On superembedding approach to multiple D-brane system. D0 story

We develop superembedding approach to multiple D-particle (D0-brane) system. In flat target D=10$D=10$ type IIA superspace this produces the supersymmetric and Lorentz covariant version of the Matrix model equations. The equations following from our superembedding approach to multiple D0 in curved type IIA superspace shows the Myers ‘dielectric brane effect’, i.e. interaction with higher form gauge fields which do not interact with a single D0-brane.     

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting Q_BRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.     

BV formulation of higher form gauge theories in a superspace

We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin–Vilkovisky (BV) formulation for 2- and 3-form gauge theories. Further we develop the superspace formulation for the BV actions for these theories. We show that the extended BRST invariant BV action for these theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. On the other hand a superspace with two Grassmann coordinates is required for a manifestly covariant formulation of the extended BRST and extended anti-BRST invariant BV actions for higher form gauge theories.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

Some remarks on the geometry of superspace supergravity

In this note, we first give a quick presentation of the supergeometry underlying supergravity theories, using an intrinsic differential geometric language. For this, we adopt the point of view of Cartan geometries, and rely as well on the work of John Lott, who has found a unified geometrical interpretation of the torsion constraints for many supergravity theories, based on the use of H-structures. In this framework, the constraints amount to requiring first-order integrability of H-structures, for a specific supergroup H.The supergroup H used by Lott is not the usual diagonal representation of the Lorentz group on superspace, but an extension of the latter. This extension appears to be natural and it can be related to the super-Poincaré group. We also observe that the constraints arising from the requirement of first-order integrability have basically the same form, in any spacetime dimension.Looking at supergravity from an affine viewpoint (i.e. as a gauge theory for the super-Poincaré group), we show that requiring first-order integrability amounts to requiring the equivalence, up to gauge transformations, between infinitesimal gauge supertranslations acting on the supervielbein and infinitesimal superdiffeomorphisms acting on the supervielbein.The latter action is performed through a covariant Lie derivative, whose expression involves naturally the supertorsion tensor. We use this expression to show that the term added to the spin connection, in the supercovariant derivative of d=11 supergravity, has a natural superspace origin. In particular, the 4-form field strength is related to a specific component of the supertorsion tensor.We conclude by some general remarks concerning Killing spinors in geometry and supergravity, discussing their possible interpretations, as Killing vector fields on a specific supermanifold on one hand, and as parallel spinors for an appropriate connection on the other hand. We show that this last interpretation is very natural from the point of view of Klein and Cartan geometries.     

Integrable Structures in Classical Off-Shell 10D Supersymmetric Yang–Mills Theory

The field equations of supersymmetric Yang–Mills theory in ten dimensions may be formulated as vanishing curvature conditions on light-like rays in superspace. In this article, we investigate the physical content of the modified SO(7) covariant superspace constraints put forward earlier [11]. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang–Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays. Received: 20 April 2000 / Accepted: 10 September 2000     

The heterotic sigma model in the presence of background gauge fields. Three-loop results

The covariant part of the β-functions for the heterotic σ-model in the presence of background gauge fields is calculated up to three-loop order. The equations β=0 are shown to coincide with the equations of motion derived from an effective space-time action. This effective action has been obtained previously via the string S-matrix approach.     

Covariant unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory

A new type of D = 10 harmonic superspace with two generations of harmonics allows us to reduce the D = 10, N = 1 Brink-Schwarz (BS) superpaticle to a system whose constraints are all first class, functionally independent and Lorentz-covariant. Given these properties, the covariant BFV-BRST quantization of the system is straightforward. By second quantizing this system, we circumvent the no-go theorem which forbids the existence of a covariant off-shell unconstrained superfield action for the linearized D = 10 super-Yang-Mills theory.     

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. Q_BRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

Supercovariant derivatives,super-Weyl groups,and N = 2 supergravity

We analyze the kinematic constraints for N = 2 Poincaré supergravity within the context of “superconformal symmetry breakdown”. We find that N = 2 supergravity is described in terms of two independent supertensors: W_αβij and T_αi. We also discuss general properties of superspace covariant derivatives to derive the relation of superspace to component approaches.     

Deformation of super Virasoro algebra in noncommutative quantum superspace

We present a twisted commutator deformation for N = 1,2 super Virasoro algebras based on GL_q(1,1) covariant noncommutative superspace.     

A six-dimensional superspace approach to extended superfields

We present an improved formalism for treating six-dimensional superspace and apply it to writing linearized N = 2 Yang-Mills theory and the N = 2 relaxed hypermultiplet in SU(2) covariant forms that are simpler than the known four-dimensional forms.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.