String techniques for the calculation of renormalization constants in field theory (original) (raw)

Gauge theory renormalizations from the open bosonic string

Physics Letters B, 1995

We present a unified point of view on the different methods available in the literature to extract gauge theory renormalization constants from the lowenergy limit of string theory. The Bern-Kosower method, based on an off-shell continuation of string theory amplitudes, and the construction of low-energy string theory effective actions for gauge particles, can both be understood in terms of strings interacting with background gauge fields, and thus reproduce, in the low-energy limit, the field theory results of the background field method. We present in particular a consistent off-shell continuation of the one-loop gluon amplitudes in the open bosonic string that reproduces exactly the results of the background field method in the Feynman gauge.

Renormalization Constants from String Theory

String Gravity and Physics at the Planck Energy Scale, 1996

We review some recent results on the calculation of renormalization constants in Yang-Mills theory using open bosonic strings. The technology of string amplitudes, supplemented with an appropriate continuation off the mass shell, can be used to compute the ultraviolet divergences of dimensionally regularized gauge theories. The results show that the infinite tension limit of string amplitudes corresponds to the background field method in field theory. (Proceedings of the Workshop "Strings, Gravity and Physics at the Planck scale ", Erice (Italy), September 1995. Preprint DFTT 82/95) 2 PAOLO DI VECCHIA ET AL.

String-derived renormalization of Yang-Mills theory

Nuclear Physics B - Proceedings Supplements, 1996

We review the application of bosonic string techniques to the calculation of renormalization constants and effective actions in Yang-Mills theory. We display the multiloop string formulas needed to compute Yang-Mills amplitudes, and we discuss how the renormalizations of proper vertices can be extracted in the field theory limit. We show how string techniques lead to the background field method in field theory, and indicate how the gauge invariance of the multiloop effective action can be inferred form the string formalism. (

The Field Theory Limit of Multiloop String Amplitudes

Gauge Theories, Applied Supersymmetry and Quantum Gravity II, 1997

We report on recent progress in the use of string techniques for the computation of field theory amplitudes. We show how one-loop renormalization constants in Yang-Mills theory can be computed using the open spinning string, we review the calculation of two-loop scalar amplitudes with the bosonic string, and we briefly indicate how the technique can be applied to the two-loop vacuum bubbles of Yang-Mills theory. *

Multi-loop open string amplitudes and their field theory limit

2013

We study the field theory limit of multi-loop (super)string amplitudes, with the aim of clarifying their relationship to Feynman diagrams describing the dynamics of the massless states. We propose an explicit map between string moduli around degeneration points and Schwinger proper-times characterizing individual Feynman diagram topologies. This makes it possible to identify the contribution of each light string state within the full string amplitude and to extract the field theory Feynman rules selected by (covariantly quantized) string theory. The connection between string and field theory amplitudes also provides a concrete tool to clarify ambiguities related to total derivatives over moduli space: in the superstring case, consistency with the field theory results selects a specific prescription for integrating over supermoduli. In this paper, as an example, we focus on open strings supported by parallel D-branes, and we present two-loop examples drawn from bosonic and RNS string theories, highlighting the common features between the two setups.

Systematics of one-loop Yang–Mills diagrams from bosonic string amplitudes

Nuclear Physics B, 2001

We present a general algorithm to compute off-shell, one-loop multigluon Green functions using bosonic string amplitudes. We identify and parametrize the regions in the space of moduli of one-loop Riemann surfaces that contribute to the field theory limit of string amplitudes. Each of these regions can be precisely associated with a Feynman-like scalar graph with cubic and quartic vertices, whose lines represent the joint propagation of ghosts and gluons. We give a procedure to compute the contribution of each graph to a gluon Green function, for arbitrarily polarized off-shell gluons, reducible and irreducible diagrams, planar and non-planar topologies. Explicit examples are given for up to six gluons. *

Scalar field theory limits of bosonic string amplitudes

Nuclear Physics B, 2000

We describe in detail the techniques needed to compute scattering amplitudes for colored scalars from the infinite tension limit of bosonic string theory, up to two loops. These techniques apply both to cubic and quartic interactions, and to planar as well as non-planar diagrams. The resulting field theories are naturally defined in the space-time dimension in which they are renormalizable. With a careful analysis of string moduli space in the Schottky representation we determine the region of integration for the moduli, which plays a crucial role in the derivation of the correct combinatorial and color factors for all diagrams. *

Prescriptions for off-shell bosonic string amplitudes

Lecture Notes in Physics

We give, in the framework of the bosonic string theory, simple prescriptions for computing, at tree and one-loop levels, off-shell string amplitudes for open and closed string massless states. In particular we obtain a tree amplitude for three open strings that in the field theory limit coincides with the three-gluon vertex in the usual covariant gauge and two-string one-loop amplitudes satisfying the property of transversality.

On the closed bosonic string effective action

Physics Letters B, 1990

We have analyzed the closed bosonic string effective action to all orders in string loops. Using the proper-time regularization of the local logarithmic infinities, we propose a renormalization scheme valid for all genera, which leaves only a dilaton potential as higher string-loop corrections to the partition function. We assume the string is propagating in a genus-dependent background in such a way that the physical (renormalized) background fields are genus-independent. After subtraction of modular infinities, the string-loop corrections to the ~functions are only cosmological terms.

The renormalization group approach to the confining string

Nuclear Physics B, 2000

The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant and Zamolodchikov's c function. Tachyon stability, glueball mass gap, renormalization group evolution of the c function and the area law for the Wilson loop are studied for a critical bosonic string vacuum corresponding to a non abelian gauge theory in four dimensional space-time. We prove that the same intrinsic geometry for the string vacuum is universal in some sense, reproducing the Yang-Mills beta function to arbitrary loop order in perturbation theory.