Showing papers on "Superspace published in 2005"

Theory and Phenomenology of SParticles: an Account of Four-Dimensional N=1 Supersymmetry in High Energy Physics

Abstract: Introduction and Overview: Supersymmetry: Why and How Supersymmetry Formalism: Preliminaries Algebraic Aspects Free Superfields in Superspace Interacting Superfields Superspace Perturbation Theory and Supergraphs General Aspects of Supersymmetry Breaking Supersymmetry Phenomenology: Basic Structure of the MSSM Soft Supersymmetry Breaking in the MSSM Higgs Bosons in the MSSM Evolution from Very High Energies Gravity Mediated Supersymmetry Breaking Gauge Mediated Supersymmetry Breaking Beyond the MSSM Supersymmetry at Colliders Supersymmetric Cosmology Conclusion: Wish List, Roadmap and Fine Tuning.

A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges

Abstract: We formulate supersymmetric Euclidean spacetime Ad* lattices whose classical continuum limits are U(N) supersymmetric Yang-Mills theories with sixteen supercharges in d=1,2,3 and 4 dimensions. This family includes the especially interesting N=4 supersymmetry in four dimensions, as well as a Euclidean path integral formulation of Matrix Theory on a one dimensional lattice.

Supersymmetry and homogeneity of M-theory backgrounds

Abstract: We describe the construction of a Lie superalgebra associated with an arbitrary supersymmetric M-theory background, and discuss some examples We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively In particular, we prove that backgrounds with more than 24 supersymmetries are necessarily (locally) homogeneous Furthermore we provide evidence that 24 is the minimal number of supersymmetries which guarantees this

Classification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics

Abstract: We present an algorithmic classification of the irreps of the $N$-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields. Our work is based on the 1-to-1 \cite{pt} correspondence between Weyl-type Clifford algebras (whose irreps are fully classified) and classes of irreps of the $N$-extended 1D supersymmetry. The complete classification of irreps is presented up to $N\leq 10$. The fields of an irrep are accommodated in $l$ different spin states. N=10 is the minimal value admitting length $l>4$ irreps. The classification of length-4 irreps of the N=12 and {\em real} N=11 extended supersymmetries is also explicitly presented.\par Tensoring irreps allows us to systematically construct manifestly ($N$-extended) supersymmetric multi-linear invariants {\em without} introducing a superspace formalism. Multi-linear invariants can be constructed both for {\em unconstrained} and {\em multi-linearly constrained} fields. A whole class of off-shell invariant actions are produced in association with each irreducible representation. The explicit example of the N=8 off-shell action of the $(1,8,7)$ multiplet is presented.\par Tensoring zero-energy irreps leads us to the notion of the {\em fusion algebra} of the 1D $N$-extended supersymmetric vacua.

Supersymmetric corrections to eleven-dimensional supergravity

Abstract: In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi identities. These identities are solved to linear order in a deformation parameter introduced via the dimension zero supertorsion given in its most general form. The theory so obtained is referred to as the deformed theory (to avoid the previously used term "off-shell"). An important by-product of this result is that any higher derivative correction to ordinary supergravity of the same dimension as R^4, but not necessarily containing it, derived e.g. from M-theory, must appear in a form compatible with the equations obtained here. Unfortunately we have not yet much to say about the explicit structure of these corrections in terms of the fields in the massless supermultiplet. Our results are potentially powerful since if the dimension zero torsion could be derived by other means, our reformulation of the Bianchi identities as a number of algebraic relations implies that the full theory would be known to first order in the deformation, including the dynamics. We mention briefly some methods to derive the information needed to obtain explicit answers both in the context of supergravity and ten-dimensional super-Yang-Mills where the situation is better understood. Other relevant aspects like spinorial cohomology, the role of the 3- and 6-form potentials and the connection of these results to M2 and M5 branes are also commented upon.

On Five-dimensional Superspaces

Abstract: Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As a first step toward elaborating such supergraph techniques, we develop in this letter a manifestly supersymmetric formulation for 5D globally supersymmetric theories with eight supercharges. Simple rules are given to reduce 5D superspace actions to a hybrid form which keeps manifest only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were carefully worked out by rewriting the component actions in terms of simple superfields). To demonstrate the power of this formalism for model building applications, two families of off-shell supersymmetric nonlinear sigma-models in five dimensions are presented (including those with cotangent bundles of Kahler manifolds as target spaces). We elaborate, trying to make our presentation maximally clear and self-contained, on the techniques of 5D harmonic and projective superspaces used at some stages in this letter.

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

Abstract: In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.

The supermembrane revisited

Abstract: The M2-brane is studied from the perspective of superembeddings. We review the derivation of the M2-brane dynamics and the supergravity constraints from the standard superembedding constraint and we discuss explicitly the induced d = 3, N = 8 superconformal geometry on the worldvolume. We show that the gauged supermembrane, for a target space with a U(1) isometry, is the standard D2-brane in a type IIA supergravity background. In particular, the D2-brane action, complete with the Dirac–Born–Infeld term, arises from the gauged Wess–Zumino worldvolume 4-form via the brane action principle. The discussion is extended to the massive D2-brane considered as a gauged supermembrane in a massive D = 11 superspace background. Type IIA supergeometry is derived using Kaluza–Klein techniques in superspace.

Eleven-dimensional supergravity in light-cone superspace

Abstract: We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant \kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured.

Covariant quantization of N=1/2 SYM theories and supergauge invariance

Abstract: So far, quantum properties of N = 1/2 nonanticommutative (NAC) super Yang– Mills theories have been investigated in the WZ gauge. The gauge independence of the results requires assuming that at the quantum level supergauge invariance is not broken by nonanticommutative geometry. In this paper we use an alternative approach which allows studying these theories in a manifestly gauge independent superspace setup. This is accomplished by generalizing the background field method to the NAC case, by moving to a momentum superspace where star products are treated as exponential factors and by developing momentum supergraph techniques. We compute the one–loop gauge effective action for NAC U(N) gauge theories with matter in the adjoint representation. Despite the appearance of divergent contributions which break (super)gauge invariance, we prove that the effective action at this order is indeed invariant.

Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace

Abstract: We extend the analysis of hep-th/0408069 on a Lorentz invariant interpretation of noncommutative spacetime to field theories on non-anticommutative superspace with half the supersymmetries broken. By defining a Drinfeld-twisted Hopf superalgebra, it is shown that one can restore twisted supersymmetry and therefore obtain a twisted version of the chiral rings along with certain Ward-Takahashi identities. Moreover, we argue that the representation content of theories on the deformed superspace is identical to that of their undeformed cousins and comment on the consequences of our analysis concerning non-renormalization theorems.

Multigluon amplitudes, N=4 constraints, and the Wess-Zumino-Witten model

Abstract: Classical N=4 Yang-Mills theory is defined by the superspace constraints. We obtain a solution of a subset of these constraints and show that it leads to the maximally helicity violating amplitudes. The action which leads to the solvable part of the constraints is a Wess-Zumino-Witten action on a suitably extended superspace. The non-maximally helicity violating tree amplitudes can also be expressed in terms of this action.

On massive tensor multiplets

Abstract: Massive tensor multiplets have recently been scrutinized in [1] and [2], as they appear in orientifold compactifications of type-IIB string theory. Here we formulate several dually equivalent models for massive = 1,2 tensor multiplets in four space-time dimensions. In the = 2 case, we employ harmonic and projective superspace techniques.

Berezinians, Exterior Powers and Recurrent Sequences

Abstract: We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V We show that traces of exterior powers of A satisfy universal recurrence relations of period q ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V) They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants We analyze the Cayley–Hamilton identity in a superspace Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule

Lorentz invariant and supersymmetric interpretation of noncommutative quantum field theory

Abstract: In this paper, using a Hopf-algebraic method, we construct deformed Poincare SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincare algebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired SUSY in non(anti)commutative superspace.

Mirror symmetry of Calabi-Yau supermanifolds

Abstract: We study super Landau–Ginzburg mirrors of the weighted projective superspace WCP3|2 which is a Calabi–Yau supermanifold and appeared in hep-th/0312171 in the topological B-model. One of them is an elliptic fibration over the complex plane whose coordinate is given in terms of two bosonic and two fermionic variables as well as Kahler parameter of WCP3|2. The other is some patch of a degree-3 Calabi–Yau hypersurface in CP2 fibered by the complex plane whose coordinate depends on both the above four variables and Kahler parameter but its dependence behaves quite differently.

6D Supersymmetry, Projective Superspace and 4D, N=1 Superfields

Abstract: In this note, we establish the formulation of 6D, N=1 hypermultiplets in terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to 6D, N=1 Yang-Mills multiplets is described. A 6D, N=1 projective superspace formulation is given in which the above multiplets naturally emerge. The covariant superspace quantization of these multiplets is studied in details.

Generalized Kahler manifolds and off-shell supersymmetry

Abstract: We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.

Superfield integrals in high dimensions

Abstract: We present an efficient, covariant, graph-based method to integrate superfields over fermionic spaces of high dimensionality. We illustrate this method with the compu- tation of the most general sixteen-dimensional Majorana-Weyl integral in ten dimensions. Our method has applications to the construction of higher-derivative supergravity actions as well as the computation of string and membrane vertex operator correlators.