Non-linear realizations of supersymmetry with off-shell central charges

We present a new class of non-linear realizations of the extended supersymmetry algebra with central charges. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as in the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. We work in two dimensions and discuss its extension to higher dimensions.     

Superspace gauge theories with central charges

The superspace constraints leading to off-shell formulations of extended supersymmetric Yang-Mills theories for N = 2 and 4 are generalised to N = 6 in the abelian case. This leads to an on-shell representation of linearized N = 6 supergravity.     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Supersymmetric gauge anomalies in 2, 4, 6, and 10 dimensions

By solving the consistency condition in Wess-Zumino gauge, we derive explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theories. In dimensions 2, 4, and 6 we present a unified formula for the on-shell anomalies, in 6 dimensions also the off-shell version and in 10 dimensions the complete on-shell result.     

A new group theoretical technique for the analysis of Bianchi identities and its application to the auxiliary field problem of D = 5 supergravity

For any (super)group and hence for any geometrical (super)theory Bianchi identities imply that certain 3-forms vanish. In order to perform a systematic analysis of their implications in the presence of constraints one needs a complete basis of independent 3-forms spanning the 3-form linear space. In this paper we discuss a general procedure for the derivation of such a basis in the case of supersymmetric theories involving commuting spinor 1-forms. Our technique is based on the decomposition of the product of group representations into irreducible components and replaces all Fierz rearrangements. We give as examples the cases of N = 1, d = 4, N = 2, d = 4 and N = 2, d = 5 supergravity. Then applying our algebraic techniques to the last of these three models, the only other known example, besides N = 1, d = 4 supergravity, of a pure geometrical theory, we derive its off-shell structure containing 48 bosons and 48 fermions. The torsion-like constraints which we implement in the Bianchis in order to obtain our set of auxiliary fields are a subset of the complete set of variational equations of the theory so that we derive our off-shell multiplet without any reference to an embedding conformal symmetry. The point with which we still need to use ingenuity is the selection of those equations which are to be kept and those which are to be thrown out.     

Supersymmetric matter gravitino multiplets

We construct all on-shell, massless, supersymmetric multiplets with maximum field spin three-halves. The supergeometry of these theories is developed. We study the off-shell N = 1 matter gravitino multiplet and exhibit the supergeometries of the known theories. Explicit superfield constructions for two new off-shell theories are presented.     

Off-shell N = 8 supersymmetry with central charges

Using a new technique of dimensional reduction by Legendre transformation we derive an off-shell formulation of the N = 8 extended supersymmetry algebra, which is realised in the maximally extended supergravity theory. The theory has an Sp(8) manifest global invariance and some of the fields satisfy differential constraints.     

Towards Higher-N Superextensions of Born–Infeld Theory

We give a brief account of supersymmetric Born–Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N = 3 supersymmetric Born–Infeld theory which admits a natural off-shell formulation in N = 3 harmonic superspace.     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

(Super-) field theories from (super-) twistors

We obtain higher spin linearized field theories through the BRST second quantization of the classical D=4 massless point particle. By applying the same procedure to the classical supersymmetric particles, one obtains linearized N-extended off-shell unconstrained superfield actions. By extending the procedure to D=10, one is led to a new spacetime geometry which reduces in some limit to the usual D=10 Minkowski geometry.     

Supersymmetric Noether Currents and Seiberg–Witten Theory

The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to derive the mass-formula for the quantized Seiberg–Witten model from the supersymmetric algebra. We check that the mass-formula of the low-energy theory agrees with that of the full theory (in the broken phase).     

ℵ0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ℵ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

The supersymmetric Adler-Bardeen theorem and regularization by dimensional reduction

We examine the subtraction scheme dependence of the anomaly of the supersymmetric, gauge singlet axial current in pure and coupled supersymmetric Yang-Mills theories. Preserving supersymmetry and gauge invariance explicitly by using supersymmetric background field theory and dimensional reduction, we show that only the one-loop value of the axial anomaly is subtraction scheme independent, and that one can always define a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory. In general this subtraction scheme may be non-minimal, but in both the pure and the coupled theories, the Adler-Bardeen theorem is satisfied to two loops in minimal subtraction.     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Dimensional reduction via a novel Higgs mechanism

Many theories of quantum gravity live in higher dimensions, and their reduction to four dimensions via mechanisms such as Kaluza–Klein compactification or brane world models have associated problems. We propose a novel mechanism of dimensional reduction via spontaneous symmetry breaking of a higher dimensional local Lorentz group to one in lower dimensions. Working in the gauge theory formulation of gravity, we couple a Higgs field to spin connections, include a potential for the field, and show that for a suitable choice of Higgs vacuum, the local Lorentz symmetry of the action gets spontaneously reduced to one in a lower dimension. Thus effectively the dimension of spacetime gets reduced by one. This provides a viable mechanism for the dimensional reduction, and may have applications in theories of quantum gravity.     

The descent of off-shell supersymmetry to the mass shell

It is shown that classical actions for some “physically interesting” quantum field theories can be obtained as effective actions from the single “fundamental” theory of the Chern–Simons form. The physical degrees of freedom are encoded in the space of cohomologies of a certain differential operator. This observation suggests a different perspective on some of the supersymmetric properties of these effective theories. Namely, it is possible to construct a superfield formalism which allows to find off-shell SUSY actions for the on-shell supersymmetric theories, where conventional superfield formalism does not work. This formalism contains even auxiliary variables λ^α in addition to conventional odd variables θ^α. This idea is similar to the Pure Spinor construction. This paper is a short review of papers [11, 12]. Original results discussed below were obtained in collaboration with V. Alexandrov, A. Gorodentsev, A. Losev and V. Lysov.     

Beta functions and central charge of supersymmetric sigma models with torsion

We present a method for the computation of the renormalization group β-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with the expression found on group manifolds.     

Superpropagator and superconformal invariants

We construct a superpropagator in maximally supersymmetric Yang–Mills theory which is invariant off-shell under a chiral half of supersymmetries. Motivated by the duality with scattering amplitudes in this theory, we apply this superpropagator to supersymmetric Wilson loop on polygonal contours. By performing explicit one-loop calculations we confirm the absence of anomalies and verify the duality between the object under study and NMHV amplitudes.     

Regularization by dimensional reduction of supersymmetric and non-supersymmetric gauge theories

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.