Nonlocal N = 1 $$ \mathcal{N}=1 $$ supersymmetry

Abstract

We construct N = 1 supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of Kähler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.

Ghost-free scalar-fermion interactions

“…whereà ab is the kinetic matrix of the redefined scalar fields f A . We note that, under the field redefinition, the Lagrangians (36), (37), and (38), are not mixed since the transformation does not include the derivatives of the fields. From the definition of the kinetic matrix, the quadratic terms in derivatives in the Lagrangian (38) can be responsible for the kinetic matrix, while linear or lower ones (37), (36) are obviously not.…”

Higgs mechanism in nonlocal field theories

“…Second, the exponential factor of the d'Alembertian in eq. (1.1) is known to make mild the UV behavior of loop diagrams and thus has been studied not only in the context of string theory [11][12][13][14][15][16][17][18][19][20][21][22] but also as an alternative approach to quantum field theories and gravity [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. It is therefore interesting to study consistency of nonlocal field theories by themselves.…”

Ghost-free vector superfield actions in supersymmetric higher-derivative theories

“…Such terms were used in several SUSY higher-derivative chiral models; low-energy effective theory [23][24][25][26], coupling to supergravity (SUGRA) [21,27] and its applications [20] to Galileons [28] and ghost condensation [22], a Dirac-Born-Infeld (DBI) inflation [29], flattening of the inflaton potential [30,31], topological solitons such as a BPS baby Skyrme model [32][33][34][35][36][37], a Skyrme model [38][39][40], BPS solitons [34,35,41] and their effective action [42], nonlinear realizations [43], and a possibility of modulated vacua [44,45]. In addition, different ghost-free higher-derivative actions of a chiral superfield are possible in the global [46] and SUGRA [47] cases as well as a non-local theory [48].…”