String techniques for the calculation of renormalization constants in field theory

Abstract

We describe a set of methods to calculate gauge theory renormalization constants from string theory, all based on a consistent prescription to continue off shell open bosonic string amplitudes. We prove the consistency of our prescription by explicitly evaluating the renormalizations of the two, three and four-gluon amplitudes, and showing that they obey the appropriate Ward identities. The field theory limit thus performed corresponds to the background field method in Feynman gauge. We identify precisely the regions in string moduli space that correspond to different classes of Feynman diagrams, and in particular we show how to isolate contributions to the effective action. Ultraviolet divergent terms are then encoded in a single string integral over the modular parameter $\tau$. Finally, we derive a multiloop expression for the effective action by computing the partition function of an open bosonic string interacting with an external non-abelian background gauge field.

54 pages, Latex, uses FEYNMAN.tex

Cited by in corpus (73)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Pinch Technique: Theory and Applications
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
• Classical gauge instantons from open strings
• From Free Fields to $AdS$
• Brane world effective actions for D-branes with fluxes
• The Pinch Technique to All Orders
• Scattering of closed strings from many D-branes
• Generalized Pinch Technique and the Background Field Method in General Gauges
• Gauge-Invariant Resummation Formalism for Two-Point Correlation Functions
• Pinch technique self-energies and vertices to all orders in perturbation theory
• Gauge Unification in Highly Anisotropic String Compactifications
• Tropical Amplitudes
• Stretched Strings in Noncommutative Field Theory
• BCJ duality and double copy in the closed string sector
• N=1/2 gauge theory and its instanton moduli space from open strings in R-R background
• Exact Combinatorics of Bern-Kosower-type Amplitudes for Two-Loop ${\Phi }^3$ Theory
• Worldline Green Functions for Arbitrary Feynman Diagrams
• Two-loop scalar diagrams from string theory
• Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)
• String Theory and Noncommutative Field Theories at One Loop
• Multiloop String Amplitudes with B-Field and Noncommutative QFT
• Gauge/Gravity Correspondence from Open/Closed String Duality
• A covariant representation of the Ball-Chiu vertex
• String Vertex Operators and Cosmic Strings
• On the Effective Potential of the Dp- anti Dp system in type II theories
• World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory
• The pinch technique at two-loops: The case of mass-less Yang-Mills theories
• Two-loop Yang-Mills theory in the world-line formalism and an Euler-Heisenberg type action
• Non(anti)commutative N=2 Supersymmetric Gauge Theory from Superstrings in the Graviphoton Background
• World Volume Action for Fractional Branes
• Multi-loop open string amplitudes and their field theory limit
• Stringy profiles of gauge field tadpoles near orbifold singularities: I. heterotic string calculations
• Scalar field theory limits of bosonic string amplitudes
• Multiloop ${\Phi }^3$ Amplitudes from Bosonic String Theory
• Consistent Off-Shell Tree String Amplitudes
• Vanishing Perturbative Vacuum Energy in Non-Supersymmetric Orientifolds
• Deformation of N=4 Super Yang-Mills Theory in Graviphoton Background
• Two-loop Euler-Heisenberg effective actions from charged open strings
• Mass corrections in string theory and lattice field theory
• Multibranes boundary states with open string interactions
• Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String
• Two-Loop ${\varphi }^4$-Diagrams from String Theory
• Cutting rules and perturbative unitarity of noncommutative electric-type field theories from string theory
• Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions
• On off-shell bosonic string amplitudes
• Scaling Violation and Gauge/String Duality
• Systematics of one-loop Yang-Mills diagrams from bosonic string amplitudes
• On Finite-Size D-Branes in Superstring Theory
• Perturbative Computation of the Gluonic Effective Action via Polyaokov's World-Line Path Integral
• One-loop adjoint masses for non-supersymmetric intersecting branes
• Integral representations of thermodynamic 1PI Green functions in the world-line formalism
• Gauge and gravitational interactions of non-BPS D-particles
• Unitarity of noncommutative field theories from string theory
• Prescriptions for Off-Shell Bosonic String Amplitudes
• Off-shell amplitudes for nonoriented closed strings
• Summability of Superstring Theory
• On the Compton Scattering in String Theory
• Geometric counter-vertex for open string scattering on D-branes
• Finite Strings From Non-Chiral Mumford Forms
• Polyakov's spin factor and new algorithms for efficient perturbative computations in QCD
• Off-shell tachyon amplitudes: analyticity and projective invariance
• A space-time approach to multigluon computations in QCD: An application to effective action terms
• On the Evaluation of Compton Scattering Amplitudes in String Theory
• On the gauge chosen by the bosonic open string
• World-line Green functions with momentum and source conservations
• Non-Commutative Gauge Theories and the Cosmological Constant
• Pinching parameters for open (super) strings
• Schwinger-type parametrization of open string worldsheets
• Stringy Threshold Corrections in D-brane Systems
• A numerical algorithm for efficiently obtaining a Feynman parameter representation of one-gluon loop QCD Feynman diagrams for a large number of external gluons