Construction of the superfield action of the = (1, 0), = 6 non-Abelian tensor multiplet based on the non-Abelian tensor hierarchies is considered. It is shown that while straightforward non-Abelian generalization of the Pasti-Sorokin-Tonin action is not a workable solution, a suitable truncation of the PST action still can be modified to include non-Abelian tensor field. In the modified action, the self-dual equation of motion of the tensor field is induced by a composite Lagrange multiplier, which is not a component of a standard dynamical tensor multiplet. As a result, the constraint that enforces the gauge group to be non-compact, as in the usual tensor hierarchies, can be avoided.

Russia

Nikolay Kozyrev

Improved non-Abelian tensor multiplet action

In this paper the harmonic superspace action of the tensor multiplet of N = (1, 0), d = 6 supersymmetry is constructed which in the bosonic limit reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field. The action involves, besides the potential containing the dynamical fields, also an auxiliary tensor multiplet and a set of analytic superfields with gauge PST scalar among them. For each of gauge symmetries of the PST action, a superfield analog is found. The equations of motion are calculated and it is shown that no extra degrees of freedom appear.

JINR

Supersymmetrizing the Pasti-Sorokin-Tonin action

In this paper we demonstrate that the different generalizations of the Schwarzians, supersymmetric or purely bosonic, can be easily constructed by using the nonlinear realizations technique.

Sergey Krivonos

Generalized Schwarzians

It was recently demonstrated that super-Schwarzian derivatives can be constructed from the Cartan forms of the superconformal supergroups <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>1</mn><mo>)</mo></mrow></math>, <math><mrow><mi>O</mi><mi>S</mi><mi>p</mi><mo>(</mo><mn>3</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>, <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></mrow></math>. Roughly speaking, the super-Schwarzian is just the component of the corresponding Cartan forms with the lowest dimension. In this paper, we apply the same approach to superalgebra <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>α</mi><mo>)</mo></math>. The minimal set of constraints we used includes: (a) introducing new superspace coordinates the Cartan forms depend on, which are completely invariant with respect to the corresponding group; (b) nullifying the form for dilatation. In contrast to the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>|</mo><mn>2</mn><mo>)</mo></math> case, the new super-Schwarzian appears to be a <math><mi>d</mi><msup><mi>θ</mi><mrow><mi>i</mi><mi>a</mi></mrow></msup></math> component of the form for <math><mi>s</mi><mi>u</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> automorphism.

<math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Schwarzian with <math><mi>D</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>;</mo><mi>α</mi><mo>)</mo></math> symmetry

In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 0, 1, 2, 3, 4 supersymmetric Schwarzians can be systematically obtained as certain projections of Maurer-Cartan forms of superconformal groups after imposing simple conditions on them. We also present the supersymmetric Schwarzian actions defined as the integrals of products of Cartan forms. In contrast with the previous attempts to obtain the super-Schwarzians within nonlinear realizations technique, our set of constraints does not impose any restriction on the super-Schwarzians.

(Super)Schwarzian mechanics

Among the solutions of string theory and supergravity which preserve some fraction of supersymmetry, the best known are those that leave one half of the supersymmetry unbroken, and there is a large number of field theory models with this pattern of supersymmetry breaking. However, a lot of brane configurations exist which preserve only <math><mn>1</mn><mo>/</mo><mn>4</mn></math>, <math><mn>1</mn><mo>/</mo><mn>8</mn></math>, or more exotic fractions of supersymmetry, and field theory side of these systems remains largely unexplored. To find whether the formalism of nonlinear realizations is useful in construction of models of this type, we consider the systems of some <math><msub><mi>N</mi><mn>0</mn></msub></math> scalar and vector <math><mi>N</mi><mo>=</mo><mn>1</mn></math>, <math><mi>d</mi><mo>=</mo><mn>3</mn></math> Goldstone supermultiplets. We find that it is possible to construct an <math><mi>S</mi><mi>O</mi><mo>(</mo><msub><mi>N</mi><mn>0</mn></msub><mo>)</mo></math> invariant theory of <math><msub><mi>N</mi><mn>0</mn></msub></math> scalar multiplets with <math><msub><mi>N</mi><mn>0</mn></msub></math> broken supersymmetries. For <math><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>3</mn></math> or <math><msub><mi>N</mi><mn>0</mn></msub><mo>≥</mo><mn>5</mn></math> its action is not of Nambu-Goto type and its structure remains universal for arbitrary <math><msub><mi>N</mi><mn>0</mn></msub></math>. The cases of <math><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>1</mn></math>, 2 correspond to the membranes in <math><mi>D</mi><mo>=</mo><mn>4</mn></math> and <math><mi>D</mi><mo>=</mo><mn>5</mn></math>, respectively, while for <math><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>4</mn></math> some arbitrariness in the action remains, and with proper choice of parameters, it is possible to obtain the action of the membrane in <math><mi>D</mi><mo>=</mo><mn>7</mn></math> in the bosonic limit. It is also shown that the <math><mi>S</mi><mi>O</mi><mo>(</mo><msub><mi>N</mi><mn>0</mn></msub><mo>)</mo></math> invariant action of <math><msub><mi>N</mi><mn>0</mn></msub></math> vector multiplets with <math><mn>1</mn><mo>/</mo><msub><mi>N</mi><mn>0</mn></msub></math> pattern of supersymmetry breaking does not exist for arbitrary <math><msub><mi>N</mi><mn>0</mn></msub></math>.

Partial breaking of arbitrary amount of <math><mi>d</mi><mo>=</mo><mn>3</mn></math> supersymmetry

The formalism of nonlinear realizations is used to construct a theory with 1/2 partial breaking of global supersymmetry with the N = (1, 0), d = 6 abelian vector multiplet as a Goldstone superfield. Much like the case of the N = 2, d = 4 Born-Infeld theory, proper irreducibility conditions of the multiplet are selected by the invariance with respect to the external automorphisms of the Poincaré superalgebra. They are found in the lowest nontrivial order in the auxiliary field. The fermionic contributions to the Bianchi identity are restored by assuming its covariance with respect to broken supersymmetry. The invariance of the action with respect to unbroken supersymmetry is checked in the lowest order in the fermionic fields. The supersymmetry preserving reduction of the d = 6 action to four dimensions is performed, resulting in the N = 4, d = 4 Born-Infeld theory. As expected, the reduced action enjoys U(1) self-duality.

Component d = 6 Born-Infeld theory with N = (2, 0) → N = (1, 0) supersymmetry breaking

We present SU(2|1) supersymmetric mechanics on n-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV equations specified by the manifold’s metric and curvature tensor. We consider the most general u(2)-valued prepotential, which contains both types (with and without spin variables), previously considered only separately. For the case of real Kähler manifolds we construct all possible interactions. For isotropic (so(n)-invariant) spaces we provide admissible prepotentials for any solution to the curved WDVV equations. All known one-dimensional SU(2|1) supersymmetric models are reproduced.

Germany

Olaf Lechtenfeld

Anton Sutulin

SU(2|1) supersymmetric mechanics on curved spaces

We present <math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric mechanics on <math><mi>n</mi></math>-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten–Dijkgraaf–Verlinde–Verlinde equations specified by the presence of the manifold’s curvature tensor. Solutions of original Witten–Dijkgraaf–Verlinde–Verlinde equations and related prepotentials defining <math><mi>N</mi><mo>=</mo><mn>4</mn></math> superconformal mechanics in flat space can be lifted to <math><mi>s</mi><mi>o</mi><mo>(</mo><mi>n</mi><mo>)</mo></math>-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of <math><mi>n</mi></math> copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.