Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.     

Second order Hamiltonian formalism and constraints algebra for non-polynomial supergravities

The second order Hamiltonian formalism for a non-polynomial N = 1D = 10 supergravity coupled to super Yang-Mills theory is developed. This is done by starting from the first order canoncial covariant formalism on group manifold. The Hamiltonian, generator of time evolution, is found as a functional of the first class constraints of this coupled system. These contraints close the constraint algebra and they are the generators of all the Hamiltonian gauge symmetries.     

Effective actions of intersecting brane worlds, fluxes and gaugino condensation

In this article we will first discuss the construction of brane world models being built either by intersecting D6-branes in type IIA orientifolds or, in the T-dual mirror picture, by D3- plus D7-branes with f-flux in type IIB orientifolds. We will show how their effective action is obtained by the calculation of scattering amplitudes between open and closed string states on intersecting D6-branes respectively on D3- and D7-branes. Secondly, turning on type IIB 3-form fluxes we will compute the induced soft supersymmetry breaking terms for the matter fields, like gaugino and scalar field masses. Finally, we will discuss the generation of 3-form flux in type IIB supergravity, which can be associated to the dynamical formation of a gaugino condensate in the confining phase of the dual N=1^* gauge theory. To cite this article: D. Lüst, C. R. Physique 5 (2004).

Résumé

Dans cet article nous discutons tout d'abord la construction de modèles de monde branaires construits soit par intersection de branes D6 dans des orientifolds de type IIA ou, dans la représentation T-duale, par des branes de type D3 et D7 avec des flux f dans les orientifolds de type IIB. Nous montrons comment obtenir leurs actions effectives en calculant les amplitudes de diffusion sur des intersections de branes de D6 et aussi sur des branes de type D3 et D7. Ensuite, nous allumons des flux pour la 3-forme de type IIB et nous calculons les termes de brisure douce de la supersymétrie pour les champs de matière, comme les masses du jaugino et des champs scalaires. Enfin, nous discutons la génération de flux pour la 3-forme de type IIB en supergravité, qui peut-être associée à la dynamique de la formation de condensat de jaugino dans la phase confinante de la théorie de jauge duale N=1^*. Pour citer cet article : D. Lüst, C. R. Physique 5 (2004).     

Error estimates for semi-discrete gauge methods for the Navier-Stokes equations

The gauge formulation of the Navier-Stokes equations for incompressible fluids is a new projection method. It splits the velocity in terms of auxiliary (nonphysical) variables and and replaces the momentum equation by a heat-like equation for and the incompressibility constraint by a diffusion equation for . This paper studies two time-discrete algorithms based on this splitting and the backward Euler method for with explicit boundary conditions and shows their stability and rates of convergence for both velocity and pressure. The analyses are variational and hinge on realistic regularity requirements on the exact solution and data. Both Neumann and Dirichlet boundary conditions are, in principle, admissible for but a compatibility restriction for the latter is uncovered which limits its applicability.

     

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F⁺ (H_graviton) where the one-particle Hilbert space H_graviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space H_graviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.     

An elementary notion of gauge equivalence

An elementary notion of gauge equivalence is introduced that does not require any Lagrangian or Hamiltonian apparatus. It is shown that in the special case of theories, such as general relativity, whose symmetries can be identified with spacetime diffeomorphisms this elementary notion has many of the same features as the usual notion. In particular, it performs well in the presence of asymptotic boundary conditions.     

Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a \(\mathcal{U}(1)\) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, similar to recently studied Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born’s rule) holds, provided the underlying model is scale free.     

Total Hamiltonian and Extended Hamiltonian for Constrained Hamilton Systems

For constrained Hamiltonian systems, the motion equations are deduced from total Hamiltonian and extended Hamiltonian with Lagrangian multipliers depending on time t and canonical variables q ⁱ and p _i . When the multipliers reduced to only depend on time t, the motion equations exactly agree with the old results. Under the same conditions (Lagrangian multipliers depend on time t and canonical variables q ⁱ and p _i ), the relation equations of coefficients in the generator of gauge transformation are deduced, but the equations have an additive term besides the well-known results. This additive term is from Lagrangian multipliers depending on canonical variables, and it might perform the gauge symmetries that needs to be discussed further. This project is supported by the fund of National Natural Science (10671086) and by National Laboratory for Superlattices and Microstructures (CHJG200605).