Contents

Idea

The incarnation of the concept of string without worldsheet supersymmetry is the bosonic string of bosonic string theory. In contrast to the spinning string/superstring.

Definition

In symplectic geometry / geometric quantization

See the reference below

Properties

Vacuum

• tachyon condensation

• Sen's conjecture

Related concepts

• Polyakov action

• sigma model, brane

  • particle, spinning particle, superparticle

  • string, spinning string, superstring

    • type II superstring, F1-brane, D1-brane, (p,q)-string

    • heterotic string

  • membrane

• string theory, string field theory

• Goddard-Thorn no-ghost theorem

• string scattering amplitude

• string field theory

• world sheets for world sheets

• D-brane, Chan-Paton gauge field, Freed-Witten-Kapustin anomaly cancellation

• string theory FAQ

References

General

The Polyakov action (but see there for more) for the bosonic string (and relation to Liouville theory in the non-critical case):

• Alexander Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207-210 [doi:10.1016/0370-2693(81)90743-7, pdf]

• Jürgen Jost, Bosonic Strings: A Mathematical Treatment, AMS/IP Stud. Adv. Math. 21 (2001) [ISBBN:978-0-8218-4336-9spire:1388134]

See the references at string theory for more.

Symplectic geometry and geometric quantization

The ordinary symplectic geometry and ordinary geometric quantization of the bosonic string sigma-model is discussed in the following references.

The symplectic structure and Kähler geometry of loop space is discussed in

• M.J. Bowick, S.G. Rajeev, String theory as the Kähler geometry of loop space Phys. Rev. Lett. 58, 535-538 (1987)

• M.J. Bowick, S.G. Rajeev, The holomorphic geometry of closed bosonic string theory and $Diff(S^1)/S^1$, Nucl. Phys. B293, 348-384 (1987)

• Jouko Mickelsson, String quantization on group manifolds and the holomorphic geometry of $Diff(S^1)/S^1$ Commun. Math. Phys. 112, 653-661 (1987) (EUCLID)

with further comments in

• Hendrik Grundlin, C. A. Hurst, The operator quantization of the open bosonic string: field algebra, Communications in mathematical physics 156 (1993) (pdf)

A correction of some points in these articles is discussed in

• Sergei Merkulov, On the geometric quantization of bosonic string, Class. Quantum Grav. 9 2267 (1992) (IOP)

See also

• Yue Yua, Han-Ying Guoa, On the geometric quantization and BRST quantization for bosonic strings, Physics Letters B Volume 216, Issues 1–2, (1989), Pages 68–74 (web)

• Yu-liang Liu, Su-qing Chen,Guang-jiong Ni, Geometrical quantization of bosonic string with Wess-Zumino term on genus-g Riemann surface, Phys. Rev. D 41, 472–477 (1990)

• A. D. Popov, Geometric quantization of strings and reparametrization invariance, Theoretical and Mathematical Physics, Volume 83, Number 3 (1990) (journal)

In multisymplectic geometry and higher geometric quantization

A discussion starting systematically with the correct symplectic form obtained by transgression from an multisymplectic extended phase space and including the BRST sector is in

• Yue Yu, Symplectic geometry and geometric quantization for the open bosonic string in the BRST formalism, Physics Letters B, Volume 216, Issue 1-2, (1989) p. 75-80.

A detailed exposition of the multisymplectic geometry of the bosonic string together with its interpretation in 2-plectic geometry is in

• John Baez, Alexander Hoffnung, Chris Rogers, Categorified Symplectic Geometry and the Classical String (arXiv:0808.0246)

and the appearance of the string Lie 2-algebra as the Heisenberg Lie 2-algebra of the string WZW-model in this context is discussed in

• John Baez, Chris Rogers, Categorified Symplectic Geometry and the String Lie 2-Algebra. arXiv:0901.4721.

Vacuum

(…)

• Jan Ambjørn?, Y. Makeenko, Stability of the nonperturbative bosonic string vacuum (arXiv:1703.05382)