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Register a new userGeneral Solution of String Inspired Nonlinear Equations
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We present the general solution of the system of coupled nonlinear equations describing dynamics of $D$--dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2)- dimensional spheres $S^{D-2}={SO(1,D-1) over SO(1,1) times SO(D-2) semiprod K_{D-2}}.$
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The anomaly cancellation equations for the $U(1)$ gauge group can be written as a cubic equation in $n-1$ integer variables, where $n$ is the number of Weyl fermions carrying the $U(1)$ charge. We solve this Diophantine cubic equation by providing a parametrization of the charges in terms of $n-2$ integers, and prove that this is the most general solution.
As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as direction of UV-completion in 4-D Quantum Field Theory (QFT), here we investigate the confinement conditions and $beta-$function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin (BRST) invariance, to the non-local theory, by using a set of exact solutions of the corresponding local theory. We show that the infinite-derivatives which are active in the UV provides finite contributions also in the infrared (IR) limit and provide a proof of confinement, granted by the absence of the Landau pole. The main difference with the local case is that the IR fixed point is moved to infinity. We also show that in the limit of the energy scale of non-locality $M rightarrow infty$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.
Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a general solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory. `Primitive solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield the general solution. We show that the ingenious methods used there have a simple geometric interpretation, corresponding to elementary constructions in number theory. Viewing them in this context allows the fully general solution to be written down directly, without the need for further operations. Our geometric method also allows us to show that the only operation Costa et al. require is permutation. It also gives a variety of other, qualitatively similar, parameterisations of the general solution, as well as a qualitatively different (and arguably simpler) form of the general solution for $n$ even.
We propose in this paper a quintom model of dark energy with a single scalar field $phi$ given by the lagrangian ${cal L}=-V(phi)sqrt{1-alpha^prime abla_{mu}phi abla^{mu}phi +beta^prime phiBoxphi}$. In the limit of $beta^primeto$0 our model reduces to the effective low energy lagrangian of tachyon considered in the literature. We study the cosmological evolution of this model, and show explicitly the behaviors of the equation of state crossing the cosmological constant boundary.
We consider a classical (string) field theory of $c=1$ matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling $g_s$. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.
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