Boundary Modes in String Field Theory
The paper entitled "Boundary Modes in String Field Theory" discusses the necessary modifications to the classical string field theory (SFT) action when the target space possesses boundaries. The paper focuses primarily on the bosonic string and articulates that to construct a well-defined variational principle, additional boundary terms need to be incorporated into the free string field theory action. It explores how these modifications influence the gauge invariance of the theory.
The authors initially address the primary challenge: defining string field theory on a manifold with boundaries leads to issues with both the variational principle and gauge invariance. These issues stem from the inability to integrate by parts the kinetic terms without generating surface contributions. The paper proposes that a simplistic boundary term, contingent only on the value of the bulk fields at the boundary, can resolve the variational principle issue. However, achieving gauge invariance necessitates the introduction of new boundary degrees of freedom which transform suitably under gauge transformations to compensate for boundary-induced gauge variations.
A notable contribution of the paper is the derivation of gauge-invariant actions for both open and closed strings at the massless level, along with the consideration of the tensionless limit of the full SFT. For the massless level, actions are constructed by adding specific boundary terms that integrate the classical obligations of gauge-invariance with the Gibbons-Hawking-York (GHY) term from general relativity. The paper describes how these appropriately modified actions reproduce linearized general relativity and lead to gauge-invariant actions for the infinite tower of massless higher-spin gauge theories corresponding to Regge trajectories. The exploration of the tensionless limit highlights that the methods discussed can scaffold the development of actions for higher-spin theories.
Quantitatively, the derived actions are proven to provide well-defined variational principles. Additionally, the authors offer a preliminary analysis of extending these results to the fully-fledged tensile string field theory, examining the first massive level of the open string.
The implications of this research are significant for the theoretical underpinnings of string field theory, particularly for scenarios akin to describing black hole observables within the string framework. By extending the SFT landscape to include boundary contributions, this paper adds crucial insights into interfacing SFT with gravitational theories. In forward-looking terms, these results may pave the way for a deeper understanding of string interactions and possibly shed light on unresolved questions concerning the quantum formulation of gravity and interactions.
Future work might extend these considerations to incorporate interactions and quantum extensions, possibly within the paradigm of cyclic homotopy algebras. Understanding interactions in this context and how the inclusion of boundaries affects them remains an open question. The paper suggests that such developments could yield new methodologies for tackling long-standing problems in string theory, quantum field theory, and beyond, including insights into quantum gravity and the mathematical structure of string-theoretic models.