Representations of KBc Algebra for Generating String Field Theory Solutions
© The Physical Society of Japan
This article is on
Generating string field theory solutions with matter operators from KBc algebra
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys.
2022,
093B09
(2022)
.
String field theory (SFT) is a nonperturbative formulation of string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. In string theory, Dbranes (short for “Dirichlet membranes”) are a class of extended objects upon which open strings can end with Dirichlet boundary conditions. However, in SFT, Dbranes can be expressed as classical solutions to the equation of motion.
Researchers have previously constructed a solution representing the tachyon vacuum (a state with no Dbranes at all). This solution requires an operator set (K,B,c) that satisfies a KBc algebra.
In this study, we present a general method for obtaining various solutions in SFT based on a solution that can be constructed with (K,B,c). To check this formalism, we have shown that this method reproduces known solutions that have been constructed previously by other methods.
Our methodology relies on the fact that a solution consisting of (K,B,c) remains a solution for another set (K',B',c') that satisfies the same KBc algebra as the original set. Notably, the new (K',B',c') set may consist of matter operators as well as the original (K,B,c) set.
In order to construct a new (K',B',c') set like this, we first constructed two operations in the original (K,B,c) space. These corresponded to the interior product and the Lie derivative. We defined these operations to satisfy the KBc algebra as proper operations in the (K,B,c) space. We then obtained the new (K',B',c') set through successive application of the Lie derivatives that were specified by a oneparameter family of “tangent vectors.”
Next, we applied our method to generate two known solutions representing a single Dbrane with matter operators by starting from a single Dbrane solution without matter operators. Thus, we identified a new (K',B',c') set and the oneparameter family of tangent vectors associated with each of the two Dbrane solutions with matter operators.
While we have primarily reproduced simpler solutions that are already known, we believe that our formalism is capable of generating unknown solutions in SFT that are physically interesting. Moreover, the fact that the operations in the space of (K,B,c) are the same as those in the theory of differential forms could provide a deeper understanding of the mathematical structure of SFT along with a unified description of classical Dbrane solutions.
Generating string field theory solutions with matter operators from KBc algebra
(PTEP Editors' Choice)
Prog. Theor. Exp. Phys.
2022,
093B09
(2022)
.
Share this topic
Fields
Related Articles

Understanding NonInvertible Symmetries in Higher Dimensions Using Topological Defects
Theoretical Particle Physics
2024927
By constructing KramersWannierWegner duality and Z_{2} duality defects and deriving their crossing relations, this study presents the first examples of codimension one noninvertible symmetries in fourdimensional quantum field theories.

Quantum Mechanics of OneDimensional ThreeBody Contact Interactions
Mathematical methods, classical and quantum physics, relativity, gravitation, numerical simulation, computational modeling
Theoretical Particle Physics
2024213
The quantum mechanical description of topologically nontrivial threebody contact interactions in one dimension is not well understood. This study explores the Hamiltonian description of these interactions using the pathintegral formalism.

Investigating Unitarity Violation of Lee–Wick’s Complex Ghost with Quantum Field Theory
Theoretical Particle Physics
2024119
Theories with fourthorder derivatives like Lee–Wick’s quantum electrodynamics model or quadratic gravity result in complex ghosts above a definite energy threshold that violate unitarity.

Investigating Δ and Ω Baryons as Meson–Baryon Bound States in Lattice Quantum Chromodynamics
Theoretical Particle Physics
2023713
We investigate Δ and Ω baryons as meson–baryon bound states in lattice quantum chromodynamics and show that their difference results from the kinematic structure of the two meson–baryon systems, and not their interaction.

Novel Insights Into Bulk Reconstruction in the Antide Sitter/Conformal Field Theory Correspondence
Theoretical Particle Physics
202361
Bulk reconstruction in antide Sitter/conformal field theory is fundamental to our understanding of quantum gravity. We show that contrary to popular belief, bulk reconstruction is rather simple and intuitive.