scholarly journals GAUGE INVARIANT EXACT RENORMALIZATION GROUP AND PERFECT ACTIONS IN THE OPEN BOSONIC STRING THEORY

2007 ◽  
Vol 22 (23) ◽  
pp. 1701-1715 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
Lattice Gauge Theory ◽  
Equations Of Motion ◽  
Finite Lattice ◽  
Open String ◽  
Scale Invariant ◽  
Gauge Invariant ◽  
Lattice Gauge ◽  
Exact Renormalization Group ◽  
The Continuum

The exact renormalization group is applied to the worldsheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be constructed to be gauge invariant. Furthermore they are valid off the (free) mass shell. This requires keeping a finite cutoff. Thus we have the interesting situation of a scale invariant worldsheet theory with a finite worldsheet cutoff. This is possible because there is infinite number of operators whose coefficients can be tuned. This is in the same sense that "perfect actions" or "improved actions" have been proposed in lattice gauge theory to reproduce the continuum results even while keeping a finite lattice spacing.

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 Exact renormalization group and loop variables: A background independent approach to string theory

2015 ◽  
Vol 30 (32) ◽  
pp. 1530055 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Flat Space ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
String Loop ◽  
Higher Spin ◽  
Exact Renormalization Group

This paper is a self-contained review of the loop variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space–time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.

scholarly journals Background independence, gauge invariance and equations of motion for closed string modes

2015 ◽  
Vol 30 (18n19) ◽  
pp. 1550105 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Renormalization Group ◽  
Equations Of Motion ◽  
Closed String ◽  
World Sheet ◽  
Gauge Invariant ◽  
Background Independence ◽  
The World ◽  
Exact Renormalization Group ◽  
Generally Covariant ◽  
Derivatives Of

In an earlier paper, gauge invariant and background covariant equations for closed string modes were obtained from the exact Renormalization Group of the world sheet theory. The background metric (but not the physical metric) had to be flat and hence the method was not manifestly background independent. In this paper, the restrictions on the background metric are relaxed. A simple prescription for the map from loop variables to space–time fields is given whereby for arbitrary backgrounds the equations are generally covariant and gauge invariant. Extra terms involving couplings of the curvature tensor to (derivatives of) the Stueckelberg fields have to be added. The background metric can thus be chosen to be the physical metric without any restrictions. This method thus gives manifestly background independent equations of motion for both open and closed string modes.

scholarly journals Gradient flow exact renormalization group

2021 ◽  
Author(s):  
Hidenori Sonoda ◽  
Hiroshi Suzuki
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Lattice Gauge Theory ◽  
Gradient Flow ◽  
Continuum Theory ◽  
Coarse Graining ◽  
Yang Mills ◽  
Guiding Principle ◽  
Lattice Gauge ◽  
Exact Renormalization Group

Abstract The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang{Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

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