ou simplement d’un manque de motivation à réaliser des profits.Mots clés: vente d’alimentation au détail, Territoires du Nord-Ouest, moyen, structure de vente de détail, gestion, Compagnie de la Baie d’Hudson, coopératives, magasins indépendant