Exotic gauge theories from tensor calculus (original) (raw)

EXTENSION OF CHERN–SIMONS FORMS AND NEW GAUGE ANOMALIES

International Journal of Modern Physics A, 2014

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher rank field-strength tensors. The integrals of these forms over the corresponding space-time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern-Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions. Of special interest are those which can be constructed in four, six, eight and ten dimensions.

Transgression forms and extensions of Chern-Simons gauge theories

Journal of High Energy Physics, 2006

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.

The gauge structure of exceptional field theories and the tensor hierarchy

Journal of High Energy Physics, 2014

ABSTRACT We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.

Gauge theories, duality relations and the tensor hierarchy

Journal of High Energy Physics, 2009

We compute the complete 3-and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the pform fields in the action and those of the same fields in the tensor hierarchy.

A covariant formalism for Chern Simons gravity

Journal of Physics A: Mathematical and General, 2003

Chern-Simons type Lagrangians in d = 3 dimensions are analyzed from the point of view of their covariance and globality. We use the transgression formula to find out a new fully covariant and global Lagrangian for Chern-Simons gravity: the price for establishing globality is hidden in a bimetric (or biconnection) structure. Such a formulation allows to calculate from a global and simpler viewpoint the energymomentum complex and the superpotential both for Yang-Mills and gravitational examples.

On Transgression Forms and Chern--Simons (Super) gravity

Arxiv preprint hep-th/0512014, 2005

A transgression form is proposed as lagrangian for a gauge field theory. The construction is first carried out for an arbitrary Lie Algebra g and then specialized to some particular cases. We exhibit the action, discuss its symmetries, write down the equations of motion and the boundary conditions that follow from it, and finally compute conserved charges. We also present a method, based on the iterative use of the Extended Cartan Homotopy Formula, which allows one to (i) systematically split the lagrangian in order to appropriately reflect the subspaces structure of the gauge algebra, and (ii) separate the lagrangian in bulk and boundary contributions. Chern-Simons Gravity and Supergravity are then used as examples to illustrate the method. In the end we discuss some further theoretical implications that arise naturally from the mathematical structure being considered.

Generalized Chern–Simons modified gravity in first-order formalism

General Relativity and Gravitation, 2013

We propose a generalization of Chern-Simons (CS) modified gravity in first-order formalism. CS modified gravity action has a term that comes from the chiral anomaly which is Pontryagin invariant. First-order CS modified gravity is a torsional theory and in a space-time with torsion the chiral anomaly includes a torsional topological term called Nieh-Yan invariant. We generalize the CS modified gravity by adding the Nieh-Yan term to the action and find the effective theory. We compare the generalized theory with the first-order CS modified gravity and comment on the similarities and differences.

An analysis of the first-order form of gauge theories

Canadian Journal of Physics, 2012

The first-order form of a Maxwell theory and U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation that leaves the action invariant is derived from the constraints present. A nonabelian generalization is similarly analyzed. This first-order three dimensional massive gauge theory is rewritten in terms of two interacting vector fields. The constraint structure when using light-cone coordinates is considered. The relationship between first- and second-order forms of the two-dimensional Einstein–Hilbert action is explored where a Lagrange multiplier is used to ensure their equivalence.

Interaction of non-Abelian tensor gauge fields

Recently we introduced an extended vector bundle X on which non-Abelian tensor gauge fields realize a connection. Our aim here is to introduce interaction of non-Abelian tensor gauge fields with fermions and bosons. We have found that there exist two series of gauge invariant forms describing this interaction. The linear sum of these forms comprises the general gauge invariant Lagrangian. Studying the corresponding Euler-Lagrange equations we found that a particular linear combination of these forms exhibits enhanced symmetry which guarantees the conservation of the corresponding high-rank currents. A possible mechanism of symmetry breaking and mass generation of tensor gauge bosons is suggested.