String theory in dimensions other than 10

[crackjack]

I have a few questions on non-critical string theory...

terminology:
1: Are "Gepner models" a subset of non-critical string theory?

technical:
2: Given a set of spectrum, are there ways to construct a non-critical string theory with enough symmetries so that the CFT becomes minimal and hence completely solvable?
3: Given a non-critical string theory (say, in d-dimensions with d<10) can one come up with an equivalent (in all sense of the word) description in terms of some compactified (to the same d-dimensions) critical string theory?

May be some introductory lecture(s) with references citing original work?

 

[suprised]

I can answer those...

1: Are "Gepner models" a subset of non-critical string theory?

Yes and no... Gepner models refers to constructions where the internal CFT is represented by combinations of (superconformal) minimal models. If the total central charge c-hat equals 9, then this will yield a critical string theory, otherwise not.

Given a set of spectrum, are there ways to construct a non-critical string theory with enough symmetries so that the CFT becomes minimal and hence completely solvable?

Yes - if the CFT is minimal model, then the theory is completely solvable, as it can be represented by a matrix model and is governed by integrable systems. This has been heavily investigated around 1990.

Given a non-critical string theory (say, in d-dimensions with d<10) can one come up with an equivalent (in all sense of the word) description in terms of some compactified (to the same d-dimensions) critical string theory?

Along the lines of thought discussed so far, not that I would know of. In non-critical strings, due to the non-cancellation of the Virasoro anomaly, the Liouville mode of the 2d metric becomes dynamical (ie, does not decouple). This is very different from any critical string theory.

But there are other notions of non-critical strings, like the strongly coupled theory in 6d, but those are constructed differently; they are not obtained from a world-sheet CFT but from decoupling limits of critical strings.

May be some introductory lecture(s) with references citing original work?

This is a good review about d<1 strings:
http://www-spires.dur.ac.uk/cgi-bin/spiface/hep/www?r=PUPT-1217
See also e.g
http://arxiv.org/pdf/hep-th/9110041

 

[crackjack]

Yes and no... Gepner models refers to constructions where the internal CFT is represented by combinations of (superconformal) minimal models. If the total central charge c-hat equals 9, then this will yield a critical string theory, otherwise not.

I will take it as "Gepner models with c \neq 9 are subsets of non-critical string theories"

In non-critical strings, due to the non-cancellation of the Virasoro anomaly, the Liouville mode of the 2d metric becomes dynamical (ie, does not decouple). This is very different from any critical string theory.

A clarification: Are you referring to the trace anomaly of stress tensor, when you say Virasoro anomaly?
Asking this because I thought the other anomaly (Weyl) is canceled in both critical & non-critical strings. In addition, cancellation of Weyl anomaly automatically cancels the trace anomaly in critical strings. Seems like this automatic cancellation does not hold for non-critical strings?

This is a good review about d<1 strings:
http://www-spires.dur.ac.uk/cgi-bin/spiface/hep/www?r=PUPT-1217
See also e.g
http://arxiv.org/pdf/hep-th/9110041

Thanks!

 

[suprised]

I will take it as "Gepner models with c \neq 9 are subsets of non-critical string theories"

yes.

A clarification: Are you referring to the trace anomaly of stress tensor, when you say Virasoro anomaly?

yes!

Happy Holidays!

 

[crackjack]

Thanks surprised, and wish you a very good year ahead!