Paolo Pasti

Covariant Action for the Super-Five-Brane of M Theory

We propose a complete, d=6 covariant and kappa-symmetric, action for the M theory five-brane propagating in D=11 supergravity background. This opens a direct way of relating a wide class of super-p -brane solutions of string theory with the five-brane of M theory, which should be useful for studying corresponding dualities and nonperturbative aspects of these theories. {copyright} {ital 1997} {ital The American Physical Society}

Covariant action for a D = 11 five-brane with the chiral field

Abstract We propose a complete Born-Infeld-like action for a bosonic 5-brane with a worldvolume chiral field in a background of gravitational and antisymmetric gauge fields of D = 11 supergravity. When the five-brane couples to a three-rank antisymmetric gauge field, local symmetries of the five-brane require the addition to the action of an appropriate Wess-Zumino term. To preseve general coordinate and Lorentz invariance of the model we introduce a single auxiliary scalar field. The auxiliary field can be eliminated by gauge fixing a corresponding local symmetry at the price of the loss of manifest d = 6 worldvolume covariance. The double dimensional reduction of the five-brane model results in the Born-Infeld action with the Wess-Zumino term for a D = 10 four-D-brane.

Lorentz-invariant actions for chiral p-forms

We demonstrate how a Lorentz-covariant formulation of the chiral p-form model in D=2(p+1) containing infinitely many auxiliary fields is related to a Lorentz-covariant formulation with only one auxiliary scalar field entering a chiral p-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all first class. In contrast with the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines the energy of a single chiral p-form. In the case of D=2 chiral scalars the constraint can be improved by use of a {open_quotes}twisting{close_quotes} procedure (without the loss of the property to be first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to the possible absence of an anomaly in an appropriate quantum version of the model. {copyright} {ital 1997} {ital The American Physical Society}

Superstrings and supermembranes in the doubly supersymmetric geometrical approach

Abstract We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor-like formulation of super p -branes. Some basic features of the embedding world supersurface into target superspace specified by a geometrodynamical condition are considered. It is shown that the main attributes of the geometrical approach, such as the second fundamental form and extrinsic torsion of the embedded surface, and the Codazzi, Gauss and Ricci equations, have their doubly supersymmetric counterparts. At the same time the embedding of the supersurface into target superspace has its particular features. For instance, the embedding may cause more rigid restrictions on the geometrical properties of the supersurface. This is demonstrated with the examples of an N = 1 twistor-like supermembrane in D = 11 and type II superstrings in D = 10, where the geometrodynamical condition causes the embedded supersurface to be minimal and puts the theories on the mass shell.

On the Equivalence of Different Formulations of the M Theory Five-Brane

Abstract We show that the field equations for the supercoordinates and the self-dual antisymmetric tensor field derived from the recently constructed κ-invariant action for the M theory five-brane are equivalent to the equations of motion obtained in the doubly supersymmetric geometrical approach at the worldvolume component level.

Note on manifest Lorentz and general coordinate invariance in duality symmetric models

Abstract We consider a generalization of a duality symmetric model proposed by Schwarz and Sen [J.H. Schwarz and A. Sen, Nucl. Phys. B 411 (1994) 35]. It is based on enlarging the model with a dynamical vector field being a time-like component of a local Lorentz frame. This allows one to preserve the manifest Lorentz invariance of the model in flat space-time. The presence of this field is regarded as a relic of gravitational interaction which respects the general coordinate invariance in curved space-time but breaks the local Lorentz symmetry in tangent space down to its spacial subgroup.

Duality symmetric actions with manifest space-time symmetries

We consider a space-time-invariant duality symmetric action for a free Maxwell field and an SL(2,R)\ifmmode\times\else\texttimes\fi{}SO(6,22)-invariant effective action describing a low-energy bosonic sector of the heterotic string compactified on a six-dimensional torus. The manifest Lorentz- and general coordinate-invariant formulation of the models is achieved by coupling dual gauge fields to an auxiliary vector field from an axionic sector of the theory.

BLG-motivated Lagrangian formulation for the chiral two-form gauge field in D=6 and M5-branes

We reveal non-manifest gauge and SO(1,5) Lorentz symmetries in the Lagrangian description of a six-dimensional free chiral field derived from the Bagger-Lambert-Gustavsson model in arXiv:0804.3629 and make this formulation covariant with the use of a triplet of auxiliary scalar fields. We consider the coupling of this self-dual construction to gravity and its supersymmetrization. In the case of the non-linear model of arXiv:0805.2898 we solve the equations of motion of the gauge field, prove that its non-linear field strength is self-dual and find a gauge-covariant form of the non-linear action. Issues of the relation of this model to the known formulations of the M5-brane worldvolume theory are discussed.

Chiral anomalies in higher dimensional supersymmetric theories

Abstract We derive explicit formulas for pure gauge anomalies in a SYM theory in 6D as well as in 10D. Each anomaly consists of two terms: a gauge cocycle and a cocycle of the superdiffeomorphisms. The derivation is based essentially on a remarkable property of supersymmetric theories which we call Weil triviality and is directly connected with the constraints. The analogous problem for Lorentz anomalies is stated in the same way. However, in general, there are difficulties concerning Weil triviality. We prove that for pure SUGRA in 6D as well as in 10D it is possible to prove Weil triviality and, consequently, to obtain explicit expressions for pure Lorentz anomalies. However, as far as SUGRA coupled to SYM a la Chapline-Manton or a la Green-Schwarz is concerned, no self-evident solution is available.

On gauge-fixed superbrane actions in AdS superbackgrounds

Abstract To construct actions for describing superbranes propagating in AdS× S superbackgrounds we propose a coset space realization of these superbackgrounds which results in a short polynomial fermionic dependence (up to the sixth power in Grassmann coordinates) of target superspace supervielbeins and superconnections. Gauge fixing κ -symmetry in a way compatible with a static brane solution further reduces the fermionic dependence down to the fourth power. Subtleties of consistent gauge fixing worldvolume diffeomorphisms and κ -symmetry of the superbrane actions are discussed.