Monotonic properties of the shift and penetration factors

We study derivatives of the shift and penetration factors of collision theory with respect to energy, angular momentum, and charge. Definitive results for the signs of these derivatives are found for the repulsive Coulomb case. In particular, we find that the derivative of the shift factor with respect to energy is positive for the repulsive Coulomb case, a long anticipated but heretofore unproven result. These results are closely connected to the properties of the sum of squares of the regular and irregular Coulomb functions; we also present investigations of this quantity.Comment: 13 pages, 1 figur

Gauging N=2 Supersymmetric Non-Linear σ\sigma-Models in the Atiyah-Ward Space-Time

We build up a class of N=2 supersymmetric non-linear $\sigma$-models in an N=1 superspace based on the Atiyah-Ward space-time of (2+2)-signature metric. We also discuss the gauging of isometries of the associated hyper-K\"ahlerian target spaces and present the resulting gauge-covariant supersymmetric action functional.Comment: 12 pages, latex, no figure

Effective range function below threshold

We demonstrate that the kernel of the Lippmann-Schwinger equation, associated with interactions consisting of a sum of the Coulomb plus a short range nuclear potential, below threshold becomes degenerate. Taking advantage of this fact, we present a simple method of calculating the effective range function for negative energies. This may be useful in practice since the effective range expansion extrapolated to threshold allows to extract low-energy scattering parameters: the Coulomb-modified scattering length and the effective range.Comment: 14 pages, 1 figur

A Note on Embedding of M-Theory Corrections into Eleven-Dimensional Superspace

By analyzing eleven-dimensional superspace fourth-rank superfield strength F-Bianchi identities, we show that M-theory corrections to eleven-dimensional supergravity can not be embedded into the mass dimension zero constraints, such as the (\g^{a b})_{\a\b} X_{a b}{}^c or i (\g^{a_1... a_5})_{\a\b} X_{a_1... a_5}{}^c -terms in the supertorsion constraint T_{\a\b}{}^c. The only possible modification of superspace constraint at dimension zero is found to be the scaling of F_{\a\b c d} like F_{\a\b c d} = (1/2) \big(\g_{c d}\big)_{\a\b} e^\Phi for some real scalar superfield \Phi, which alone is further shown not enough to embed general M-theory corrections. This conclusion is based on the dimension zero F-Bianchi identity under the two assumptions: (i) There are no negative dimensional constraints on the F-superfield strength: F_{\a\b\g\d} = F_{\a\b\g d} =0; (ii) The supertorsion T-Bianchi identities and F-Bianchi identities are not modified by Chern-Simons terms. Our result can serve as a powerful tool for future exploration of M-theory corrections embedded into eleven-dimensional superspace supergravity.Comment: 14 pages, latex, some minor typos corrected, as well as old section 5 deleted, due to the subtlety about Chern-Simons term in F-Bianchi identitie

Self-Dual N=8 Supergravity as Closed N=2(4) Strings

As open N=2 or 4 strings describe self-dual N=4 super Yang-Mills in 2+2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) N=8 supergravity. These theories are conveniently formulated in a chiral superspace with general supercoordinate and local OSp(8|2) gauge invariances. The super-light-cone and covariant-component actions are analyzed. Because only half the Lorentz group is gauged, the gravity field equation is just the vanishing of the torsion.Comment: 17 pg., (uuencoded dvi file; revision: forgot 1 stupid term in the last equation) ITP-SB-92-3

Vortex deformation and breaking in superconductors: A microscopic description

Vortex breaking has been traditionally studied for nonuniform critical current densities, although it may also appear due to nonuniform pinning force distributions. In this article we study the case of a high-pinning/low-pinning/high-pinning layered structure. We have developed an elastic model for describing the deformation of a vortex in these systems in the presence of a uniform transport current density $J$ for any arbitrary orientation of the transport current and the magnetic field. If $J$ is above a certain critical value, $J_c$, the vortex breaks and a finite effective resistance appears. Our model can be applied to some experimental configurations where vortex breaking naturally exists. This is the case for YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) low angle grain boundaries and films on vicinal substrates, where the breaking is experienced by Abrikosov-Josephson vortices (AJV) and Josephson string vortices (SV), respectively. With our model, we have experimentally extracted some intrinsic parameters of the AJV and SV, such as the line tension $\epsilon_l$ and compared it to existing predictions based on the vortex structure.Comment: 11 figures in 13 files; minor changes after printing proof

The N=4 string is the same as the N=2 string

We redo the quantization of the N=4 string, taking into account the reducibility of the constraints. The result is equivalent to the N=2 string, with critical dimension D=4 and signature (++--). The N=4 formulation has several advantages: the sigma-model field equations are implied classically, rather than by quantum/beta-function calculations; self-duality/chirality is one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This reveals that the theory includes fermions, and is apparently spacetime supersymmetric.Comment: 7 pg (uuencoded dvi file; otherwise same as original

T-duality and closed string non-commutative (doubled) geometry

We provide some evidence that closed string coordinates will become non-commutative turning on H-field flux background in closed string compactifications. This is in analogy to open string non-commutativity on the world volume of D-branes with B- and F-field background. The class of 3-dimensional backgrounds we are studying are twisted tori (fibrations of a 2-torus over a circle) and the their T-dual H-field, 3-form flux backgrounds (T-folds). The spatial non-commutativity arises due to the non-trivial monodromies of the toroidal Kahler resp. complex structure moduli fields, when going around the closed string along the circle direction. In addition we study closed string non-commutativity in the context of doubled geometry, where we argue that in general a non-commutative closed string background is T-dual to a commutative closed string background and vice versa. Finally, in analogy to open string boundary conditions, we also argue that closed string momentum and winding modes define in some sense D-branes in closed string doubled geometry.Comment: 31 pages, references added, extended version contains new sections 3.3., 3.4 and

D-branes in N=2 Strings

We study various aspects of D-branes in the two families of closed N=2 strings denoted by \alpha and \beta in hep-th/0211147. We consider two types of N=2 boundary conditions, A-type and B-type. We analyse the D-branes geometry. We compute open and closed string scattering amplitudes in the presence of the D-branes and discuss the results. We find that, except the space filling D-branes, the B-type D-branes decouple from the bulk. The A-type D-branes exhibit inconsistency. We construct the D-branes effective worldvolume theories. They are given by a dimensional reduction of self-dual Yang-Mills theory in four dimensions. We construct the D-branes gravity backgrounds. Finally, we discuss possible N=2 open/closed string dualities.Comment: 25 pages, Latex2

Families of N=2 Strings

In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings of the same symmetry algebra in the same ``pre-theory.'' We then apply it to N=2 strings and formulate the recipe for finding the associated parameter spaces of gauging. Flat and curved target spaces of both (4,0) and (2,2) signatures are considered. We broadly divide the gauging choices into two classes, denoted by alpha and beta, and show them to be related by T-duality. The distinction between them is formulated topologically and hinges on some unique properties of 4d manifolds. We determine what their parameter spaces of gauging are under certain simplicity ansatz for generic flat spaces (R^4 and its toroidal compactifications) as well as some curved spaces. We briefly discuss the spectra of D-branes for both alpha and beta families.Comment: 66+1 pages, 2 tables, latex 2e, hyperref. ver2: typos corrected, reference adde