Abelian and non‐abelian D‐brane effective actions

We review a method to find the non-abelian open superstring effective action,\nthereby settling the issue of the ordering ambiguities. We start from solutions\nto Yang-Mills which, in D-brane context, define certain BPS configurations.\nStudying their deformations in the abelian case shows that the Born-Infeld\naction is the unique deformation which admits solutions of this type. By\napplying the method to the non-abelian case we calculated the full effective\naction through O(\\alpha'^3). The presence of derivative terms turns out to be\nessential. Testing the result by comparing the spectrum in the presence of a\nconstant magnetic background field with the string theory prediction, we obtain\nperfect agreement.\n

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.

Duality equivalence between self-dual and topologically massive non-abelian models

The effective action of a Higgs theory should be gauge-invariant. However, the quantum and/or thermal contributions to the effective potential seem to be gauge-dependent, posing a problem for its physical interpretation. In this paper, we identify the source of the problem and argue that in a Higgs theory perturbative contributions should be evaluated with the Higgs fields in the polar basis, not in the Cartesian basis. Formally, this observation can be made from the derivation of the Higgs theorem, which we provide. We show explicitly that, properly defined, the effective action for the Abelian Higgs theory is gauge-invariant to all orders in perturbation expansion when evaluated in the covariant gauge in the polar basis. In particular, the effective potential is gauge-invariant. We also show the equivalence between the calculations in the covariant gauge in the polar basis and the unitary gauge. These points are illustrated explicitly with the one-loop calculations of the effective action. With a field redefinition, we obtain the physical effective potential. The SU(2) non-Abelian case is also discussed.

Groups with cofinite Zariski topology and potential density

We are going to analyze through a first order perturbative formulation the local loss of symmetry when a source of non-Abelian Yang-Mills and gravitational fields interacts with an external agent that perturbes the original geometry associated to the source. Then, as the symmetry in Abelian and non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local orthogonal planes of symmetry that we previously called blades one and two, the loss of symmetry will be manifested by the tilting of these planes under the influence of the external agent. It was found already that there is an algorithm to block diagonalize the Yang-Mills field strength isospace projections in a local gauge invariant way. Independently, it was also found an algorithm to diagonalize the Yang-Mills stress-energy tensor in a gauge invariant way. Using these results and perturbative analysis from a previous manuscript dealing with the Abelian case, we are going to demonstrate how to develop an algorithm for constructing local energy-momentum conserved currents inside both local orthogonal planes. As the interaction proceeds, the planes are going to tilt perturbatively, and in this strict sense the original local symmetries will be lost. But we will prove that the new blades at the same point will correspond after the tilting generated by perturbation, to new symmetries, with associated new local currents, both on each new local planes of symmetry. Old symmetries will be broken, new will arise. There will be a local symmetry evolution in the non-Abelian case as well.

Gauge independence as a consequence of gauge covariance

It is shown how vector Stueckelberg fields can be introduced to ensure gauge invariance for mass terms for an antisymmetric tensor field. Scalar Stueckelberg fields allow one to have gauge invariance for these vector fields. Both the Abelian and non-Abelian cases are considered. Fully antisymmetric rank-three tensor fields and symmetric rank-two tensor fields are also discussed. PACS No.: 11.15-1

This paper aims at treating a study on Sylow theorem of different algebraic structures as groups, order of a group, subgroups, along with the associated notions of automorphisms group of the dihedral groups, split extensions of groups and vector spaces arises from the varying properties of real and complex numbers. We must have used the Sylow theorems of this work when it's generalized. Here we discuss possible subgroups of a group in different types of order which will give us a practical knowledge to see the applications of the Sylow theorems. In algebraic structures, we deal with operations of addition and multiplication and in order structures, those of greater than, less than and so on. It is through the study of Sylow theorems that we realize the importance of some definitions as like as the exact sequences and split extensions of groups, Sylow p-subgroup and semi-direct product. Thus it has been found necessary and convenient to study these structures in detail. In situations, where it was found that a given situation satisfies the basic axioms of structure and having already known the properties of that structure. Finally, we find out possible subgroups of a group in different types of order for abelian and non-abelian cases.

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.

We show that the Born-Infeld action with the Wess-Zumino terms for the Ramond-Ramond fields, which is the D3-brane effective action, is a solution to the Hamilton-Jacobi (H-J) equation of type IIB supergravity. Adopting the radial coordinate as time, we develop the ADM formalism for type IIB supergravity reduced on $S^5$ and derive the H-J equation, which is the classical limit of the Wheeler-De Witt equation and whose solutions are classical on-shell actions. The solution to the H-J equation reproduces the on-shell actions for the supergravity solution of a stack of D3-branes in a $B_2$ field and the near-horizon limit of this supergravity solution, which is conjectured to be dual to noncommutative Yang Mills and reduces to $AdS_5 \times S^5$ in the commutative limit. Our D3-brane effective action is that of a probe D3-brane, and the radial time corresponds to the vacuum expectation value of the Higgs field in the dual Yang Mills. Our findings can be applied to the study of the holographic renormalization group.

Vector field effective action in the open superstring theory

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, mathcal{Y} , as opposed to simply a T6. Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact “local model” and take the compactification manifold to be mathcal{Y}={mathrm{mathcal{M}}}_{mathrm{GH}}times {T}^2 , where ℳGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on mathcal{Y} . The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of mathcal{Y} depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. We examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

Energy crisis or a new soliton in the noncommutative CP(1) model?

The effective action lies at very heart of many deep properties of quantum field theory. It generalizes the classical action and is the generating functional of one-particle irreducible (1PI) proper functions. Moreover, it has a broad range of applications in physics, e.g. in the perturbative renormalization programme, in condensed matter physics, in quantum cosmology and in quantum gravity. For example, the 1PI proper functions play a crucial role in the renormalization programme, since it is necessary and sufficient to make them finite to get rid of all ultraviolet divergences. First, a naive definition of effective action is introduced, which yields the effective field equations. Unfortunately, neither the effective action is gauge-invariant, nor the effective field equations are gaugecovariant. Vilkovisky’s improvement is then described to make the effective action gauge-invariant. Last, the effective action for gauge theories is presented, with application to Yang-Mills theory and gravitation.