280 research outputs found

    Notes on the Wess-Zumino-Witten-like structure: L∞L_{\infty } triplet and NS-NS superstring field theory

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    In the NS-NS sector of superstring field theory, there potentially exist three nilpotent generators of gauge transformations and two constraint equations: It makes the gauge algebra of type II theory somewhat complicated. In this paper, we show that every NS-NS actions have their WZW-like forms, and that a triplet of mutually commutative L∞L_{\infty } products completely determines the gauge structure of NS-NS superstring field theory via its WZW-like structure. We give detailed analysis about it and present its characteristic properties by focusing on two NS-NS actions proposed by arXiv:1512.03379 and arXiv:1403.0940.Comment: 23+3 pages; Published ve

    A∞/L∞A_\infty / L_\infty structure and alternative action for WZW-like superstring field theory

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    We propose new gauge invariant actions for open NS, heterotic NS, and closed NS-NS superstring field theories. They are based on the large Hilbert space, and have Wess-Zumino-Witten-like expressions which are the Z2\mathbb{Z}_{2}-reversed versions of the conventional WZW-like actions. On the basis of the procedure proposed in arXiv:1505.01659, we show that our new WZW-like actions are completely equivalent to A∞/L∞A_{\infty }/L_{\infty } actions proposed in arXiv:1403.0940 respectively.Comment: 23+21 pages; Published ve

    Light-cone reduction of Witten's open string field theory

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    We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for A∞A_{\infty }. The covariant string field splits into the light-cone string field and trivial excitations of BRST quartets: The latter generates the gauge symmetry and covariance. We first show that the reduction of gauge degrees can be performed by applying the lemma, which gives a refined version of the no-ghost theorem of covariant strings. Then, we demonstrate that after the reduction, gauge-fixed theory can be regarded as a kind of effective field theory and it provides an exact gauge-fixing procedure taking into account interactions. As a result, a novel light-cone string field theory is obtained from Witten's open string field theory.Comment: Published version: section3.4 refined, 20 + 6 page

    Perturbative path-integral of string field and the A∞A_{\infty } structure of the BV master equation

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    The perturbative path-integral gives a morphism of the (quantum) A∞A_{\infty } structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the BV formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a (quantum) A∞A_{\infty } structure, the path-integral preserves this intrinsic A∞A_{\infty } structure of quantum field theory, where A∞A_{\infty } reduces to L∞L_{\infty } whenever multiplications of space-time fields are graded commutative. We apply these ideas to string field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite Ξ±β€²\alpha ^{\prime }, reduction of gauge and unphysical degrees, SS-matrix and gauge invariant observables.Comment: 41 pages, appendix adde

    On the BV formalism of open superstring field theory in the large Hilbert space

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    We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as space-time antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string antifields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partially gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: Reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.Comment: 24 + 4 pages; Published ve
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