D-branes in a plane-wave background

The D-branes of the maximally supersymmetric plane-wave background are described.Comment: 6 pages; contribution to the proceedings of the 35th Symposium Ahrenshoop, 2002; v2: minor correction

An SL(2,Z) anomaly in IIB supergravity and its F-theory interpretation

The SL(2,Z) duality transformations of type IIB supergravity are shown to be anomalous in generic F-theory backgrounds due to the anomalous transformation of the phase of the chiral fermion determinant. The anomaly is partially cancelled provided the ten-dimensional type IIB theory lagrangian contains a term that is a ten-form made out of the composite U(1) field strength and four powers of the curvature. A residual anomaly remains uncancelled, and this implies a certain topological restriction on consistent backgrounds of the euclidean theory. A similar, but slightly stronger, restriction is also derived from an explicit F-theory compactification on K3 x M8 (where M8 is an eight-manifold with a nowhere vanishing chiral spinor) where the cancellation of tadpoles for Ramond--Ramond fields is only possible if M8 has an Euler character that is a positive multiple of 24. The interpretation of this restriction in the dual heterotic theory on T2 x M8 is also given.Comment: Argument has been streamlined and references have been added. 18 pages, harvmac (b

The mechanisms of temporal inference

The properties of a temporal language are determined by its constituent elements: the temporal objects which it can represent, the attributes of those objects, the relationships between them, the axioms which define the default relationships, and the rules which define the statements that can be formulated. The methods of inference which can be applied to a temporal language are derived in part from a small number of axioms which define the meaning of equality and order and how those relationships can be propagated. More complex inferences involve detailed analysis of the stated relationships. Perhaps the most challenging area of temporal inference is reasoning over disjunctive temporal constraints. Simple forms of disjunction do not sufficiently increase the expressive power of a language while unrestricted use of disjunction makes the analysis NP-hard. In many cases a set of disjunctive constraints can be converted to disjunctive normal form and familiar methods of inference can be applied to the conjunctive sub-expressions. This process itself is NP-hard but it is made more tractable by careful expansion of a tree-structured search space

Multiparticle one-loop amplitudes and S-duality in closed superstring theory

Explicit expressions for one-loop five supergraviton scattering amplitudes in both type II superstring theories are determined by making use of the pure spinor formalism. The type IIB amplitude can be expressed in terms of a doubling of ten-dimensional super Yang--Mills tree amplitude, while the type IIA amplitude has additional pieces that cannot be expressed in that manner. We evaluate the coefficients of terms in the analytic part of the low energy expansion of the amplitude, which correspond to a series of terms in an effective action of the schematic form D^{2k}R^5 for 0\le k \le 5 (where R is the Riemann curvature). Comparison with earlier analyses of the tree amplitudes and of the four-particle one-loop amplitude leads to an interesting extension of the action of SL(2,Z) S-duality on the moduli-dependent coefficients in the type IIB theory. We also investigate closed-string five-particle amplitudes that violate conservation of the U(1) R-symmetry charge -- processes that are forbidden in supergravity. The coefficients of their low energy expansion are shown to agree with S-duality systematics. A less detailed analysis is also given of the six-point function, resulting in the vanishing of the analytic parts of the R^6 and D^4 R^6 interactions in the ten-dimensional effective action, but not in lower dimensions.Comment: 62 pages, Mathematica notebook on integral expansion included in submission. v2: minor modifications, references added, matches published versio

String Bit Models for Superstring

We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies for surmounting them. As with previous work on bosonic string we work within the light-cone gauge. The bit model possesses a good deal less symmetry than the continuous string theory. For one thing, the bit model is formulated as a Galilei invariant theory in $(D-2)+1$ dimensional space-time. This means that Poincar\'e invariance is reduced to the Galilei subgroup in $D-2$ space dimensions. Naturally the supersymmetry present in the bit model is likewise dramatically reduced. Continuous string can arise in the bit models with the formation of infinitely long polymers of string bits. Under the right circumstances (at the critical dimension) these polymers can behave as string moving in $D$ dimensional space-time enjoying the full $N=2$ Poincar\'e supersymmetric dynamics of type II-B superstring.Comment: 43 pages, phyzzx require

Matching the (DR4)-R-6 interaction at two-loops

The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included.Comment: 40 pages, various typos and coefficients corrected in version

Anomalous Creation of Branes

In certain circumstances when two branes pass through each other a third brane is produced stretching between them. We explain this phenomenon by the use of chains of dualities and the inflow of charge that is required for the absence of chiral gauge anomalies when pairs of D-branes intersect.Comment: 7 pages, two figure

Remarks on the Classical Size of D-Branes

We discuss different criteria for `classical size' of extremal Dirichlet p-branes in type-II supergravity. Using strong-weak coupling duality, we find that the size of the strong-coupling region at the core of the (p<3)-branes, is always given by the asymptotic string scale, if measured in the weakly coupled dual string metric. We also point out how the eleven-dimensional Planck scale arises in the classical 0-brane solution, as well as the ten-dimensional Planck scale in the D-instanton solution.Comment: 8 pp, harvma