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 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 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 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.

MASSIVE AXIAL GAUGE IN THE EXACT RENORMALIZATION GROUP APPROACH

2001 ◽  
Vol 16 (11) ◽  
pp. 2101-2104 ◽  
Author(s):  
P. PANZA ◽  
R. SOLDATI
Keyword(s):  
Renormalization Group ◽  
Wilson Loop ◽  
Gauge Theories ◽  
Massless Limit ◽  
Group Approach ◽  
Gauge Invariant ◽  
Axial Gauge ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group

The Exact Renormalization Group (ERG) approach to massive gauge theories in the axial gauge is studied and the smoothness of the massless limit is analysed for a formally gauge invariant quantity such as the Euclidean Wilson loop.

scholarly journals LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (14) ◽  
pp. 1037-1045
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Equations Of Motion ◽  
Interaction Strength ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Gauge Invariant ◽  
Free Case ◽  
New Feature ◽  
Generally Covariant

Applying the loop variable proposal to a sigma model (with boundary) in a curved target space, we give a systematic method for writing the gauge and generally covariant interacting equations of motion for the modes of the open string in a curved background. As in the free case described in an earlier paper, the equations are obtained by covariantizing the flat space (gauge invariant) interacting equations and then demanding gauge invariance in the curved background. The resulting equation has the form of a sum of terms that would individually be gauge invariant in flat space or at zero interaction strength, but mix amongst themselves in curved space when interactions are turned on. The new feature is that the loop variables are deformed so that there is a mixing of modes. Unlike the free case, the equations are coupled, and all the modes of the open string are required for gauge invariance.

scholarly journals Energy–Momentum Pseudotensor and Superpotential for Generally Covariant Theories of Gravity of General Form

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 173
Author(s):  
Roman Ilin ◽  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Wide Class ◽  
Equations Of Motion ◽  
General Covariance ◽  
Independent Variables ◽  
Theories Of Gravity ◽  
Generally Covariant ◽  
Derivatives Of ◽  
Mimetic Gravity

The current paper is devoted to the investigation of the general form of the energy–momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general covariance of the action without any restrictions on the order of derivatives of the independent variables in it or their transformation laws. As a result of the generalized Noether procedure, we obtain a recurrent chain of the equations, which allows one to express canonical pEMT as a divergence of the superpotential. The explicit expression for this superpotential is also given. We discuss the structure of the obtained expressions and the conditions for the derived pEMT conservation laws to be satisfied independently (fully or partially) by the equations of motion. Deformations of the superpotential form for theories with a change in the independent variables in action are also considered. We apply these results to some interesting particular cases: general relativity and its modifications, particularly mimetic gravity and Regge–Teitelboim embedding gravity.

Sign in / Sign up

Export Citation Format

Share Document