Dmitri Sorokin

Superbranes and superembeddings

Abstract We review a geometrical approach to the description of the dynamics of superparticles, superstrings and, in general, of super- p -branes, Dirichlet branes and the M5-brane, which is based on a generalization of the elements of surface theory to the description of the embedding of supersurfaces into target superspaces. Being manifestly supersymmetric in both, the superworldvolume of the brane and the target superspace, this approach unifies the Neveu–Schwarz–Ramond and the Green–Schwarz formulation and provides the fermionic κ -symmetry of the Green–Schwarz-type superbrane actions with a clear geometrical meaning of standard worldvolume local supersymmetry. The dynamics of superbranes is encoded in a generic superembedding condition. Depending on the superbrane and the target-space dimension, the superembedding condition produces either only off-shell constraints (as in the case of N =1 superparticles and N =1 superstrings), or also results in the full set of the superbrane equations of motion (as, for example, in the case of the M-theory branes). In the first case worldvolume superspace actions for the superbranes can be constructed, while in the second case only component or generalized superfield actions are known. We describe the properties of the doubly supersymmetric brane actions and show how they are related to the standard Green–Schwarz formulation. In the second part of the article basic geometrical grounds of the (super)embedding approach are considered and applied to the description of the M2-brane and the M5-brane. Various applications of the superembedding approach are reviewed.

Superparticle Models with Tensorial Central Charges

A generalization of the Ferber–Shirafuji formulation of superparticle mechanics is considered. The generalized model describes the dynamics of a superparticle in a superspace extended by tensorial central charge coordinates and commuting twistor–like spinor variables. The D = 4 model contains a continuous real parameter a ≥ 0 and at a = 0 reduces to the SU(2,2|1) supertwistor Ferber–Shirafuji model, while at a = 1 one gets an OSp(1|8) supertwistor model of ref. [1] which describes BPS states with all but one unbroken target space supersymmetries. When 0 1 the supertwistor group becomes OSp(1,1|8). We quantize the model and find that its quantum spectrum consists of massless states of an arbitrary (half)integer helicity. The independent discrete central charge coordinate describes the helicity spectrum. We also outline the generalization of the a = 1 model to higher space–time dimensions and demonstrate that in D = 3,4,6 and 10, where the quantum states are massless, the extra degrees of freedom (with respect to those of the standard superparticle) parametrize compact manifolds. These compact manifolds can be associated with higher–dimensional helicity states. In particular, in D = 10 the additional “helicity” manifold is isomorphic to the sphere S 7 .

OSp supergroup manifolds, superparticles, and supertwistors

We construct simple twistor-like actions describing superparticles propagating on a coset superspace OSp(1|4)/SO(1,3) (containing the D=4 anti-de-Sitter space as a bosonic subspace), on a supergroup manifold OSp(1|4) and, generically, on OSp(1|2n). Making two different contractions of the superparticle model on the OSp(1|4) supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of OSp(1|2n) we obtain even Sp(2n)-valued Cartan forms which are quadratic in Grassmann coordinates of OSp(1|2n). This result may simplify the structure of brane actions in super-AdS backgrounds. For instance, the twistor-like actions constructed with the use of the even OSp(1|2n) Cartan forms as supervielbeins are quadratic in fermionic variables. We also show that the free bosonic twistor particle action describes massless particles propagating in arbitrary space-times with a conformally flat metric, in particular, in Minkowski space and AdS space. Applications of these results to the theory of higher spin fields and to superbranes in AdS superbackgrounds are mentioned.

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.

DUALITY OF SELF-DUAL ACTIONS

Abstract Using examples of a D = 2 chiral scalar and a duality-symmetric formulation of D = 4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D = 4 case, upon performing a duality transformation of an auxiliary scalar field, which ensures Lorentz covariance of the action, we arrive at a new covariant duality-symmetric Maxwell action, which contains a two-form potential as an auxiliary field. When the two-form field is gauge fixed this action reduces to a duality-symmetric action for Maxwell theory constructed by Zwanziger. We consider properties of this new covariant action and discuss its coupling to external dyonic sources. We also demonstrate that the formulations considered are self-dual with respect to a dualization of the field strengths of the chiral fields.

The M5-brane Hamiltonian

Abstract We obtain the Hamiltonian form of the world-volume action for the M5-brane is a general D = 11 supergravity background. We use this result to obtain a new version of the covariant M5-brane Lagrangian in which the tension appears as a dynamical variable, although this Lagrangian has some unsatisfactory features which we trace to peculiarities of the null limit. We also show that the M5-brane action is invariant under all (super)isometries of the background.

Harmonics, notophs and chiral bosons

A way of covariantizing duality symmetric actions is described. The presence of self–dual fields or, in more general case, duality–symmetric fields in field–theoretical and string models reflects their duality properties whose extreme importance for understanding a full quantum theory has been appreciated during an impetuous development of the duality field happened during last few years. The knowledge of duality–symmetric effective actions is useful for carrying out more systematic study of the classical and quantum properties of the theory, and in this memorial contribution we would like to demonstrate how fruitful physical ideas and mathematical techniques which Victor Isakovich Ogievetsky and his colleagues have developed helped us to construct a covariant Lagrangian formulation applicable to all known models with duality–symmetric fields in space–time of Lorentz signature. The problem of constructing and studying models described by duality–invariant actions has a rather long history. It goes back to time when Poincare and later on Dirac noticed electric–magnetic duality symmetry of the free Maxwell equations, and, Dirac assumed the existence of magnetically charged particles (monopoles and dyons) [1] admitting the duality symmetry to be also held for the Maxwell equations in the presence of charged sources. To describe monopoles and dyons on an equal footing with electrically charged particles one should have a duality–symmetric form of the Maxwell action. This problem was studied (among others) by Schwinger and Alexander von Humboldt fellow. On leave from Kharkov Institute of Physics and Technology, Kharkov, 310108, Ukraine.

Duality and Selfduality of Chiral Boson Fields in Various Dimensions

Duality-symmetric and self-dual fields (chiral bosons) are an important part of various theoretical models which are considered in the modern superstring theory. For a long period of time there has been a problem of how to construct an action for such fields which would simultaneously possess both duality symmetry and Lorentz-covariance.