Left chiral “zero modes” in a super-self-dual Yang-Mills background

A super-self-duality constraint can be imposed on the curvature two-form in supersymmetric Yang-Mills theories formulated in euclidean superspace. If left covariantly chiral superfields are coupled to such a background, part of this space of superfields is annihilated by a superspace operator constructed from the quadratic part of the action. These are analogous to the zero modes of the Dirac equation which occur in the presence of a multi-instanton. Using the supersymmetric version of the ADHM formalism, this space of left covariantly chiral “zero mode” superfields is constructed in the fundamental representation of an SU(n) gauge group. It is shown to be spanned by a set of k superfields, where k is the instanton number of the bosonic component of the Yang-Mills background.     

Dynamical symmetry breaking in SYM theories as a non-semiclassical effect

We study supersymmetry breaking effects in N=1 SYM from the point of view of quantum effective actions. Restrictions on the geometry of the effective potential from superspace are known to be problematic in quantum effective actions, where explicit supersymmetry breaking can and must be studied. On the other hand the true ground state can be determined from this effective action, only. We study the problem whether some parts of superspace geometry are still relevant for the effective potential and discuss whether the ground states found this way justify a low energy approximation based on this geometry. The answer to both questions is negative. Essentially non-semiclassical effects change the behavior of the auxiliary fields completely and lead to the demand of a new interpretation of superspace geometry. These non-semiclassical effects can break supersymmetry. Received: 10 January 2002 / Revised version: 13 April 2002 / Published online: 18 October 2002 RID="*" ID="*" Work supported in part by the Schweizerischer Nationalfonds RID="a" ID="a" e-mail: bergamin@tph.tuwien.ac.at     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

Higher derivative modifications ofD=10 superspace Yang-Mills theories

We extend the superspace treatment of higher derivative supersymmetric Yang-Mills theories, emphasizing the role played by manifestD=10 Lorentz covariance and supersymmetry invariance. As an example, the superspace formulation of the effective action is considered for the massless fields in the open superstring, as well as in theSO(32) andE ₈×E₈ superstring theories. We show that there exists a unique modification of thef-tensor supercurrent which can provide the embedding of theO(α'³) string corrections in the slope parameter expansion for the Yang-Mills sector inD=10 superspace. The new correction term is relevant for the understanding of nonperturbative effects.     

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.     

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     

Global structures for the moduli of (punctured) super riemann surfaces

A fine moduli superspace for algebraic super Riemann surfaces with a level-n structure is constructed as a quotient of the split superscheme of local spin-gravitivo fields by an étale equivalence relation. This object is not a superscheme, but still has an interesting structure: it is an algebraic superspace, that is, an analytic superspace with sufficiently many meromorphic functions. The moduli of super Riemann surfaces with punctures (fixed points in the supersurface) is also constructed as an algebraic superspace. Moreover, when one only considers ordinary punctures (fixed points in the underlying ordinary curve), it turns out that the moduli is a true superscheme. We prove furthermore that this moduli superscheme is split.     

Superspace geometry and N = 1 non-minimal supergravity

We investigate superspace geometry for supergravity with non-minimal auxilliary fields. We find that the kinematic constraints and the superspace Bianchi identities are sufficient to obtain complete component expansions of all superspace quantities, including the vielbein and connection superfields. We include a detailed pedagogical discussion on the analysis of constrained superspace Bianchi identities, demonstrating how these are used to derive component field content and transformation laws. We also note that local, chiral supersymmetry representations which form arbitrary representations of the Lorentz group can exist only within the context of supergravity with non-minimal auxilliary fields.     

A superspace formulation of BRS/anti-BRS symmetric Yang-Mills effective action

We give a superspace formulation that generates the BRS/anti BRS invariant Yang Mills effective action of Baulieu Thierry-Mieg. This work generalizes our earlier work on superspace formulation for Faddeev Popov effective action. Our work differs from earlier works by other workers in that our superfields are completely unconstrained and our superspace is not just a formal device but allows superrotations. We construct a generating functions W? that has (broken) invariance under two separate sets of superrotations that mix x^μ with grassmannian coordinates λ and θ.These allow the BRS and anti-BRS WT identities for W? formulated as two simple elegant equations involving (?W?/?θ) and (?W?/?λ). We also note that quadratic guages can be naturally included straightforwardly in this superspace formulation.     

Renormalization theory in superspace

The auxiliary mass BPHZ renormalization procedure is extended to include theories defined in superspace. Ultraviolet and infrared power counting formulas for Feynman integrands in superspace are derived. A general momentum-superspace subtraction scheme is given which allows time-ordered Green functions of superfields to be defined as tempered distributions. Superfield normal product Green functions are introduced and the Zimmermann identity relating differently subtracted such products is established. Finally normal product field equations and the renormalized quantum action principle in superspace are derived.     

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.     

A superspace normal coordinate derivation of the density formula

Using normal coordinate expansions we derive by purely superspace methods the density formula giving the component action corresponding to a superspace supergravity-matter action.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

Superspace formulation of the dynamical symmetries of the Dirac magnetic monopole

The superspace formulation for the dynamical supersymmetry of the Pauli system in the presence of a Dirac magnetic monopole is presented. It is used to prove that Osp(1, 1) is the largest dynamical invariance group of this system. The action of finite transformations on the parameters of superspace and on the supervariables is given.     

Superspace and the spinning string

An ansatz is made for the supervierbein in the (2 + 2)-dimensional superspace appropriate for the spinning string. It is shown that, after substituting into a superspace action and integrating over the Grassmann co-ordinates, we obtain the locally supersymmetric action for the string in ordinary two-dimensional space.     

The density multiplet in superspace

We calculate the components of the density multipletE inN=1 superspace and the last component of the chiral density multiplet ? inSU(2) extended superspace with a minimal set of auxiliary fields.     

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.