Related papers: On $p$-adic string amplitudes in the limit $p$ app…

This article is a survey of our recent work on the connections between Koba-Nielsen amplitudes and local zeta functions (in the sense of Gel'fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the…

We establish rigorously the regularization of the p-adic open string amplitudes, with Chan-Paton rules and a constant B-field, introduced by Ghoshal and Kawano. In this study we use techniques of multivariate local zeta functions depending…

We prove that the p-adic Koba-Nielsen type string amplitudes are bona fide integrals. We attach to these amplitudes Igusa-type integrals depending on several complex parameters and show that these integrals admit meromorphic continuations…

This article is related to construction of zeta strings from $p$-adic ones. In addition to investigation of $p$-adic string for a particular prime number $p$, it is also interesting to study collective effects taking into account all primes…

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's…

p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By…

We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the…

The amplitudes for the tree-level scattering of the open string tachyons, generalised to the field of p-adic numbers, define the p-adic string theory. There is empirical evidence of its relation to the ordinary string theory in the p_to_1…

We consider the construction of Lagrangians that might be suitable for describing the entire $p$-adic sector of an adelic open scalar string. These Lagrangians are constructed using the Lagrangian for $p$-adic strings with an arbitrary…

We propose a formalism inspired by matrix models to compute open and closed topological string amplitudes in the B-model on toric Calabi-Yau manifolds. We find closed expressions for various open string amplitudes beyond the disk, and in…

Inspired by earlier results on recursions for open-string tree-level amplitudes, and by a result of Brown and Dupont relating open- and closed-string tree-level amplitudes via single-valued periods, we identify a recursive relation for…

In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our…

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri…

We revisit the tree-level closed superstring amplitude and identify its alpha'-expansion as series with single-valued multiple zeta values as coefficients. The latter represent a subclass of multiple zeta values originating from…

The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at…

We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where…

Some nonlocal and nonpolynomial scalar field models originated from p-adic string theory are considered. Infinite number of spacetime derivatives is governed by the Riemann zeta function through d'Alembertian $\Box$ in its argument.…

We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of…

We show that certain type II string amplitudes at genus $g$ are given by the topological partition function $F_g$ discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional…

In this paper we show that in perturbative string theory the genus-one contribution to formal 2-point amplitudes can be related to the genus-zero contribution to 4-point amplitudes. This is achieved by studying special linear combinations…