TWO-LOOP BETA FUNCTION IN THE OPEN STRING SIGMA MODEL AND EQUIVALENCE WITH STRING EFFECTIVE EQUATIONS OF MOTION

1988 ◽  
Vol 03 (14) ◽  
pp. 1349-1359 ◽  
Author(s):  
O.D. ANDREEV ◽  
A.A. TSEYTLIN
Keyword(s):  
Vector Field ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Beta Function ◽  
Open String ◽  
Equation Of Motion ◽  
Β Function ◽  
The Given

We consider the sigma-model on the disc corresponding to the open bose string in external abelian vector field and compute the order ∂3F3-terms in its two-loop β-function. The vanishing of the two-loop β-function (modulo diffeomorphism and gauge terms) is shown to be equivalent (to the given order) to the equation of motion for the string theory effective action reconstructed from the string scattering amplitudes.

scholarly journals THE PROPER TIME EQUATION AND THE ZAMOLODCHIKOV METRIC

1996 ◽  
Vol 11 (16) ◽  
pp. 2887-2906 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Electromagnetic Field ◽  
Renormalization Group ◽  
Vector Field ◽  
Proper Time ◽  
Beta Function ◽  
Open String ◽  
Point Function ◽  
Gauge Invariant ◽  
Electromagnetic Field Strength ◽  
Uniform Electromagnetic Field

The connection between the proper time equation and the Zamolodchikov metric is discussed. The connection is twofold. First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. Second, the condition that the two-point function is the Zamolodchikov metric implies the proper time equation. We study the massless vector of the open string in detail. In the exactly calculable case of a uniform electromagnetic field strength we recover the Born-Infeld equation. We describe the systematics of the perturbative evaluation of the gauge-invariant proper time equation for the massless vector field. The method is valid for nonuniform fields and gives results that are exact to all orders in derivatives. As a nontrivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation.

scholarly journals g-FUNCTION IN PERTURBATION THEORY

2004 ◽  
Vol 19 (15) ◽  
pp. 2545-2559
Author(s):  
ANATOLY KONECHNY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Beta Function ◽  
Open String ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
The Given

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

THE SUPERSYMMETRIC CURCI-PAFFUTI RELATION AND VANISHING OF THE DILATON BETA FUNCTION IN THE N=2 SUSY SIGMA MODEL

1990 ◽  
Vol 05 (08) ◽  
pp. 1561-1573 ◽  
Author(s):  
PETER E. HAAGENSEN
Keyword(s):  
Recent Result ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Minimal Subtraction ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Similar Relation ◽  
Β Function

We extend the Curci-Paffuti relation of bosonic sigma models to the supersymmetric case. In the N=1 model, a similar relation is found, while in the N=2 model, a vanishing result ensues for the dilaton β-function. One contribution to the dilaton β-function in the N=2 model is identified as a previous result of Grisaru and Zanon; however, if we remain within a minimal subtraction scheme, other terms coming from finite subtractions appear which precisely cancel that and give a vanishing result. This is in agreement with a recent result of Jack and Jones.

scholarly journals A COMPARISON OF THE PROPER-TIME EQUATION AND THE RENORMALIZATION GROUP β-FUNCTION IN STRING THEORY

1995 ◽  
Vol 10 (21) ◽  
pp. 1565-1575
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Proper Time ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
The Other ◽  
Proportionality Factor ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Full Equation ◽  
Gauge Covariance ◽  
Β Function

It is known that there is a proportionality factor relating the β-function and the equations of motion viz. the Zamolodchikov metric. Usually this factor has to be obtained by other methods. The proper-time equation, on the other hand, is the full equation of motion. We explain the reasons for this and illustrate it by calculating corrections to Maxwell’s equation. The corrections are calculated to cubic order in the field strength, but are exact to all orders in derivatives. We also test the gauge covariance of the proper-time method by calculating higher (covariant) derivative corrections to the Yang-Mills equation.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

scholarly journals A worldsheet for Kerr

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Alfredo Guevara ◽  
Ben Maybee ◽  
Alexander Ochirov ◽  
Donal O’Connell ◽  
Justin Vines
Keyword(s):  
Black Hole ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Equations Of Motion ◽  
Kerr Black Hole ◽  
Single Copy ◽  
Kerr Solution

Abstract We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $$ \sqrt{\mathrm{Kerr}} $$ Kerr solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

ON THE RENORMALIZATION GROUP APPROACH TO STRING EQUATIONS OF MOTION

1989 ◽  
Vol 04 (16) ◽  
pp. 4249-4278 ◽  
Author(s):  
A. A. TSEYTLIN
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Beta Function ◽  
Massive String ◽  
Group Approach ◽  
New Approach ◽  
Interaction Terms ◽  
Cutoff Dependence ◽  
Renormalization Group Approach

We discuss the program of deriving the string field theory equations of motion for all (massless and massive) string modes as the renormalization group fixed point equations for the most general sigma model containing all possible ("nonrenormalizable") interactions. We review the approach based on the Wilson RG equation and point out the problem of cutoff dependence of the interaction term in the corresponding "quadratic" beta function. The relation between the sigma model path integral and the string scattering amplitudes is clarified. We suggest a new approach to the derivation of the generalized sigma model beta functions in which the central role is played by the condition of completeness of the set of interaction terms ("vertex opeators") present in the sigma model action. The use of the completeness relation makes it possible to obtain closed expressions for the sigma model partition function and the beta functions. The resulting beta functions contain all higher powers of the couplings (fields).

scholarly journals LOOP VARIABLES AND THE (FREE) OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (04) ◽  
pp. 227-242 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Systematic Method ◽  
Curved Space ◽  
Generally Covariant ◽  
Space Equation

Using the loop variable formalism as applied to a sigma model in curved target space, we give a systematic method for writing down gauge and generally covariant equations of motion for the modes of the free open string in curved space. The equations are obtained by covariantizing the flat space equation and then demanding gauge invariance, which introduces additional curvature couplings. As an illustration of the procedure, the spin-two case is worked out explicitly.

scholarly journals Crack Detection, Localization and Estimation of the Intensity in a Turbo Rotor

1996 ◽  
Author(s):  
R.-W. Park
Keyword(s):  
Crack Detection ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Time Behaviour ◽  
Rotating Shaft ◽  
Advanced Method ◽  
Local Stiffness ◽  
The Given ◽  
Crack Position ◽  
Nonlinear State

The goal of this paper is to describe an advanced method of a crack detection, a new way to localize the crack position and to estimate the intensity of the depth with reference to a rotating shaft. As a first step, the shaft is physically modelled with a finite element method as usual and the dynamic mathematical model is derived from it using the Hamilton-principle and in this way the system is modelled by various subsystems. The equations of motion with crack is established by adaption of the local stiffness change through breathing and gaping from the crack to the equation of motion with undamaged shaft. This is supposed to be regarded as reference for the given system. Based on the fictitious model of the time behaviour induced from vibration phenomena measured at the bearings, a nonlinear State Observer is designed in order to detect the crack on the shaft. This is elementary NL-observer (EOB). Using the elementary observer, an Estimator (Observer) Bank is established and arranged at the certain position on the shaft. In case a crack is found and its position is known, the procedure for the estimation of the depth is going to begin.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

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