On-shell Supersymmetry Research Articles

On-shell supersymmetry and higher-spin amplitudes

We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for mathcal{N} = 1, 2 and 4 theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with mathcal{N} = 4 Supersymmetry in 3+1 dimensions.

On-shell supersymmetry breaking in the Abelian Chern-Simons-matter model in three dimensions of spacetime

This study examines on-shell supersymmetry breaking in the Abelian $\mathcal{N}=1$ Chern-Simons-matter model within a three-dimensional spacetime. The classical Lagrangian is scale-invariant, but two-loop radiative corrections to the effective potential break this symmetry, along with gauge and on-shell supersymmetry. To investigate this issue, the Renormalization Group Equation is used to calculate the two-loop effective potential.

Unconstrained massless higher spin supermultiplet in AdS4 spacetime

We consider unconstrained formulation of the higher spin gauge theory in anti--de Sitter (AdS) spacetime, given by actions [A. Y. Segal, arXiv:0103028; M. Najafizadeh, Phys. Rev. D 98, 125012 (2018)], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin supermultiplet in four-dimensional ${\mathrm{AdS}}_{4}$. Such an irreducible supermultiplet $({\mathrm{\ensuremath{\Phi}}}_{1},{\mathrm{\ensuremath{\Phi}}}_{2};{\mathrm{\ensuremath{\Psi}}}_{1},{\mathrm{\ensuremath{\Psi}}}_{2})$ contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank $s=0,1,\dots{},\ensuremath{\infty}$), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin $s=\frac{1}{2},\frac{3}{2},\dots{},\ensuremath{\infty}$).

Correspondence between the twisted N=2 super-Yang-Mills and conformal Baulieu-Singer theories

We characterize the correspondence between the twisted $N=2$ super-Yang-Mills theory and the Baulieu-Singer topological theory quantized in the self-dual Landau gauges. While the first is based on an on-shell supersymmetry, the second is based on an off-shell Becchi-Rouet-Stora-Tyutin symmetry. Because of the equivariant cohomology, the twisted $N=2$ in the ultraviolet regime and Baulieu-Singer theories share the same observables, the Donaldson invariants for 4-manifolds. The triviality of the Gribov copies in the Baulieu-Singer theory in these gauges shows that working in the instanton moduli space on the twisted $N=2$ side is equivalent to working in the self-dual gauges on the Baulieu-Singer one. After proving the vanishing of the $\beta$ function in the Baulieu-Singer theory, we conclude that the twisted $N=2$ in the ultraviolet regime, in any Riemannian manifold, is correspondent to the Baulieu-Singer theory in the self-dual Landau gauges -- a conformal gauge theory defined in Euclidean flat space.

On the ubiquity of electromagnetic-duality rotations in 4D, 𝒩 = 1 holoraumy tensors for on-shell 4D supermultiplets

Holoraumy is a tool being developed for dimensional enhancement (supersymmetry holography) where the goal is to build higher-dimensional supersymmetric multiplets from lower-dimensional supersymmetric multiplets. In this paper, for the first time we investigate holoraumy for on-shell supersymmetry. Specifically, the holoraumy tensors for a number of familiar 4D, [Formula: see text] multiplets are calculated. It is shown in all of these cases of on-shell theories, the holoraumy is of the form of an electromagnetic duality charge multiplying a composite transformation involving an electromagnetic duality rotation through an angle of [Formula: see text] times a space–time translation. The details of our calculations can be found at the HEPTHools Data Repository .

Euclidean supergravity

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. We also briefly discuss the non-linear supermultiplet. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity upon introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.

The higher derivative regularization and quantum corrections in [formula omitted] supersymmetric theories

We construct a new version of the higher covariant derivative regularization for a general N=2 supersymmetric gauge theory formulated in terms of N=1 superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest N=1 supersymmetry and under the second hidden on-shell supersymmetry. The regularizing N=2 supersymmetric higher derivative term is found in the explicit form in terms of N=1 superfields. Thus, N=2 supersymmetry is broken only by the gauge fixing procedure. Then we analyze the exact NSVZ β-function and prove that in the considered model its higher loop structure is determined by the anomalous dimension of the chiral superfield Φ in the adjoint representation which is the N=2 superpartner of the gauge superfield V. Using the background field method we find that this anomalous dimension is related with the anomalous dimension of the hypermultiplet and vanishes if the effective action is invariant under N=2 background supersymmetry. As a consequence, in this case the higher loop contributions to β-function also vanish. The one-loop renormalization structure in the considered regularization is also studied by the explicit calculations of the one-loop renormalization constants.

Scattering amplitudes of massiveN=2gauge theories in three dimensions

We study the scattering amplitudes of mass-deformed Chern-Simons theories and Yang-Mills-Chern-Simons theories with $\mathcal{N}=2$ supersymmetry in three dimensions. In particular, we derive the on-shell supersymmetry algebras which underlie the scattering matrices of these theories. We then compute various 3 and 4-point on-shell tree-level amplitudes in these theories. For the mass-deformed Chern-Simons theory, odd-point amplitudes vanish and we find that all of the 4-point amplitudes can be encoded elegantly in superamplitudes. For the Yang-Mills-Chern-Simons theory, we obtain all of the 4-point tree-level amplitudes using a combination of perturbative techniques and algebraic constraints and we comment on difficulties related to computing amplitudes with external gauge fields using Feynman diagrams. Finally, we propose a Britto-Cachazo-Feng-Witten recursion relation for mass-deformed theories in three dimensions and discuss the applicability of this proposal to mass-deformed $\mathcal{N}=2$ theories.

Semichiral Sigma models with 4D hyperkähler geometry

Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such models and find that a rather general ansatz for the additional supersymmetry (not involving central charge transformations) leads to hyperk\"ahler geometry. We give non-trivial examples of these models.

Maximal super Yang-Mills theories on curved background with off-shell supercharges

We construct d<=7 dimensional maximally supersymmetric Yang-Mills theories on a class of curved backgrounds with off-shell supercharges. The off-shell supersymmetry is mainly a generalization of on-shell supersymmetry constructed previously by Blau. We present several examples of backgrounds and discuss the number of the preserved supersymmetries on these backgrounds. We also construct another maximally supersymmetric Yang-Mills theories on S^3 by dimensional reducing along the R-direction of N=4 super Yang-Mills theory on RxS^3.

Three particle superstring amplitudes with massive legs

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.

Simple superamplitudes in higher dimensions

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.

On-shell supersymmetry for massive multiplets

The consequences of on-shell supersymmetry are studied for scattering amplitudes with massive particles in four dimensions. Using the massive version of the spinor-helicity formalism, the supersymmetry transformations relating products of on-shell states are derived directly from the on-shell supersymmetry algebra for any massive representation. Solutions to the resulting Ward identities can be constructed as functions on the on-shell superspaces that are obtained from the coherent-state method. In simple cases, it is shown that these superspaces allow one to construct explicitly supersymmetric scattering amplitudes. Supersymmetric on-shell recursion relations for tree-level superamplitudes with massive particles are introduced. As examples, simple supersymmetric amplitudes are constructed in Supersymmetric Quantum Chromodynamics (SQCD), the Abelian Higgs model, the Coulomb branch of $\mathcal{N}=4$, QCD with an effective Higgs-gluon coupling and for massive vector-boson currents.

Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of algebraic renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.

Covariant representation theory of the Poincaré algebra and some of its extensions

There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the Poincaré algebra quantum numbers of the particles involved. Technically, this is most easily done using the well-known four dimensional spinor helicity method. In this article a natural generalization to all dimensions higher than four is obtained based on a covariant version of the representation theory of the Poincaré algebra. Covariant expressions for all possible polarization states, both bosonic and fermionic, are constructed. For the fermionic states the analysis leads directly to pure spinors. The natural extension to the representation theory of the on-shell supersymmetry algebra results in an elementary derivation of the supersymmetry Ward identities for scattering amplitudes with massless or massive legs in any integer dimension from four onwards. As a proof-of-concept application a higher dimensional analog of the vanishing helicity-equal amplitudes in four dimensions is presented in (super) Yang-Mills theory, Einstein (super-)gravity and superstring theory in a flat background.

Boundary conditions in the Mirabelli and Peskin model

We show how the (globally supersymmetric) model of Mirabelli and Peskin can be formulated in the boundary (``downstairs'' or ``interval'') picture. The necessary Gibbons-Hawking-like terms appear naturally when using (codimension one) superfields. This formulation is free of the \delta(0) ambiguities of the orbifold (``upstairs'') picture while describing the same physics since the boundary conditions on the fundamental domain are the same. The (natural) boundary conditions follow from the variational principle and form a closed orbit under supersymmetry variation. They reduce to the ``odd =0'' boundary conditions in the absence of bulk-boundary coupling. We emphasize that the action is supersymmetric without the use of any boundary conditions in the off-shell formulation (but some boundary conditions are necessary for on-shell supersymmetry!).

Accelerating D-branes

Higher derivative terms are computed in the one-loop effective action governing the interactions of D3-branes, in two ways: (1) in a formalism with N=2 supersymmetry preserved off-shell, and (2) in the standard background field formalism, with only on-shell supersymmetry. It is shown that these calculations only agree using tree-level equations of motion. The off-shell supersymmetric calculation exhibits acceleration terms that appear in terms with four derivatives. These may imply disagreement at two-loop order between supergravity and Yang-Mills descriptions of D-brane dynamics.

Induced on-shell supersymmetry in eikonal scattering.

Generically coupled neutral scalar bosons and fermions are shown, in the eikonal kinematical limit, to be described by a reduced (free field) theory with $N=1$ on-shell supersymmetry. Charged scalars and spinors turn out to be described in the eikonal limit by a reduced interacting theory with a modified and restricted on-shell $N=1$ supersymmetry. Consequences of such a symmetry for the nontrivial scattering amplitudes in this latter case are discussed.

Supersymmetric reduction of the Wess-Zumino model

The symmetry reduction of the Wess-Zumino model by subgroups of the Poincare group is investigated. A class of bidimensional subgroups of SO(3, 1) leading to supersymmetric residual systems is given. The reduction by a representative is carried out and the on-shell residual supersymmetry transformations are exhibited.