相关论文: Stirling number Identities and High energy String …
Recently, Witten proposed a topological string theory in twistor space that is dual to a weakly coupled gauge theory. In this lectures we will discuss aspects of the twistor string theory. Along the way we will learn new things about…
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
Following the proposal of arXiv:1312.6673, multi-particle scattering amplitudes are represented as conserved higher-spin charges. The advantage of such reformulation is that multi-particle amplitudes acquire the form of an integral of a…
Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded…
We review, in a self-contained and pedagogical manner, recent developments and techniques for the evaluation of the scattering amplitudes of planar N=4 SYM theory at both weak and strong coupling. Special emphasis is placed on the newly…
Recent progress on the physical states and scattering amplitudes of the $W_3$ string is reviewed with particular emphasis on the relation between this string theory and the Ising model.
In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients…
Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic…
An explicit derivation of the four-dilatino scattering amplitude from type II superstring theory is presented. This is obtained by using the Kawai-Lewellen-Tye relations for closed string scattering amplitudes in terms of the product of two…
We compute the cross section for scattering of light string probes by randomly excited closed strings. For high energy probes, the cross section factorizes and can be used to define effective form factors for the excited targets. These form…
We study the scattering of low-energy tensor multiplet particles against a BPS saturated cosmic string. We show that the corresponding S-matrix is largely determined by symmetry considerations. We then apply a specific supersymmetric model…
I discuss some current thoughts on how low-energy measurements and consistency constrain theories at high energies with emphasis on string theory. I also discuss some recent work on the dynamics of supersymmetric gauge theories.
We extend previous techniques for calculations of transplanckian-energy string-string collisions to the high-energy scattering of massless closed strings from a stack of N Dp-branes in Minkowski spacetime. We show that an effective…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We discover a stringy scaling behavior for a class of n-point Regge string scattering amplitudes (RSSA). The number of independent kinematics variables is found to be reduced by dim M.
In the note, the authors give a unified proof of Identities~67, 84, and~85 in the monograph "M. Z. Spivey, The Art of Proving Binomial Identities, Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 2019; available online…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.