Constrained Superfields and Standard Realization of Nonlinear Supersymmetry

A constrained superfield formalism has been proposed recently to analyze the low energy physics related to Goldstinos. We prove that this formalism can be reformulated in the language of standard realization of nonlinear supersymmetry. New relations have been uncovered in the standard realization of nonlinear supersymmetry.Comment: 8+1 pages, Latex, expanded discussions on scalar and vector field

Nonlinear Realization of Spontaneously Broken N=1 Supersymmetry Revisited

This paper revisits the nonlinear realization of spontaneously broken N=1 supersymmetry. It is shown that the constrained superfield formalism can be reinterpreted in the language of standard realization of nonlinear supersymmetry via a new and simpler route. Explicit formulas of actions are presented for general renormalizable theories with or without gauge interactions. The nonlinear Wess-Zumino gauge is discussed and relations are pointed out for different definitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials.Comment: 1+18 pages, LaTe

A Bound on the Superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, 2|W|< f_a F, where f_a and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss several possible applications.Comment: 20 page

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

We consider a manifold endowed with two different vielbeins $E^{A}{}_{\mu}$ and $L^{A}{}_{\mu}$ corresponding to two different metrics $g_{\mu\nu}$ and $f_{\mu\nu}$. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu}$ can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.Comment: 20 pages. Section 7, prop. 6 and 7. added. Some results made more precis

Goldstino superfields for spontaneously broken N=2 supersymmetry

We examine spontaneously broken N=2 supersymmetry in four dimensions and associate a spinor superfield with each Goldstino via a finite supersymmetry transformation with parameters that are the Grassmann coordinates of N=2 superspace. Making use of a special choice of coset parametrization allows us to develop a version of nonlinearly realized N=2 supersymmetry for which the associated Goldstino superfields are defined on harmonic superspace, thereby providing a natural mechanism for construction of a Goldstino action. The corresponding superfield Lagrangian is an O(4) multiplet. This property is used to reformulate the Goldstino action in projective superspace and in conventional N=2 superspace. We show how to generate matter couplings of the Goldstinos to supersymmetric matter using the N=2 harmonic, projective and full superspaces. As a bi-product of our consideration, we also derive an N=2 chiral Goldstino action.Comment: 20 pages, typos corrected, comments adde

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde