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

Sathiapalan, B.

doi:10.1016/j.nuclphysb.2012.04.006

Cited by 5 publications

(10 citation statements)

References 60 publications

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“…Gauge invariant equations obtained were similar to those obtained using BRST string field theory [ [18] - [24]]. The interacting open string was described in [25,26]. This involved using the exact renormalization group (ERG) [27,28,29,30] 1 of the world sheet theory, written in terms of loop variables.…”

Section: Introductionmentioning

confidence: 60%

“…The interaction terms ("gauge invariant field strengths" [25,26]) expressed in terms of loop variables can be mapped to space-time fields using the same three step procedure. A new feature that enters is that the interaction involves a product of two such field strengths at different points on the world sheet.…”

Section: Interacting Open String: Levelmentioning

confidence: 99%

“…We will explain the procedure and work out a few illustrative examples for both open and closed string equations. Note that in [25,26,2,1]gauge invariant loop variable expressions are available along with their maps to space time in flat space. We will simply use them and describe a consistent map to space time fields in curved space-time in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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

Sathiapalan

2015

Int. J. Mod. Phys. A

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In an earlier paper [arXiv:1408.0484] gauge invariant and background covariant equations for closed string modes were obtained from the exact renormalization group equation 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 is chosen to be the physical metric without any restrictions. This method thus gives manifestly background independent gauge invariant and general covariant equations of motion for both open and closed string modes.

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Section: Introductionmentioning

confidence: 60%

Section: Interacting Open String: Levelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sathiapalan

2015

Int. J. Mod. Phys. A

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“…It can easily be checked that it is not gauge invariant. The resolution of this problem, described in [28,29], is to introduced all derivatives in the loop variable. The basic idea is that the gauge variation of vertex operators of a given level should be of the form λ n ∂ ∂xn of lower order vertex operators.…”

Section: Interacting Equationsmentioning

confidence: 99%

“…A more satisfactory interacting theory is obtained by applying ERG transformation [28,29]. The ERG is a quadratic equation.…”

Section: Introductionmentioning

confidence: 99%

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

Sathiapalan

2015

Int. J. Mod. Phys. A

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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.

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

Sathiapalan¹

2013

Nuclear Physics B

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In arXiv:1202.4298 gauge invariant interacting equations were written down for the spin 2 and spin 3 massive modes using the exact renormalization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant "field strengths" and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invariant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space time and this is also outlined.

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

Cited by 5 publications

References 60 publications

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

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

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

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

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