Bosonic string theory
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Bosonic String Theory: Key Developments and Insights
Nonrelativistic Expansion of Closed Bosonic Strings
Recent advancements in bosonic string theory have introduced a novel approach to nonrelativistic closed bosonic strings. This method involves a 1/c² expansion of the relativistic string, where c represents the speed of light. This approach eliminates the need to consider a near-critical Kalb-Ramond background. The 1/c²-expanded Polyakov action at next-to-leading order aligns with the known action of nonrelativistic string theory, provided the target space adheres to a specific foliation constraint. The spectrum in a flat target space, with one circle direction wound by the string, up to next-to-leading order, matches the spectrum of the Gomis-Ooguri string .
Bosonic String Theory with Dust
Another intriguing modification in bosonic string theory involves the inclusion of a pressureless 'dust' field on the string worldsheet. This dust, a real scalar field with a unit gradient, disrupts conformal invariance. The Hamiltonian analysis reveals a time reparametrization constraint linear in the dust field momentum and a spatial diffeomorphism constraint. This setup allows for a 'dust time' gauge, analogous to the parametrized particle. In this gauge, a complete and self-consistent Fock quantization of the theory is achieved for dimensions less than 26. The resulting Hamiltonian is not a constraint, leading to a Hilbert space and mass spectrum characterized by an additional parameter, which includes the usual string spectrum as a special case. Notably, some new particle spectra emerging from this theory are free of tachyons .
Nonperturbative AdS Vacua in Bosonic String Theory
Explorations into the existence of nonperturbative anti-de Sitter (AdS) vacua within bosonic string theory have shown promising results. Building on the work of Hohm and Zwiebach, it has been demonstrated that such vacua could exist when all α' corrections are included. Additionally, there is a possibility for the coexistence of nonperturbative de Sitter (dS) and AdS vacua, expanding the potential landscape of bosonic string theory .
Deformed Energy Momentum Relations and Nontachyonic Bosonic Strings
Research into deformed dispersion relations within the bosonic string action has revealed that embedding coordinates can still propagate linearly on the worldsheet in certain theories. Both string modes and the center of mass propagate with deformed dispersion relations, while the speed of light remains energy-independent. Canonical quantization of these strings shows that ghost modes can still decouple, and in some cases, the tachyon is eliminated from the free bosonic string spectrum, offering a potential path to nontachyonic bosonic strings .
Bosonic M Theory
A conjecture in the field suggests the existence of a strong coupling limit of bosonic string theory, analogous to the relationship between 11-dimensional M theory and superstring theory. Specifically, it is proposed that bosonic string theory is the compactification on a line interval of a 27-dimensional theory, whose low-energy limit includes gravity and a three-form potential. In the strong coupling limit, the line interval becomes infinite, potentially providing a stable ground state for the theory .
General Bosonic σ Models and String Effective Actions
The renormalization of general bosonic two-dimensional σ models, including torsion, has been thoroughly discussed. This framework allows for the definition of finite local dimension 2 composite operators and their products, extending the Curci-Paffuti relation. It also derives conditions for the vanishing of the trace of the energy momentum tensor from an action to all orders of perturbation theory. This derivation is related to Zamolodchikov's c-theorem, and detailed calculations up to two loops verify the constructed action's compatibility with gauge invariance .
Conclusion
Bosonic string theory continues to evolve with significant theoretical advancements. From nonrelativistic expansions and the inclusion of dust fields to the exploration of nonperturbative vacua and deformed energy momentum relations, these developments are expanding our understanding of the fundamental nature of strings. The conjecture of a bosonic M theory and the detailed renormalization of σ models further enrich the theoretical landscape, offering new avenues for research and potential applications in understanding the universe's fundamental structure.
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