Logarithmic conformal field theory

{{Short description|Conformal field theory with logarithmic short distance behavior}}

In theoretical physics, a logarithmic conformal field theory is a conformal field theory in which the

correlators of the basic fields are allowed to be logarithmic at short distance, instead of being powers of the fields' distance. Equivalently, the dilation operator is not diagonalizable.

Examples of logarithmic conformal field theories include critical percolation.

In two dimensions

Just like conformal field theory in general, logarithmic conformal field theory has been particularly well-studied in two dimensions. Some two-dimensional logarithmic CFTs have been solved:

The Gaberdiel–Kausch CFT at central charge $c=-2$ , which is rational with respect to its extended symmetry algebra, namely the triplet algebra.
The $GL(1|1)$ Wess–Zumino–Witten model, based on the simplest non-trivial supergroup.
The triplet model at $c=0$ is also rational with respect to the triplet algebra.

References

{{Reflist|refs =

{{cite journal | last1=Schomerus | first1=Volker | last2=Saleur | first2=Hubert | title=The GL(1 - 1) WZW model: From Supergeometry to Logarithmic CFT | journal=Nucl. Phys. B | year=2006 | volume=734 | issue=3 | pages=221–245 | doi=10.1016/j.nuclphysb.2005.11.013 | arxiv=hep-th/0510032 | bibcode=2006NuPhB.734..221S | s2cid=16530989 }}

{{Cite arXiv| last1=Runkel | first1=Ingo | last2=Gaberdiel | first2=Matthias R. | last3=Wood | first3=Simon | title=Logarithmic bulk and boundary conformal field theory and the full centre construction | date=2012-01-30 | class=hep-th | eprint=1201.6273v1 }}

{{cite journal | last=Gurarie | first=V. | title=Logarithmic Operators in Conformal Field Theory | journal=Nuclear Physics B | date=1993-03-29 | volume=410 | issue=3 | pages=535–549 | doi=10.1016/0550-3213(93)90528-W | arxiv=hep-th/9303160 | bibcode=1993NuPhB.410..535G | s2cid=17344227 }}

{{cite journal | last1=Hogervorst | first1=Matthijs | last2=Paulos | first2=Miguel | last3=Vichi | first3=Alessandro | title=The ABC (in any D) of Logarithmic CFT | journal=Journal of High Energy Physics | date=2016-05-12 | volume=2017 | issue=10 | doi=10.1007/JHEP10(2017)201 | arxiv=1605.03959v1 | s2cid=62821354 }}

{{cite journal | last1=Creutzig | first1=Thomas | last2=Ridout | first2=David | title=Logarithmic Conformal Field Theory: Beyond an Introduction | journal=Journal of Physics A: Mathematical and Theoretical | date=2013-03-04 | volume=46 | issue=49 | page=494006 | doi=10.1088/1751-8113/46/49/494006 | arxiv=1303.0847v3 | bibcode=2013JPhA...46W4006C | s2cid=118554516 }}

{{cite journal | last1=Gaberdiel | first1=Matthias R. | last2=Kausch | first2=Horst G. | title=A Local Logarithmic Conformal Field Theory | journal=Nuclear Physics B | year=1999 | volume=538 | issue=3 | pages=631–658 | doi=10.1016/S0550-3213(98)00701-9 | arxiv=hep-th/9807091 | bibcode=1999NuPhB.538..631G | s2cid=15554654 }}

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Category:Conformal field theory