Topological Open P-Branes

By Jae-Suk Park. 2000

138 citations recorded by the source corpus.

By exploiting the BV quantization of topological bosonic open membrane, we argue that flat 3-form C-field leads to deformations of the algebras of multi-vectors on the Dirichlet-brane world-volume as 2-algebras. This would shed some new light on geometry of M-theory 5-brane and associated decoupled theories. We show that, in general, topological open p-brane theory has a structure of (p+1)-algebra in the bulk, while a structure of p-algebra in the boundary. The bulk/boundary correspondences are exactly as the generalized Deligne conjecture (a theorem of Kontsevich) in the algebraic world of p-algebras. It also imply that the algebras of quantum observables of (p-1)-brane are ``close to'' the algebras of its classical observables as p-algebras. We interpret above as deformation quantization of (p-1)-brane, generalizing the p=1 case. We argue that there is such quantization based on the direct relation between BV master equation and Ward identity of the bulk topological theory. The path integral of the theory will lead to the explicit formula. We also discuss some applications to topological strings and conjecture that the homological mirror symmetry has further generalizations to the categories of p-algebras.

Subfields: Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/5f1df901bd50814379df47832862cb901c60ea55

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Citations in the corpus

M5-brane in three-form flux and multiple M2-branes (2008, unknown): “Since we can neglect the Nambu-Goto part (which contains the metric), the action becomes that of the topological membrane [24],”
Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, methodology): “which is the action of the H-twisted Poisson sigma-model with target space M [68, 57].”
Classical BV Theories on Manifolds with Boundary (2011, methodology): “old. 22 ALBERTO S. CATTANEO, PAVEL MNEV, AND NICOLAI RESHETIKHIN 3.7. Boundary conditions. In the current paper we insist on having free boundary conditions. An alternative approach, ﬁrst explored in [18, 43], ﬁxes boundary conditions in a way compatible with the BFV structure on the boundary. This ”
On the structure of graded symplectic supermanifolds and Courant algebroids (2002, background): “Special cases include the Chern-Simons gauge theory (when M0 is a point) and Park’s topological membrane theory [12] (when E is an exact Courant algebroid).”
AKSZ–BV Formalism and Courant Algebroid-Induced Topological Field Theories (2006, unknown): “Cattaneo-Felder [4] and Park [8] further refined the AKSZ procedure by generalizing it to the case of manifolds with boundary, and produced new examples: Cattaneo and Felder studied the Poisson sigma-model [11] on the disk [3] [4], while Park considered its higher-dimensional generalizations, the to”
On the AKSZ Formulation of the Poisson Sigma Model (2001, methodology): “e A and B models [17]. In [8] the application to the Rozansky–Witten [12] theory was considered. In [6] the method has been applied to BF theories by choosing Σ an s-manifold and Y = g[1]×g∗[s−2]. In [11], topological open branes are deﬁned by choosing Σ an s-manifold with boundary and Y = (ΠT)s−2ΠT”
Quasi-Lie Bialgebroids and Twisted Poisson Manifolds (2001, methodology): “In the latter case, we start by adding a closed 3-form φ to the standard structure on (TM, T ∗M), and then twist by π (this is the way Park [14] arrived at twisted Poisson manifolds in string-theoretic context).”
Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory (2003, background): “Recently, closed 3-form fields appeared in Park’s work on string theory [46], and in the work on topological field theory of Klimčik and Strobl, who recognized the appearance of a new geometrical structure which they called WZW-Poisson manifolds [29].”