Non-uniqueness of the supersymmetric extension of the O(3) σ-model

Yokokura

2018

We investigate three-form gauge theories with higher derivative interactions and their supersymmetric extensions in four space-time dimensions. For the bosonic three-form gauge theories, we show that derivatives on the field strength of the 3-form gauge field yield a tachyon as far as the Lagrangian contains a quadratic kinetic term, while such the term with opposite sign gives rise to a ghost. We confirm that there is neither a tachyon nor a ghost when all higher derivative terms are given by functions of the field strength. For this ghost/tachyon-free Lagrangian, we determine the boundary term necessary for the consistency between the equation of motion and energy-momentum tensor. For supersymmetric extensions, we present ghost/tachyon-free higher derivative interactions of arbitrary order of the field strength and corresponding boundary terms as well. * nitta@phys-h.keio.ac.jp † ryokokur@keio.jp 1 Introduction 3-form gauge theories in four-dimensional (4D) spacetime have been studied extensively in the past decades. They were first considered in the context of quantum chromodynamics (QCD) to describe a long-range confinement force between quarks [1,2]. Furthermore, a 3-form gauge field can be regarded to provide an effective description of a Chern-Simons 3-form in Yang-Mills theories [2,3], in particular in the context of the U(1) problem [4,5] and the strong CP problem [6][7][8]. In cosmology, a 3-form gauge field was used for dynamical neutralization of the cosmological constant [9-16], quintessence [17], inflationary models [18][19][20][21][22][23]. A relation between the 3-form gauge theories and condensed matter physics was also discussed, see e.g. [24]. A supersymmetric (SUSY) extension of the 3-form gauge fields was first formulated in Ref. [25]. The SUSY 3-form gauge fields naturally appear in superstring theory and M-theory, therefore they were studied extensively with various applications: supergravity (SUGRA) [26][27][28] (see Refs. [29,30] as a review), Stückelberg coupling [31-34], topological coupling [33,35,36], coupling with a membrane [37-39], alternative formulation of old-minimal SUGRA [37, 40-42], gaugino condensation in SUSY Yang-Mills theories [43, 44], the cosmological constant problem [41], SUSY breaking [41,45], string effective theories [42,[46][47][48], and inflationary models [35,49]. Complex 3-form gauge theories were also considered in Refs. [38,39,42].One of the characterizations of p-form gauge fields is their couplings to extended objects. As 1-form and 2-form gauge fields can be electrically coupled to a particle and string, respectively in 4D spacetime, a 3-form gauge field can be electrically coupled to a membrane [1]. Since membranes and 3-form gauge fields naturally arise in string theory and M-theory as fundamental degrees of freedom, 3-form gauge fields in 4D spacetime appear as 4D compactification of these theories. Another characteristic feature of the 3form gauge field is its coupling to scalar fields. Since a field strength of the 3-form gauge field is a 4-form, the ...

Section: Hd (Bulk)mentioning

confidence: 99%

Higher derivative three-form gauge theories and their supersymmetric extension

Yokokura

2018

“…In four dimensional (4D) N = 1 SUSY theories, a classification of higher-derivative terms free from ghosts and the auxiliary field problem was given for chiral superfields [18][19][20][21] as well as for vector superfields [22]. Such higherderivative interactions of chiral superfields were applied to low-energy effective theory [23][24][25][26] (see also [27]), coupling to SUGRA [20,28], Galileons [19], ghost condensation [21], a Dirac-Born-Infeld (DBI) inflation [29], flattening of the inflaton potential [30,31], a (baby) Skyrme model [32][33][34][35][36][37][38][39][40], other BPS solitons [34,35,41,42], and modulated vacua [43,44], while higher-derivative interactions of vector superfields were applied to the DBI action [45][46][47], SUGRA coupling [45,[48][49][50], SUSY Euler-Heisenberg action [17,28,51,52], and non-linear self-dual actions [4...…”

Section: Introductionmentioning

confidence: 99%

Ghostbusters in f (R) supergravity

Fujimori

Ohashi

et al. 2018

f (R) supergravity is known to contain a ghost mode associated with higherderivative terms if it contains R n with n greater than two. We remove the ghost in f (R) supergravity by introducing auxiliary gauge field to absorb the ghost. We dub this method as the ghostbuster mechanism [1]. We show that the mechanism removes the ghost supermultiplet but also terms including R n with n ≥ 3, after integrating out auxiliary degrees of freedom. For pure supergravity case, there appears an instability in the resultant scalar potential. We then show that the instability of the scalar potential can be cured by introducing matter couplings in such a way that the system has a stable potential.

“…[19][20][21][22]. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Fujimori

Ohashi

et al. 2017

Abstract:We systematically construct ghost-free higher-derivative actions of Abelian vector supermultiplets in four-dimensional N = 1 global supersymmetric theories. After giving a simple example which illustrates that a naive introduction of a higher-derivative term gives rise to a ghost, we discuss possible building blocks for a ghost-free action and explicitly show that their bosonic parts have no ghost mode and the auxiliary field D does not propagate. Higher-derivative terms yield higher powers of the auxiliary field D in the actions, and the D-term equations of motion consequently admit multiple solutions in general. We confirm that the well-known supersymmetric Dirac-Born-Infeld action falls into this class. We further give another example in which the standard quadratic kinetic term (Maxwell term) is corrected by a quartic term of the field strength. We also discuss possible couplings to matter fields and a deformed D-term potential.