Homotopy operators and identity-based solutions in cubic superstring field theory

Inatomi, Shoko; Kishimoto, Isao; Takahashi, Tomohiko

doi:10.1007/jhep10(2011)114

Cited by 7 publications

(6 citation statements)

References 36 publications

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“…2.7, there is no need for these zeros to be at z = ±1, which correspond to open string boundaries. We note that we can find similar results in the study of homotopy operators for the BRST operator around the identity-based scalar solutions, 7), 23) in which homotopy operators exist only if the zeros are on the unit circle. Here, we should comment on another identity-based solution discussed in Ref.…”

Section: )supporting

confidence: 76%

Observables for identity-based tachyon vacuum solutions

Kishimoto

Masuda

Takahashi

2014

Progress of Theoretical and Experimental Physics

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We consider a modified KBc algebra in bosonic open string field theory expanded around identity-based scalar solutions. By use of the algebra, classical solutions on the background are constructed and observables for them, including energy densities and gauge invariant overlaps, are calculable. These results are applied to evaluate observables analytically for both of the identity-based trivial pure gauge solution and the identity-based tachyon vacuum solution. §1. IntroductionAn analytic tachyon vacuum solution was constructed on the basis of the identity string field, the BRST current, and the ghost field in bosonic cubic open string field theory. 1), 2), 3) The identity string field is a fundamental object in the open string field theory 4) and indeed it is a building block of the KBc algebra 5) by which wedge-based solutions 6) can be easily reconstructed. Then, the identity-based solutions were found by some left-right splitting algebra, 1) which is similar to the KBc algebra in a sense, and a certain type of the identitybased solutions can be regarded as the tachyon vacuum solution. This is supported by evidence from study of the theory expanded around the solution: vanishing cohomology, 2), 3) , 7) no open string excitations, 8) and the existence of the perturbative vacuum solution. 9), 10) Hence, it appears highly probable that observables for the identity-based tachyon vacuum solution agree with those expected for the tachyon vacuum, although, due to characteristic subtleties of the identity string field, it has been difficult to perform direct evaluation of the observables.Recently, significant progress has been made in the investigation of identity-based marginal solutions. We have obtained a gauge equivalence relation including the identity-based marginal solutions and some kind of wedge-based tachyon vacuum solutions and, using this relation, we can directly evaluate observables for the identify-based solutions. 11), 12) The key ingredient is a combined technique for the identity-based solutions and the KBc algebra 13), 14) and it has potentiality for investigating string field theory. In fact, it has been applied to construct a new solution, 15) which has the same algebraic structure as a wedge-based marginal solution 16) and is gauge equivalent to the identity-based marginal solution.The main purpose of this paper is, based on these developments, to confirm directly that the identity-based scalar solution provides the correct observables as expected.The identity-based scalar solution is given by 1)where Q L (f ) and C L (f ) are integrations of the BRST current j B (z) and the ghost c(z), which are multiplied by a function f (z) along a half unit circle. We find that the equation of motion holds for the function h(z) such that h(−1/z) = h(z) and h(±i) = 0. Moreover, the reality condition of (1 . 1) imposes the function h(z) to satisfy (h(z)) * = h(1/z * ).Expanding the string field Ψ around the solution as Ψ = Ψ 0 + Φ, we obtain an action for fluctuation:

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Section: )supporting

confidence: 76%

Observables for identity-based tachyon vacuum solutions

Kishimoto

Masuda

Takahashi

2014

Progress of Theoretical and Experimental Physics

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“…Here, we have considered a theory only around an identity-based marginal solution in SSFT and we found that G ′ K ′ Bcγ algebra has the same algebraic structure with undeformed GKBcγ algebra. If we consider a theory around another type of identitybased universal solutions found in [28], we expect that the algebraic structure might be changed when a homotopy operator exists. Using such an algebra, vacuum energy and/or gauge invariant overlap might be evaluated directly.…”

Section: Discussionmentioning

confidence: 99%

On nontrivial solutions around a marginal solution in cubic superstring field theory

Inatomi

Kishimoto

Takahashi

2012

J. High Energ. Phys.

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We construct tachyon vacuum and half-brane solutions, using an extension of KBc algebra, in the theory around a type of identity-based marginal solutions in modified cubic superstring field theory. With explicit computations, we find that their vacuum energies are the same as those of corresponding solutions around the original theory. It implies that the vacuum energy for the identity-based marginal solution vanishes although straightforward computation of it is subtle. We also evaluate the gauge invariant overlaps for those nontrivial solutions. The values for them are deformed according to the marginal solution in the same way as the case of bosonic string field theory.

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“…It is known that the analytic solutions for tachyon condensation [1,2,3] in open bosonic string field theory [4] as well as the ones [5,6,7] in cubic superstring field theory [8] are formally gauge equivalent to identity based solutions [9,10,11,12,13]. Identity based solutions are constructed as a product of certain linear combination of ghost number one operators with the identity string field [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

“…Since a string field belonging to the GSO(−) sector has half-integer conformal weight, Φ 2 changes its sign under the conformal transformation R 2π representing the 2π rotation of the unit disk[28] 3. Although the identity based solution formally satisfies the equation of motion (2.9), it is a pathological solution in the sense that it brings ambiguous analytic result for the value of the energy[9,14,15,16].…”

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confidence: 99%

A singular one-parameter family of solutions in cubic superstring field theory

Arroyo

2016

J. High Energ. Phys.

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Performing a gauge transformation of a simple identity-like solution of superstring field theory, we construct a one-parameter family of solutions, and by evaluating the energy associated to this family, we show that for most of the values of the parameter the solution represents the tachyon vacuum, except for two isolated singular points where the solution becomes the perturbative vacuum and the half brane solution.

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Homotopy operators and identity-based solutions in cubic superstring field theory

Cited by 7 publications

References 36 publications

Observables for identity-based tachyon vacuum solutions

Observables for identity-based tachyon vacuum solutions

On nontrivial solutions around a marginal solution in cubic superstring field theory

A singular one-parameter family of solutions in cubic superstring field theory

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