Non-perturbative procedure for stable K-brane
AbstractWe proposea novel ﬁrst-orderformalism for a type of K-branesystems. An examplesolution is presented and studied. We illustratehow the noncanonical kinetic term can aﬀect the properties of the model, such as the stability of the solutions, the localization offermion and graviton. We argue that our solution is stable against linear perturbations. The tensor zero mode of graviton can belocalized while the scalar zero mode cannot. The localization condition for fermion is also discussed.Keywords: Large extra dimension, noncanonical kinetic terms, gravitational perturbationsPACS: 04.50.-h, 11.27.+d, 98.80.Cq1. IntroductionScalar ﬁelds with noncanonicalkinetic terms, namely, the K-ﬁelds were initially introduced to cosmology as a new mech-anism of inﬂation [1–3]. Since then, K-ﬁelds are extensivelystudied in many ﬁelds. One of its interesting applications i s themodeling of thick K-branes. Unlike the standard thick branemodels, where branes are usually generated by canonical scalarﬁeld(s) (see [4–13] for some of the original papers of braneworld, and Refs. [14–17] for reviews), thick K-branes are do-main wall branes generated by scalar ﬁelds with noncanonica lkinetic terms [18–23].Like any kind of brane world model, the study of thick K-brane models also contains at least three nontrivial issues: solu-tions, stability, and properties (for example, the localization ofbulk matter ﬁelds and gravitons). The stability of thick K-branehas been generally discussed in Ref. [24], where the stabilityconditions for solutions of a large class of thick K-brane mod-els were derived.As to the issue of ﬁndingsolutions, it is worthto mentiontha tthere are interesting dualities between some K-ﬁeld models andthe standard model. In other words, some K-ﬁeld models sup-port the same solution given by the model with standard kineticterm of scalar ﬁeld [25]. Such K-ﬁeld models are called thetwin-like models of the correspondingstandard model, and viceversa. Inspired by the original work [25], some authors studiedtwin-like models in brane world [26–29]. The twin-like dualityoﬀers us an alternative way to ﬁnd simple analytical K-branesolutions. However, some of the models can be distinguishedfrom the standard model only when linear perturbations (espe-cially, the scalar perturbations) are considered, while some are