scholarly journals Interior product, Lie derivative and Wilson line in the KBc subsector of open string field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hiroyuki Hata ◽  
Daichi Takeda
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Wilson Line ◽  
Tangent Vector ◽  
Open String ◽  
Three Dimensions ◽  
Simons Theory ◽  
Lie Derivative ◽  
Formal Similarity ◽  
Brane Solution

Abstract The open string field theory of Witten (SFT) has a close formal similarity with Chern-Simons theory in three dimensions. This similarity is due to the fact that the former theory has concepts corresponding to forms, exterior derivative, wedge product and integration over the manifold. In this paper, we introduce the interior product and the Lie derivative in the KBc subsector of SFT. The interior product in SFT is specified by a two-component “tangent vector” and lowers the ghost number by one (like the ordinary interior product maps a p-form to (p − 1)-form). The Lie derivative in SFT is defined as the anti-commutator of the interior product and the BRST operator. The important property of these two operations is that they respect the KBc algebra.Deforming the original (K, B, c) by using the Lie derivative, we can consider an infinite copies of the KBc algebra, which we call the KBc manifold. As an application, we construct the Wilson line on the manifold, which could play a role in reproducing degenerate fluctuation modes around a multi-brane solution.

scholarly journals Analytic construction of multi-brane solutions in cubic string field theory for any brane number

2019 ◽  
Vol 2019 (8) ◽  
Author(s):  
Hiroyuki Hata
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Equations Of Motion ◽  
Open String ◽  
Three Dimensions ◽  
Simons Theory ◽  
Analytic Construction ◽  
Pure Gauge ◽  
Brane Solution ◽  
Chern Simons

Abstract We present an analytic construction of multi-brane solutions with any integer brane number in cubic open string field theory (CSFT) on the basis of the ${K\!Bc}$ algebra. Our solution is given in the pure-gauge form $\Psi=U{Q_\textrm{B}} U^{-1}$ by a unitary string field $U$, which we choose to satisfy two requirements. First, the energy density of the solution should reproduce that of the $(N+1)$-branes. Second, the equations of motion (EOM) of the solution should hold against the solution itself. In spite of the pure-gauge form of $\Psi$, these two conditions are non-trivial ones due to the singularity at $K=0$. For the $(N+1)$-brane solution, our $U$ is specified by $[N/2]$ independent real parameters $\alpha_k$. For the 2-brane ($N=1$), the solution is unique and reproduces the known one. We find that $\alpha_k$ satisfying the two conditions indeed exist as far as we have tested for various integer values of $N\ (=2, 3, 4, 5, \ldots)$. Our multi-brane solutions consisting only of the elements of the ${K\!Bc}$ algebra have the problem that the EOM is not satisfied against the Fock states and therefore are not complete ones. However, our construction should be an important step toward understanding the topological nature of CSFT, which has similarities to the Chern–Simons theory in three dimensions.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

ONE-LOOP VACUUM ENERGY AT THE TACHYON VACUUM

2013 ◽  
Vol 21 ◽  
pp. 157-158
Author(s):  
SHOKO INATOMI
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
String Field Theory ◽  
Vacuum Energy ◽  
Open String ◽  
Brst Operator ◽  
Identity Based ◽  
Homotopy Operators

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Ql in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Ql, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

scholarly journals BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

scholarly journals Classical Solutions and Order of Zeros in Open String Field Theory

2005 ◽  
Vol 114 (3) ◽  
pp. 695-706 ◽  
Author(s):  
Y. Igarashi ◽  
K. Itoh ◽  
F. Katsumata ◽  
T. Takahashi ◽  
S. Zeze
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Open String ◽  
Classical Solutions

The bosonic open string field theory with Wess-Zumino term

1989 ◽  
Vol 217 (4) ◽  
pp. 421-426
Author(s):  
Yu-liang Liu ◽  
Guang-jiong Ni
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Open String

scholarly journals Gauge-invariant observables and marginal deformations in open string field theory

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Matěj Kudrna ◽  
Toru Masuda ◽  
Yuji Okawa ◽  
Martin Schnabl ◽  
Kenichiro Yoshida
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Open String ◽  
Gauge Invariant ◽  
Marginal Deformations

scholarly journals Thermofield dynamics extension of the open string field theory

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
M. Botta Cantcheff ◽  
R. J. Scherer Santos
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Open String
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