Nonlinear Realizations Of Supersymmetry And Study On Relations Of Scattering Amplitudes

Supersymmetry (SUSY) connects bosons and fermions. It could be realized in nature as one possible extension beyond the standard model. It has also provided crucial insights in the computation of scattering amplitudes in quantum field theories. If SUSY does exist, it must be broken below the TeV scale and preferably, broken spontaneously. For theoretical and phenomenological purposes, it is thus of importance to have efficient formulations of its effective theories at low energy. One line of the thesis is to study relations between different formulations of low-energy effective theories and insights gained from each. The second line of the thesis is a study on scattering amplitudes. The importance of scattering amplitudes is self-evident, as they connect theoretical and experimental physics. Recent progresses in calculating amplitudes are closely related to theoretical experimentations with SUSY. Specifically, we will discuss the following issues:(1) Traditionally, low-energy effective theories for spontaneously broken SUSY are ex-pressed in terms of the so-called standard nonlinear realization. Recently, a constrained superfield formalism has been proposed to analyze the same physics. We prove that the constrained formalism can be reformulated in the language of standard realization of non-linear SUSY. New relations are uncovered in the standard realization of nonlinear SUSY.(2) We construct a Goldstino field in the nonlinear realization of SUSY from an appro-priate chiral super-multiplet of the linear theory, in general O’Raifeartaigh-like models. The linear theories are reformulated into their nonlinear versions, via a standard proce-dure. The Goldstino field disappears totally from the original Lagrangian in the process, butreemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space-time derivative, as one would have expected. (3) We revisit the nonlinear realization of spontaneously broken N=1SUS Y. The con-strained superfield formalism as proposed in can be reinterpreted in the language of stan-dard realization of nonlinear SUSY via anew 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 defi-nitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials.(4) We provide a self-contained discussion of the so-called Akulov-Volkov action SAV, which is traditionally taken to be the leading-order action of Goldstino field. Explicit ex-pressions for SAV and its chiral version SAVch are presented. We show how these actions are related to the leading-order action SNL proposed in the newly proposed constrained super-field formalism.SNL may yield SAV/SAVch or a totally different action SKS, depending on how the auxiliary field in the former is integrated out. However, SKS and SAv/SAVch always yield the same S-matrix elements, as expected from general considerations in quantum field theory.(5) A UV SUSY-breaking theory can be realized either linearly or nonlinearly and they form dual descriptions of the UV SUSY-breaking theory. Guided by this observation, we find subtle identities involving the Goldstino field and matter fields in the standard nonlin-ear realization from trivial ones in the linear realization.Rather complicated integrands in the standard nonlinear realization are identified as total-divergences. Especially, identities only involving the Goldstino field reveal the self-consistency of the Grassmann algebra. As an application of these identities, we prove that the nonlinear Kahler potential without or with gauge interactions is unique, if the corresponding linear one is fixed. Our identities pick out the total-divergence terms and guarantee this uniqueness.(6) In BCFW recursion relations, boundary terms do not always vanish if one chooses arbitrarily pairs of external momentum for reference. Boundary contributions were found to be closely related to roots of amplitudes. We use a novel way to re-derive BCFW recursion relations with boundary contributions. We generalize factorization limits to z-dependent ones, where information of roots is more transparent. Then, we demonstrate our analysis with several examples.(7) Algebraic relations are extensively studied, as they provide significant simplifications in calculations of scattering amplitudes. Tree-level BCJ relations reveal a duality between color and kinematic structure, which can be used to reduce the number of independent color-ordered amplitudes. At one-loop level in Yang-Mills theory, we investigate a similar BCJ relation[]. The four-point one-loop example in N=4SYM gives hints about the relations between integrands. The five-point example suggests that the general formula can be proven by the unitary-cut method. We prove a ’general’ BCJ relation for one-loop inte-grands by D-dimension unitary cut, which can be regarded as a non-trivial generalization of the (fundamental) BCJ relation given in.