Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite power series in the auxiliary metric given by ref. \cite{s14}, but just picks out the first term from the series formally. New effective interactions of the theories are revealed. That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinite terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite power series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This non-linearity is inevitable to the requirement the two dual actions are equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions added; v3: concision made; v4: minor modification mad

Stabilization of Extra Dimensions at Tree Level

By considering the effects of string winding and momentum modes on a time dependent background, we find a method by which six compact dimensions become stabilized naturally at the self-dual radius while three dimensions grow large.Comment: 15 pages, 2 figures, minor typos correcte

Higher Dimensional Taub-NUTs and Taub-Bolts in Einstein-Maxwell Gravity

We present a class of higher dimensional solutions to Einstein-Maxwell equations in d-dimensions. These solutions are asymptotically locally flat, de-Sitter, or anti-de Sitter space-times. The solutions we obtained depend on two extra parameters other than the mass and the nut charge. These two parameters are the electric charge, q and the electric potential at infinity, V, which has a non-trivial contribution. We Analyze the conditions one can impose to obtain Taub-Nut or Taub-Bolt space-times, including the four-dimensional case. We found that in the nut case these conditions coincide with that coming from the regularity of the one-form potential at the horizon. Furthermore, the mass parameter for the higher dimensional solutions depends on the nut charge and the electric charge or the potential at infinity.Comment: 11 pages, LaTe

Time-dependent backgrounds from supergravity with gauged non-compact R-symmetry

We obtain a general class of time-dependent, asymptotically de Sitter backgrounds which solve the first order bosonic equations that extremize the action for supergravity with gauged non-compact $R$-symmetry. These backgrounds correspond only to neutral fields with the correct sign of kinetic energy. Within N=2 five-dimensional supergravity with vector-superfields we provide examples of multi-centered charged black holes in asymptotic de Sitter space, whose spatial part is given by a time-dependent hyper-K\"ahler space. Reducing these backgrounds to four dimensions yields asymptotically de Sitter multi-centered charged black hole backgrounds and we show that they are related to an instanton configuration by a massive T-duality over time. Within N=2 gauged supergravity in four (and five)-dimensions with hyper-multiplets there could also be neutral cosmological backgrounds that are regular and correspond to the different de Sitter spaces at early and late times.Comment: 28 pages, Latex; minor changes and add reference

Numerical experiments with p F- and q D-strings: the formation of (p,q) bound states

We investigate the behaviour of (p,q) string networks, focusing on two aspects: (1) modelling more realistic (p,q) string networks than the Z_N networks used so far and (2) investigating the effect of long-range interactions on the evolution of the network. We model the network with no long-range interactions using two sets of fields, complex scalars coupled to gauge fields, with a potential chosen such that the two types of strings will form bound states. This way we can model junctions of 3 strings with different tension; in Z_N models used so far in simulations all the strings have identical tensions. In order to introduce long-range interactions we also study a network in which one of the scalars forms global strings. We observe that in the absence of long-range interactions the formation of bound states has a significant influence on the evolution of the network. When long-range interactions are turned on the bound states are short-lived and have a minimal effect on the network evolution.Comment: 17 pages, 8 figures, JCAP styl

A class of solvable Lie algebras and their Casimir Invariants

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of n_{n,1} and of its solvable extensions are calculated. For n=4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.Comment: 16 page

Backlund Transformations, D-Branes, and Fluxes in Minimal Type 0 Strings

We study the Type 0A string theory in the (2,4k) superconformal minimal model backgrounds, focusing on the fully non-perturbative string equations which define the partition function of the model. The equations admit a parameter, Gamma, which in the spacetime interpretation controls the number of background D-branes, or R-R flux units, depending upon which weak coupling regime is taken. We study the properties of the string equations (often focusing on the (2,4) model in particular) and their physical solutions. The solutions are the potential for an associated Schrodinger problem whose wavefunction is that of an extended D-brane probe. We perform a numerical study of the spectrum of this system for varying Gamma and establish that when Gamma is a positive integer the equations' solutions have special properties consistent with the spacetime interpretation. We also show that a natural solution-generating transformation (that changes Gamma by an integer) is the Backlund transformation of the KdV hierarchy specialized to (scale invariant) solitons at zero velocity. Our results suggest that the localized D-branes of the minimal string theories are directly related to the solitons of the KdV hierarchy. Further, we observe an interesting transition when Gamma=-1.Comment: 17 pages, 3 figure

Constraining the string scale: from Planck to Weak and back again

String and field theory ideas have greatly influenced each other since the so called second string revolution. We review this interrelation paying particular attention to its phenomenological implications. Our guiding principle is the radical shift in the way that we think about the fundamental scale, in particular the way in which string models have been able to accommodate values from the Planck $M_\mathrm{Pl}\sim 10^{18}$ GeV down to the electroweak scale $M_{EW}\sim$ TeV.Comment: Invited review aimed at an experimental audienc

Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D

In this paper we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalise the vacuum plane-wave solutions in 3+1 dimensions to the 4+1 dimensional case. By doing a Kaluza-Klein reduction we obtain solutions to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalise the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain 3+1 dimensional solutions to the Einstein equations with a scalar field.Comment: 16 pages, no figure

Quark Soup al dente: Applied Superstring Theory

We discuss the application of the AdS/CFT correspondence to possibly gain new physical insights for the strongly coupled quark-gluon plasma. This article provides an informal summary of a talk given by RCM at the 18th International Conference on General Relativity and Gravitation in July 2007.Comment: This article provides an informal summary of a talk given by RCM at the 18th International Conference on General Relativity and Gravitation in July 200