Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory

Sathiapalan, B.

doi:10.1142/s0217732307023985

“…In section 3 we give a review of loop variables and derive the ERG using the loop variable language and we derive the gauge invariant version. This is substantially different from the approach in [23] as mentioned earlier in the introduction. Section 4 contains some explicit calculations for spin 2 and spin 3 fields.…”

Section: Introductionmentioning

confidence: 72%

“…In this sense string field theory [31,30,32,33] can be thought of as a way of keeping a finite cutoff while maintaining gauge invariance. In [23,18] an exact ERG was written down in position space and equations of motion derived. A proposal to make it gauge invariant was given.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is organized as follows: In Section 2 we review the derivation the ERG in position space and also the application to gauge fixed backgrounds -as one would in the "old covariant formulation" of string theory. This is a review of earlier work [23] and is included here for convenience. In section 3 we give a review of loop variables and derive the ERG using the loop variable language and we derive the gauge invariant version.…”

Section: Introductionmentioning

confidence: 99%

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Loop variables and gauge invariant exact renormalization group equations for (open) string theory

Sathiapalan

¹

2012

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An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non zero mass is essential for this. This is reminiscent of Abelian Born-Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.

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“…In this sense string field theory [31,30,32,33] can be thought of as a way of keeping a finite cutoff while maintaining gauge invariance. In [23,18] an exact ERG was written down in position space and equations of motion derived. A proposal to make it gauge invariant was given.…”

Section: Introductionmentioning

confidence: 99%

“…For discussions on various aspects of ERG see[38,39,40,41] in addition to the original references. The position space ERG for the string world sheet has also been discussed in[8,42,43].…”

mentioning

confidence: 99%

Loop Variables and Gauge Invariant Exact Renormalization Group Equations for Closed String Theory

Sathiapalan

¹

2013

Int. J. Mod. Phys. A

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An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non zero mass is essential for this. This is reminiscent of Abelian Born-Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.

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Gauge invariance and equations of motion for closed string modes

Sathiapalan

¹

2014

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We continue earlier discussions on loop variables and the exact renormalization group on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motionthis is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space time curvature of the (arbitrary) background is zero. The exact RG equations give quadratic equations of motion for all the modes including the physical graviton. The level (2,2) massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory.

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Gauge Invariant Exact Renormalization Group and Perfect Actions in the Open Bosonic String Theory

Cited by 6 publications

References 42 publications

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

Loop Variables and Gauge Invariant Exact Renormalization Group Equations for Closed String Theory

Gauge invariance and equations of motion for closed string modes

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