Related papers: Second Variations of String Actions

The relative motion of many particles can be described by the geodesic deviation equation. This can be derived from the second covariant variation of the point particle's action. It is shown that the second covariant variation of the string…

We calculate the background field equations for the T-duality symmetric string building on previous work by including the effect of the Dilaton up to two-loops. Inclusion of the Dilaton allows us to obtain the full beta functionals of the…

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string…

We improve and extend a method introduced in an earlier paper for deriving string field equations. The idea is to impose conformal invariance on a generalized sigma model, using a background field method that ensures covariance under very…

For a permutation $\pi$, and the corresponding permutation matrix, we introduce the notion of {\em discrete derivative}, obtained by taking differences of successive entries in $\pi$. We characterize the possible derivatives of…

We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…

In this didactic note, we describe a procedure to derive successive approximations of $\pi$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations,…

We prove that for every separately twice differentiable solution $f$ of the PDE $f"_{xx}=f"_{yy}$ is of the form $f(x,y)=\phi(x+y)+\psi(x-y)$ for some twice differentiable functions $\phi, \psi$.

We review the basics of the dynamics of closed strings moving along the discretized line \Z. The string excitations are described by a field \phi_x(\tau) where x is the position of the string in the embedding space and \tau is a…

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…

A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are…

In this article, we study $(\sigma, \tau)$-derivations of number rings by considering them as commutative unital $\mathbb{Z}$-algebras. We begin by characterizing all $(\sigma, \tau)$-derivations and inner $(\sigma, \tau)$-derivations of…

T-duality has been shown to constrain the higher derivative corrections of string theory. We revisit the problem of understanding the T-duality constraints imposed on the $\alpha'$ corrections using the language of a torsionful connection.…

In this article we give a calculation of the two-loop $\sigma$-model corrections to the T-duality map in string theory. We use the effective action approach, and analyze two-loop corrections in a specific subtraction scheme. Focusing on…

The problem of Gamma + Pi --> Pi + Pi is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. Single variable dispersion relation is assumed. Using elastic unitarity relation, an integral equation equation…

The loop variable technique (for open strings in flat space) is a gauge invariant generalization of the renormalization group method for obtaining equations of motion. Unlike the beta functions, which are only proportional to the equations…

This paper is devoted to derivations in bimodules over group rings using previously proposed methods which are related to character spaces over groupoids. The theorem describing the arising spaces of derivations is proved. We consider some…

We have determined $R_{\tau/P}\equiv \Gamma(\tau \to P \nu_\tau [\gamma]) / \Gamma(P \to\mu \nu_\mu[\gamma])$ ($P=\pi, K$). Whereas $P$ decays are calculated by using Chiral Perturbation Theory (ChPT), $\tau$ decays have been studied with…

It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity…

A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…