Non-abelian Chern-Simons Action Research Articles

Conformal supergravity in five dimensions: new approach and applications

We develop a new off-shell formulation for five-dimensional (5D) conformal supergravity obtained by gauging the 5D superconformal algebra in superspace. An important property of the conformal superspace introduced is that it reduces to the superconformal tensor calculus (formulated in the early 2000's) upon gauging away a number of superfluous fields. On the other hand, a different gauge fixing reduces our formulation to the SU(2) superspace of arXiv:0802.3953, which is suitable to describe the most general off-shell supergravity-matter couplings. Using the conformal superspace approach, we show how to reproduce practically all off-shell constructions derived so far, including the supersymmetric extensions of $R^2$ terms, thus demonstrating the power of our formulation. Furthermore, we construct for the first time a supersymmetric completion of the Ricci tensor squared term using the standard Weyl multiplet coupled to an off-shell vector multiplet. In addition, we present several procedures to generate higher-order off-shell invariants in supergravity, including higher-derivative ones. The covariant projective multiplets proposed in arXiv:0802.3953 are lifted to conformal superspace, and a manifestly superconformal action principle is given. We also introduce unconstrained prepotentials for the vector multiplet, the ${\cal{O}}(2)$ multiplet (i.e., the linear multiplet without central charge) and ${\cal{O}}(4+n)$ multiplets, with $n=0,1,\dots$ Superform formulations are given for the BF action and the non-abelian Chern-Simons action. Finally, we describe locally supersymmetric theories with gauged central charge in conformal superspace.

Non-Abelian Chern-Simons actions in three-dimensional projective superspaces

We construct an action for the superconformal Chern-Simons theory with non-Abelian gauge groups in three-dimensional N=3 projective superspace. We propose a Lagrangian given by the product of the function of the tropical multiplet, that represents the N=3 vector multiplet, and the O(-1,1) multiplet. We show how the tropical multiplet is embedded into the O(-1,1) multiplet by comparing our Lagrangian with the Chern- Simons Lagrangian in the N=2 superspace. We also discuss N=4 generalization of the action.

Supergravity-matter actions in three dimensions and Chern-Simons terms

We study off-shell N-extended Yang-Mills multiplets coupled to conformal supergravity in three spacetime dimensions. Superform formulations are presented for the non-Abelian Chern-Simons actions in the cases N=1, 2, 3, and the corresponding component actions are explicitly worked out. Such a Chern-Simons action does not exist for N=4. In the latter case, a superform formulation is given for the BF term that describes the coupling of two Abelian vector multiplets with self-dual and anti-self-dual superfield strengths respectively. The superform results obtained are used to construct linear multiplet action principles in the cases N=2, 3, 4. The N=3 and N=4 actions are demonstrated to be universal in the sense that all known off-shell supergravity-matter systems (with the exception of pure conformal supergravity) may be described using such an action. Starting from the N=3 and N=4 Abelian vector multiplets, we also construct composite O(2) multiplets which are analogues of the four-dimensional construction of an N=2 reduced chiral scalar engineered from the improved tensor multiplet. Using these composites, we present the superfield equations of motion for N=3 and N=4 anti-de Sitter and topologically massive supergravity theories. We also sketch the construction of a large family of higher derivative couplings for N=3 and N=4 vector multiplets.

On supersymmetric Chern-Simons-type theories in five dimensions

We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor multiplet is described in superspace for the first time.

Induction of the four-dimensional Lorentz-breaking non-Abelian Chern-Simons action

A four-dimensional Lorentz-breaking non-Abelian Chern-Simons-like action is generated as a one-loop perturbative correction via an appropriate Lorentz-breaking coupling of the non-Abelian gauge field to a spinor field. This term is shown to be regularization dependent, but nevertheless it can be found unambiguously in different regularization schemes at zero and at finite temperature.

Non-Abelian Chern-Simons action is topological invariant on 3 simple knot

Under SU(2) gauge transformation, the non-Abelian Chern-Simons action is invariant on a class of three dimensional manifold—3 simple knot.

On the gauge invariance and coordinate transformations of non-abelian D-brane actions

We study the variations of the worldvolume fields in the non-Abelian action for multiple D-branes. Using T-duality we find that the embedding scalars transform non-trivially under NS-NS gauge transformations as \delta X ~ [X, X] and prove that the non-Abelian Chern-Simons action is invariant under these transformations. Given that T-duality relates the (part of the) NS-NS transformation with (part of the) general coordinate transformations, we can get some insight in the structure of non-Abelian coordinate transformations.

The gauge invariance of the non-Abelian Chern–Simons action for D-branes revisited

We present an elegant method to prove the invariance of the Chern–Simons part of the non-Abelian action for N coinciding D-branes under the R–R and NS–NS gauge transformations, by carefully defining what is meant by a background gauge transformation in the non-Abelian world volume action. We study as well the invariance under massive gauge transformations of the massive Type IIA supergravity and show that no massive dielectric couplings are necessary to achieve this invariance. We show that this result is consistent with (massive) T-duality from the non-Abelian action for N D9-branes.

Vector non-Abelian Chern-Simons duality

Abelian Chern-Simons gauge theory is known to possess an $``S\ensuremath{-}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{f}\ensuremath{-}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{l}''$ action where its coupling constant k is inverted, i.e., $k\ensuremath{\leftrightarrow}1/k.$ Here a vector non-Abelian duality is found in the pure non-Abelian Chern-Simons action at the classical level. The dimensional reduction of the dual Chern-Simons action to two dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.

CONFORMAL EDGE CURRENTS IN CHERN-SIMONS THEORIES

We develop elementary canonical methods for the quantization of Abelian and non-Abelian Chern-Simons actions, using well-known ideas in gauge theories and quantum gravity. Our approach does not involve choice of gauge or clever manipulations of functional integrals. When the spatial slice is a disc, it yields Witten’s edge states carrying a representation of the Kac-Moody algebra. The canonical expressions for the generators of diffeomorphisms on the boundary of the disc are also found, and it is established that they are the Chern-Simons version of the Sugawara construction. This paper is a prelude to our future publications on edge states, sources, vertex operators, and their spin and statistics in 3D and 4D topological field theories.