The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

Superspace,dimensional reduction,and stochastic quantization

The equivalence between a 6-dimensional stochastic classical scalar field theory and the corresponding 4-dimensional quantum field theory has been shown to stem from a hidden supersymmetry of the former. This has led to a formulation of quantum field theory in a superspace of 6 commuting and 2 anticommuting dimensions. We study gauge and spinor field theories defined on this superspace, showing that the dimensional reduction is a consequence of the geometry of the superspace, and that the stochastic formalism for gauge theories is a natural consequence of the structure of the superspace theory. This allows us to extend the stochastic formalism to include spinors.     

The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

Deformed Super-Yang-Mills in Batalin-Vilkovisky Formalism

In this paper we will analyse a three dimensional super-Yang-Mills theory on a deformed superspace with boundaries. We show that it is possible to obtain an undeformed theory on the boundary if the bulk superspace is deformed by imposing a non-vanishing commutator between bosonic and fermionic coordinates. We will also analyse this theory in the Batalin-Vilkovisky (BV) formalism and show that these results also hold at a quantum level.     

Superspace unmasked: The physical interpretation of supergravity theory

Supergravity admits a geometric formulation in terms of an expanded algebra of functions on ordinary spacetime. This formulation, called graded manifold theory, is equivalent to the usual superspace supergravity constructions but avoids the anticommuting coordinates of superspace. The geometry suggests an operational interpretation of supergravity theory in terms of measurements made by local observers in spacetime.     

A homogeneous superspace relevant to superconformal field theory

An infinite-dimensional homogeneous superspace, determined by the choice of annihilation operators in a superconformal field theory, is introduced. Regularization of the field theory induces a central extension for the group which acts transitively on the space, and the cocycle for the central extension is computed. The vacuum states for the theory form a line bundle over the homogeneous superspace, and the curvature of the line bundle is calculated.     

A comment on superspace Bianchi identities and six-dimensional spacetime

We investigate the Bianchi identities for a superspace with a six-dimensional spacetime, under the assumption of certain superspace kinematic constraints. It is shown that these constraints lead to the supergravity theory recently discussed by Breitenlohner and Kabelschacht. However, we conclude that the resulting theory is consistent only if the curvature scalar of the six-dimensional spacetime vanishes.     

N=2 superparticles,RR fields,and noncommutative structures of (super)-spacetime

The recent developments in superstring theory prompted the study of non-commutative structures in superspace. Considering bosonic and fermionic strings in a constant antisymmetric background yields a non-vanishing commutator between the bosonic coordinates of the spacetime. Likewise, the presence of constant Ramond–Ramond (RR) background leads to a non-vanishing anti-commutator for the Grassmann coordinates of the superspace. The non-vanishing commutation relation between bosonic coordinates can also be derived using a particle moving in a magnetic background, we use superparticle to show how the non-commutative structures emerge in superspace. The derivation is original and it is shown that only a D0-brane in supergravity background reproduces the results obtained in string theory.     

A superspace formulation of the BV action for higher derivative theories

We first analyse the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under shift symmetry in the Batalin–Vilkovisky (BV) formalism. We show that the action for this theory can be written in a manifestly extended BRST invariant manner in superspace formalism using one Grassmann coordinate. It can also be written in a manifestly extended BRST invariant manner and on-shell manifestly extended anti-BRST invariant manner in superspace formalism using two Grassmann coordinates.     

Local BRS transformations and OSp(3,1¦2) symmetry of Yang-Mills theories

We consider a certain local generalization of BRS transformations of Yang-Mills theory in which the anti-commuting parameter is space time dependent. While these are not exact symmetries, they do lead to a new nontrivial WT identity. We make a precise connection between the “local BRS” and the broken orthosymplectic symmetry recently found in superspace formulation of Yang-Mills theory by showing that the local BRS WT identity is precisely the WT identity obtained in the superspace formulation via a superrotation. This “local BRS” WT identity could lead to new consequences not contained in the usual BRS WT identity.     

Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three-dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described in both superfield and component field forms. The relationship between these models and similar models in four-dimensional Minkowski space is described.     

Remarks about the thin sandwich conjecture

The thin sandwich conjecture in the initial value problem of general relativity is investigated by means of differential geometrical methods, in connection to the definition of arc length in a Wheeler superspace. The conjecture is proved to be false by good physical reasons. Its failure on a flat space is related to the “functional dimension” of the superspace and to the behaviour in the linearized theory of quantum gravitation.     

Superplane integrability and three dimensional supergravity

The requirement of integrability in all light-like superplanes yields the proper kinematical constraints for the three-dimensional supergravity theory formulated in superspace. The theory with the Breitenlohner set of auxiliary fields is obtained.     

On the interpretation of anticommuting variables in the theory of superspace

On the basis of cohomology theory, we consider a possible topological interpretation of Grassmann algebra used in the definition of superspace.     

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     

Superspace as a fibre space

Starting from the vector space of anticommuting elements and using the theory of fibre space, the superspace and supersymmetry theory is obtained from a geometrical point of view.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.