RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

scholarly journals Quantum Fields without Wick Rotation

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 373 ◽  
Author(s):  
Alessio Baldazzi ◽  
Roberto Percacci ◽  
Vedran Skrinjar
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Coarse Graining ◽  
Conformal Factor ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Simple Application ◽  
Wick Rotation ◽  
Definition Of ◽  
Method Of Steepest Descent

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.

scholarly journals HOLOMORPHIC FACTORIZATION AND RENORMALIZATION GROUP IN CLOSED STRING THEORY

2005 ◽  
Vol 20 (15) ◽  
pp. 1161-1176 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Open String ◽  
Renormalization Group Equation ◽  
Closed String ◽  
Group Equation ◽  
Sums Of Products

The prescription of Kawai, Lewellen and Tye for writing closed string tree amplitudes as sums of products of open string tree amplitudes, is applied to the worldsheet renormalization group equation. The main point is that regularization of the Minkowski (rather than Euclidean) worldsheet theory allows factorization into left-moving and right-moving sectors to be maintained. Explicit calculations are done for the tachyon and the (gauge fixed) graviton.

scholarly journals Renormalization group and diffusion equation

2020 ◽  
Author(s):  
Masami Matsumoto ◽  
Gota Tanaka ◽  
Asato Tsuchiya
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Diffusion Equation ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Initial Time ◽  
Group Equation ◽  
Cutoff Function ◽  
Exact Renormalization Group ◽  
And Diffusion

Abstract We study relationship between renormalization group and diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

GRAVITON AMPLITUDES, EFFECTIVE ACTION AND STRING GENERATING FUNCTIONAL ON THE DISC

1989 ◽  
Vol 04 (13) ◽  
pp. 3269-3304 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
General Expression ◽  
Effective Field Theory ◽  
Effective Action ◽  
Closed String ◽  
Effective Field ◽  
Generating Functional ◽  
S Matrix ◽  
String Amplitudes

We discuss some issues related to computation and renormalization of closed string amplitudes and effective action on the disc. The general expression for the O (ln ε) term in the string theory and effective field theory generating functionals for the S matrix is found. It is emphasized that in order to establish the correspondence between the string theory and the effective field theory it is necessary to compare the total coefficients of all (“local” plus “modular” and “N-dependent” plus “N-independent”) infinities present in the amplitudes. The regularized expression for the N=3 graviton amplitude on the disc is explicitly computed and it is suggested that a proper regularization is a key to a resolution of a paradox discussed previously in the literature.

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