Perturbative Relations between Gravity and Gauge Theory

We review the relations that have been found between multi-loop scattering amplitudes in gauge theory and gravity, and their implications for ultraviolet divergences in supergravity.Comment: LaTex with package axodraw.sty. 10 pages. Presented by L.D. at Strings 99. Cosmetic changes onl

The principle of least action and the geometric basis of D-branes

We analyze thoroughly the boundary conditions allowed in classical non-linear sigma models and derive from first principle the corresponding geometric objects, i.e. D-branes. In addition to giving classical D-branes an intrinsic and geometric foundation, D-branes in nontrivial H flux and D-branes embedded within D-branes are precisely defined. A well known topological condition on D-branes is replaced

Comment on ''Properties of highly clustered networks"

We consider a procedure for generating clustered networks previously reported by Newman [Phys. Rev. E 68, 026121 (2003)]. In the same study, clustered networks generated according to the proposed model have been reported to have a lower epidemic threshold under susceptible-infective-recovered-type network epidemic dynamics. By rewiring networks generated by this model, such that the degree distribution is conserved, we show that the lower epidemic threshold can be closely reproduced by rewired networks with close to zero clustering. The reported lower epidemic threshold can be explained by different degree distributions observed in the networks corresponding to different levels of clustering. Clustering results in networks with high levels of heterogeneity in node degree, a higher proportion of nodes with zero connectivity, and links concentrated within highly interconnected components of small size. Hence, networks generated by this model differ in both clustering and degree distribution, and the lower epidemic threshold is not explained by clustering alone

On Large N Gauge Theories from Orientifolds

We consider four dimensional ${\cal N}=1$ supersymmetric gauge theories obtained via orientifolds of Type IIB on Abelian C^3/G orbifolds. We construct all such theories that have well defined world-sheet expansion. The number of such orientifolds is rather limited. We explain this fact in the context of recent developments in four dimensional Type IIB orientifolds. In particular, we elaborate these issues in some examples of theories where world-sheet description is inadequate due to non-perturbative (from the orientifold viewpoint) states arising from D-branes wrapping (collapsed) 2-cycles in the orbifold. We find complete agreement with the corresponding statements recently discussed in the context of Type I compactifications on toroidal orbifolds. This provides a non-trivial check for correctness of the corresponding conclusions. We also find non-trivial agreement with various field theory expectations, and point out their origin in string language. The orientifold gauge theories that do possess well defined world-sheet description have the property that in the large N limit computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ oriented theory.Comment: 21 pages, revtex, minor errors and misprints corrected (to appear in Phys. Rev. D

Stringy KLT relations, global symmetries, and E_7(7) violation

We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.Comment: 23 pages, published versio

From Markovian to pairwise epidemic models and the performance of moment closure approximations

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness

Minimal Basis for Gauge Theory Amplitudes

Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)! amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.Comment: v2: typos corrected, some rephrasing of the general discussion. Captions to figures added. Version to appear in PRL. 4 pages, 5 figure

The Orbifolds of Permutation-Type as Physical String Systems at Multiples of c=26 IV. Orientation Orbifolds Include Orientifolds

In this fourth paper of the series, I clarify the somewhat mysterious relation between the large class of {\it orientation orbifolds} (with twisted open-string CFT's at $\hat c=52$) and {\it orientifolds} (with untwisted open strings at $c=26$), both of which have been associated to division by world-sheet orientation-reversing automorphisms. In particular -- following a spectral clue in the previous paper -- I show that, even as an {\it interacting string system}, a certain half-integer-moded orientation orbifold-string system is in fact equivalent to the archetypal orientifold. The subtitle of this paper, that orientation orbifolds include and generalize standard orientifolds, then follows because there are many other orientation orbifold-string systems -- with higher fractional modeing -- which are not equivalent to untwisted string systems.Comment: 22 pages, typos correcte