nLab non-critical string

Idea

For both the bosonic string and the superstring, the corresponding Polyakov action has a gauge anomaly for the conformal symmetry, depending on the dimension $D$ of target spacetime, and on the strength of the dilaton background field. For vanishing dilaton field this anomaly vanishes exactly for $D = 26$ for the bosonic model, and in $D = 10$ for the superstring. String theories at these dimensions are known as critical string theories. By contrast, string theories in dimensions different from these are known as non-critical string theories.

Often, the term “non-critical” string is used to refer to a string theory formulated on dimensions less than the critical dimensions. However, it is also possible to consider theories in dimensions greater than the critical dimensions, provided an appropriate dilaton profile is used. In this way, one may more precisely speak of subcritical and supercritical strings.

Subcritical strings

(some motivation, e.g. an alternative to compactifications)

Supercritical strings

Hellerman 04 motivates looking at supercritical heterotic strings by conjecturing an S-duality between these and type I string theory with additional D9 brane-antibrane pairs.

References

General non-critical strings

• Ali H. Chamseddine: A Study of noncritical strings in arbitrary dimensions, Nucl. Phys. B 368 98 (1992) [doi:10.1016/0550-3213(92)90199-L]

• Robert C. Myers: New Dimensions For Old Strings, Phys. Lett. B 199 3 (1987) 371-376 [doi:10.1016/0370-2693(87)90936-1]

• Héctor Parra De Freitas. T-duality for non-critical heterotic strings (2024). (arXiv:2407.12923).

Subcritical strings

Supercritical strings

• Simeon Hellerman. On the Landscape of Superstring Theory in D > 10 (2004). (hep-th/0405041).

• Simeon Hellerman, Xiao Liu. Dynamical Dimension Change in Supercritical String Theory (2004). (hep-th/0409071).

• Simeon Hellerman, Ian Swanson. Cosmological solutions of supercritical string theory (2006). (hep-th/0611317).

• Simeon Hellerman, Ian Swanson. Dimension-changing exact solutions of string theory (2006). (hep-th/0612051).

• Simeon Hellerman, Ian Swanson. Charting the landscape of supercritical string theory (2007). (arXiv:0705.0980).

• Simeon Hellerman, Ian Swanson. Supercritical N = 2 string theory (2007). (arXiv:0709.2166).

• Simeon Hellerman, Matthew Kleban. Dynamical Cobordisms in General Relativity and String Theory (2010). (arXiv:1009.3277).