Logarithmic conformal field theory

<h2 id="in-two-dimensions">In two dimensions</h2>
Just like conformal field theory in general, logarithmic conformal field theory has been particularly well-studied in <a href="/facts/Two-dimensional_conformal_field_theory/xHpQ5dbW">two dimensions</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2">2</a><a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> Some two-dimensional logarithmic CFTs have been solved:

<ul><li>The Gaberdiel–Kausch CFT at central charge 
 
 
 
 c
 =
 −
 2
 
 
 {\displaystyle c=-2}
 
, which is rational with respect to its extended symmetry algebra, namely the triplet algebra.<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a></li>
<li>The 
 
 
 
 G
 L
 (
 1
 
 |
 
 1
 )
 
 
 {\displaystyle GL(1|1)}
 
 <a href="/facts/Wess%25E2%2580%2593Zumino%25E2%2580%2593Witten_model/WHNuzt64">Wess–Zumino–Witten model</a>, based on the simplest non-trivial <a href="/facts/Supergroup_(physics)/m7U6FFVR">supergroup</a>.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a></li>
<li>The triplet model at 
 
 
 
 c
 =
 0
 
 
 {\displaystyle c=0}
 
 is also rational with respect to the triplet algebra.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Hogervorst, Matthijs; Paulos, Miguel; Vichi, Alessandro (2016-05-12). "The ABC (in any D) of Logarithmic CFT". Journal of High Energy Physics. 2017 (10). arXiv:1605.03959v1. doi:10.1007/JHEP10(2017)201. S2CID 62821354. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Gurarie, V. (1993-03-29). "Logarithmic Operators in Conformal Field Theory". Nuclear Physics B. 410 (3): 535–549. arXiv:hep-th/9303160. Bibcode:1993NuPhB.410..535G. doi:10.1016/0550-3213(93)90528-W. S2CID 17344227. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Creutzig, Thomas; Ridout, David (2013-03-04). "Logarithmic Conformal Field Theory: Beyond an Introduction". Journal of Physics A: Mathematical and Theoretical. 46 (49): 494006. arXiv:1303.0847v3. Bibcode:2013JPhA...46W4006C. doi:10.1088/1751-8113/46/49/494006. S2CID 118554516. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Gaberdiel, Matthias R.; Kausch, Horst G. (1999). "A Local Logarithmic Conformal Field Theory". Nuclear Physics B. 538 (3): 631–658. arXiv:hep-th/9807091. Bibcode:1999NuPhB.538..631G. doi:10.1016/S0550-3213(98)00701-9. S2CID 15554654. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Schomerus, Volker; Saleur, Hubert (2006). "The GL(1 - 1) WZW model: From Supergeometry to Logarithmic CFT". Nucl. Phys. B. 734 (3): 221–245. arXiv:hep-th/0510032. Bibcode:2006NuPhB.734..221S. doi:10.1016/j.nuclphysb.2005.11.013. S2CID 16530989. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Runkel, Ingo; Gaberdiel, Matthias R.; Wood, Simon (2012-01-30). "Logarithmic bulk and boundary conformal field theory and the full centre construction". arXiv:1201.6273v1 [hep-th]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
</ol>

Logarithmic conformal field theory open-in-new

Logarithmic conformal field theory